Mahesh

The strategic use of TS 10th Class Maths Model Papers Set 7 can significantly enhance a student’s problem-solving skills.

TS SSC Maths Model Paper Set 7 with Solutions

Time: 3 Hours
Maximum Marks: 80

General Instructions:

1. Answer all the questions under Part – A on a separate answer book.
2. Write the answers to the questions under Part – B on the question paper itself and attach it to the answer book of Part – A.

Part – A (60 Marks)
Section – I (6 × 2 = 12 Marks)

Note:

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 1.
Is 7 × 5 × 3 × 2 + 3a composite number ? Justify your answer.
Answer:
Given number is 7 × 5 × 3 × 2 + 3
= 3(7 × 5 × 2 + 1)
= 3 × (70 + 1)
= 3 × 71
Here 3 and 71 are the prime numbers so the product of two primes is a composite number.
∴ 7 × 5 × 3 × 2 + 3 is a composite number.

Question 2.
p(x) = x² – 2x – 3, find the values of p(1) and p(0).
Answer:
Given polynomial is p(x) = x² – 2x – 3
p(1) = 1² – 2(1) – 3 = 1 – 2 – 3 = 1 – 5 = – 4
p(0) = 0² – 2(0) – 3 = 0 – 0 – 3 = – 3

Question 3.
Find the roots of x² – x – 12 = 0 using factorization method.
Answer:
x² – x – 12 = 0
x² – x – 12 = x² – 4x + 3x – 12
= x(x – 4) + 3(x – 4)
= (x – 4)(x + 3)
The roots of x² – x – 12 = 0 are the values of x for which (x – 4)(x + 3) = 0
x – 4 = 0 or x + 3 = 0
x = 4 or x = -3
Therefore the roots of x² – x -12 = 0 are 4 and -3.

Question 4.
Are the given triangles similar ?

Answer:
i) No,
ii) No.

Question 5.
Consider the following situations. In each find out whether you need volume or area.
i) Quantity of water inside a bottle.
ii) Canvas need for making a tent.
Answer:
i) Volume
ii) Area.

Question 6.
A die is thrown once. Calculate the probability of getting a number less than 3.
Answer:
Possible outcomes in a single throw of a die is (1, 2, 3, 4, 5, 6} ∴ n(S) = 6
There are two numbers {1,2} less than 3.
∴ n(E) = 2
∴ Required probability = \(\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{2}{6}\) = \(\frac{1}{3}\)

Section – II (6 × 4 = 24 Marks)

Note :

1. Answer ALL the following questions,
2. Each question carries 4 marks.

Question 7.
If log(\(\frac{x+y}{3}\)) = \(\frac{1}{2}\) (log x + log y) then prove that x² + y² = 7xy
Answer:
Given, log (\(\frac{x+y}{3}\)) = \(\frac{1}{2}\) (log x + log y)
log (\(\frac{x+y}{3}\)) = \(\frac{1}{2}\) log (xy) = log (xy)^1/2
⇒ \(\frac{x+y}{3}\) = (xy)^1/2
x + y = 3(xy)^1/2
squaring on both sides, (x + y)² = 9xy
x² + y² + 2xy = 9xy
x² + y² = 9xy – 2xy = 7xy
∴ x² + y² = 7xy

Question 8.
Obtain all other zeroes of x³ + 3x² – x – 3 if one of its zeroes is 1.
Answer:
Given polynomial x³ + 3x² – x – 3
One of its zeroes is 1
Therefore we can divide the polynomial by x – 1

x³ + 3x² – x – 3
= (x – 1) (x² + 4x + 3)
= (x – 1) (x² + 3x + x + 3)
= (x – 1) (x (x + 3) + 1 (x + 3)
= (x – 1)(x + 3)(x + 1)
The other zeroes of the given polynomial are -3 and -1.

Question 9.
The outer dimensions of a bordered table are 72 cm and 108cm of the area of the table, excluding the border is 6400 cm². Write a quadratic equation.
Answer:
Let the width of the border be x cm
Length of the rectangle excluding the border = (108 – 2x) cm
Breadth of the rectangle excluding the border = (7x – 2x)cm
Area of the table excluding the border = (108 – 2x)(72 – 2x) = 6400.

= 7776 – 216x – 144x + 4x² = 6400
4x² = 360x + 7776 – 6400 = 0
x² – 90x + 344 = 0

Question 10.
The king, queen and jack of clubs are removed from a pack of 52 playing cards and then the remaining pack is well shuffled. One card is selected from the remaining cards. Find the probability of getting:
i) a heart,
ii) a king,
iii) a club.
Answer:
Remaining cards = 52 – 3 = 49
P(heart) = \(\frac{13}{49}\); P(king) = \(\frac{3}{49}\)
P(club) = \(\frac{10}{49}\)

Question 11.
State whether the following statements are true or false. Justify your answer.
i) cot A is the product of cot and A.
ii) sin θ = \(\frac{4}{3}\) for some angle θ.
Answer:
i) False.
Cot A is used as an abbrevation for “the cotangent of the angle A.” It is the symbol which can not be separated.

ii) False.
The hypotenuse is the longest side in a right angled triangle. The value of Sin is always less than 1. (Refer here Sin θ = \(\frac{4}{3}\) which is greaterthan 1 and it is not possible for any θ.)

Question 12.
A person who is 1.65 m tall casts 1.8 in shadow. At the same instance, a lamp-post casts a shadow of 5.4 m. Find the height of the lamp-post
Answer:
In ΔABC and ΔPQR, ∠B = ∠Q = 90°, ∠C = ∠R (AC || PR, all the sun rays are parallel at any instance)
ΔABC ~ ΔPQR (by AA similarity)
\(\frac{A B}{P Q}\) = \(\frac{\mathrm{BC}}{\mathrm{QR}}\) (corresponding parts of similar triangles)
\(\frac{1.65}{P Q}=\frac{1.8}{5.4}\)
PQ = \(\frac{1.64 \times 5.4}{1.8}\) = 4.95 m
∴ The height of the lamp post is 4.95 m

Section – III (4 × 6 = 24 Marks)

Note :

1. Answer any 4 of the following questions,
2. Each question carries 6 marks.

Question 13.
If the sum of first 7 terms of an AP is 49 and that of 17 terms is 289, find the sum of first h terms.
Answer:
Sum of first 7 terms S_n = 49
S₇ = \(\frac{7}{2}\) [2a + (n – 1)d] = 49
= 7[2a + (7 – 1) d] = 98
2a + 6d = \(\frac{98}{7}\) = 14
a + 3d = 7 → (1)
Sum of first 17 terms
S₁₇ = 289
\(\frac{n}{2}\) [2a + (n – 1)d] = 289
\(\frac{17}{2}\)[2a + (17 – 1)d] = 289
\(\frac{17}{2}\) [2a + 16d] = 289
2a + 16d = 289 × \(\frac{2}{17}\)
2a + 16d = 34
a + 8d = 17 → (2)
Solving equation (1) & (2) by eliminating method

Substitute d = 2 in equation (1)
a + 3(2) = 7
a + 6 = 7
a = 7 – 6 = 1
Sum of first n terms
a + 3(2) =7
S_n = \(\frac{n}{2}\)[2a + (n – 1)d]
S_n = \(\frac{n}{2}\)[2 × 1 + (n – 1)2]
= \(\frac{n}{2}\)[2 + 2n – 2]
S_n = \(\frac{n}{2}\) × 2n = n².

Question 14.
In a competitive exam, 3 marks are to be awarded for every correct answer and for every wrong answer, 1
mark will be deducted. Madhu scored 40 marks in this exam. Had 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer,Madhu would have scored 50 marks. How many questions were there in the test? (Madhu attempted all the questions)
Answer:
Let the number of correct answers be x; and the number of wrong answers be y. When 3 marks are given for each correct answer and 1 mark deducted for each wrong answer, his score is 40 marks.
3x – y = 40 ………….. (1) His score would have been 50 marks if 4 marks were given for each correct answer and 2 marks deducted for each wrong answer. 4x – 2y = 50 ………….. (2)
Substitution method from equation (1),
y = 3x – 40 substitute in equation (2)
4x – 2 (3x – 40) = 50
4x – 6x + 80 = 50
– 2x = 50 – 80 = – 30
x = -30/-2
= 15
Substitute the value of x in equation (1) : 3(15)
-y = 40 ⇒ 45 – y = 40 ⇒ v =45 – 40 = 5
Total number of questions = x + y
= 15 + 5 = 20

Question 15.
Draw a circle of radius 6cm. From a point 10 cm away from its centre, construct tire pair of tangents to the circle and measure their lengths. Verify by using Pythagoras Theorem.
Answer:

Steps of construction:
i) Let the centre of the given circle ‘O’ and ‘P’ be an external point Join PO and draw the perpendicular bisector of PO, which cuts it at the mid point M,
ii) Taking M as centre with radius PM or MO, we draw a circle that intersects the given circle at two points A and B.
iii) Join PA and PB. These are the required tangents of the circle.
Proof : From the figure, PO = 10 cm, OA = 6 cm.
Also ΔPOA is a right angled triangle.
By Pythagoras theorem,
PO² = PA² + OA² ⇒
PA² = PO² – OA² = 10² – 6² = 100 – 36 = 64
∴ PA = \(\sqrt{64}\) = 8 cm
In ΔOPB, ∠OBP = 90°. OB = 6 cm,
OP = 10 cm.
By Pythagoras theorem
OP² = OB² + BP²
⇒ BP² = OP² – OB²
BP² = 10² – 6² = 100 – 36 = 64
BP = \(\sqrt{64}\) = 8 cm.

Question 16.
Draw the graph for the polynomial p(x) = x² + 3x – 4 and hence find the zeroes from the graph.
Answer:
p(x) = x² + 3x – 4

Zeroes of the given polynomial are -4, 1.

Question 17.
Sum of the areas of two squares is 468 m². If the difference of their perimeters is 24m find the sides of two squares.
Answer:
Let the sides of two squares be xm and ym.
Area of the first square is x²sq.m
Area of the second square is y²sq.m
Sum of the areas of two squares is x² + y²
Given sum of the areas is 468
x² + y² = 468 ……… (1)
Perimeter of the first square = 4x m
Perimeter of the second square = 4ym
Difference of their perimeters = 24
4x – 4y = 24
x – y = 6
x = 6 + y …………… (2)
Substitute x value in (1)
(6 + y)² + y² = 468
36 + 12y + y² + y² = 468
2y² + 12y + 36 – 468 = 0
2y² + 12y – 432 = 0
y² + 6y -216 = 0 which is a quadratic equation.
Here a = 1; b = 6; c = -216.
b² – 4ac = (6)² – 4 × 1(216)
= 36 + 864 = 900
Therefore y = \(\frac{-6 \pm \sqrt{900}}{2 \times 1}=\frac{-6 \pm 30}{2}\)
y = \(\frac{-6+30}{2}\), y = \(\frac{-6-30}{2}\) = \(\frac{24}{2}\) = 12 = \(\frac{-36}{2}\) = -18
Side of a square cannot be negative
∴ y = 12
x = 6 + y ⇒ x = 6 + 12 = 18
∴ Sides of the two square are 12m and 18m.

Question 18.
A container shaped like a right circular cylinder having diameter 12 cm. and height 15 cm. is full of ice cream. The icecream is to be filled into cones of height 12 cm. and diameter 6 era., having a hemispherical shape on the top. Find the number of such cones which can be filled with ice cream.
Answer:
Diameter of cylinder = d = 12 cm
⇒ Radius of the cylinder = \(\frac{d}{2}\) = \(\frac{12}{2}\) cm = 6 cm
Height of the cylinder = h = 15 cm
Volume of the cylinder = πr²h
= \(\frac{22}{7}\) × 6 × 6 × 15 = \(\frac{11880}{7}\) cm³
Diameter of each cone = d₁ = 6 cm
Radius of cone = r₁ = \(\frac{d_1}{2}\) = \(\frac{12}{2}\)cm = 3cm
Height of cone = h₁ = 12 cm
Volume of cone = \(\frac{1}{3}\). πr₁²h₁
= \(\frac{1}{3}\) × \(\frac{22}{7}\) × 3 × 3 × 12 = \(\frac{792}{7}\) cm³
Radius of hemispherical top of the cone = r₁ = 3cm
Volume of hemispherical top = \(\frac{2}{3}\) πr₁³
\(\frac{2}{3}\) × \(\frac{22}{7}\) × 3 × 3 × 3 = \(\frac{396}{7}\) cm³
Volume of ice cream in one cone
= \(\frac{792}{7}\) = \(\frac{396}{7}\) = \(\frac{1188}{7}\) cm³
No of required cones
= \(\frac{\text { Volume of icecream in container }}{\text { Volume of icecream in one cone }}\)
= \(\frac{11880 / 7}{1188 / 7}\) = \(\frac{11880}{7}\) \(\frac{7}{1188}\) = 10

Part – B (20 Marks)

Note :

1. Answer all the questions,
2. Each question carries 1 mark,
3. Answers are to be written in Question paper only,
4. Marks will not be awarded in any case of over uniting, rewriting or erased answers.

Note : Write the capital letters (A, B, C, D) showing the correct answer for the following questions in the brackets provided against them.

Question 1.
If A ⊂B then A∪(B – A) =
A) A
B) B
C) Φ
D) µ
Answer:
B) B

Question 2.
If the points (a, 0) (0, b) and (1, 1) are collinear, then \(\frac{1}{a}\) + \(\frac{1}{b}\) = …………….
A) 0
B) 1
C) 2
D) -1
Answer:
B) 1

Question 3.
In which quadrant does the point (-3, -3) lie ?
A) Q₁
B) Q₂
C) Q₃
D) Q₄
Answer:
C) Q₃

Question 4.
The sum of first n terms of the series a, 3a, 5a, …………. is
A) na
B) (2 n – 1) a
C) n²a
D) n²a²
Answer:
C) n²a

Question 5.
No. of odd numbers between 0 and 50
A) 24
B) 25
C) 23
D) 26
Answer:
B) 25

Question 6.
The roots of the quadratic equation \(\frac{11}{3+x}\) = 4 (3 – x)m
A) ±\(\frac{1}{5}\)
B) ±\(\frac{5}{2}\)
C) ±2
D) ±5
Answer:
B) ±\(\frac{5}{2}\)

Question 7.
The quadratic equation whose one root is 3 + √5 is
A) x² – 6x + 4 = 0
B) x² – 6x – 4 = 0
C) x² + 6x + 4 = 0
D) x² + 6x + 5 = 0
Answer:
A) x² – 6x + 4 = 0

Question 8.
The pair of equations x = 0 and y = 0 represents
A) parallel
B) perpendicular

D) ↔
Answer:
B) perpendicular

Question 9.
If α, β are zeroes of p(x) = x² – 5x + k and α – β = 1, then the value of ‘k’ is
A) µ
B) -6
C) 6
D) 5
Answer:
C) 6

Question 10.
The rational number between √2 and √3 is
A) \(\frac{6}{5}\)
B) \(\frac{3}{4}\)
C) \(\frac{3}{2}\)
D) \(\frac{4}{5}\)
Answer:
C) \(\frac{3}{2}\)

Question 11.
A man goes 150 m towards East and then 200 m towards North. How far is he from the starting point ?
A) 250 m
B) 160 m
C) 180 m
D) 150 m
Answer:
A) 250 m

Question 12.
A parallelogram ABCD and a triangle ABC are on the same and between the same parallel lines. If the area of the triangle ABE is 20 cm², then area of parallelogram ABCD is ……………. cm².
A) 20
B) 16
C) 40
D) 90
Answer:
C) 40

Question 13.
The number of tangents that can be drawn to a circle is …………….
A) 1
B) 2
C) 0
D) infinite
Answer:
D) infinite

Question 14.
Two spheres are in the ratio 3 : 5, what is the ratio of their surface areas ?
A) 9 : 16
B) 9 : 25
C) 25: 9
D) 16 : 1
Answer:
B) 9 : 25

Question 15.
Tan θ = 3/4 , then \(\frac{1-\cos \theta}{1+\cos \theta}\) = …………..
A) 9
B) -1
C) \(\frac{1}{9}\)
D) -9
Answer:
C) \(\frac{1}{9}\)

Question 16.
The length of the shadow of a tower is equal to its height, then the angle of elevation of the sun is ……………
A) 45°
B) 70°
C) 60°
D) 90°
Answer:
A) 45°

Question 17.
Two or more events of an experiment, where occurrence of all other events are called …………………… events.
A) Mutual
B) Non-considerable
C) Mutually exclusive
D) Considerable
Answer:
C) Mutually exclusive

Question 18.
The probability of getting a perfect square number from the number 1 to 10 is ………………..
A) \(\frac{1}{10}\)
B) \(\frac{3}{11}\)
C) \(\frac{2}{5}\)
D) \(\frac{1}{5}\)
Answer:
D) \(\frac{1}{5}\)

Question 19.
The median of scores x₁, x₂ and 2x is 6 and x₁ < 2x < x₂ then x₁ = ……………
A) 7
B) 3
C) 13
D) 31
Answer:
B) 3

Question 20.
Which of the following is not a measure of central tendancy ?
A) Mean
B) Median
C) Mode
D) Range
Answer:
C) Mode

Thoroughly analyzing TS 10th Class Social Model Papers Set 5 with Solutions helps students identify their strengths and weaknesses.

TS 10th Class Social Model Paper Set 5 with Solutions

Time: 3 hours
Max. Marks:80

Instructions:

1. Read the questions carefully, understand them, and answer.
2. Write the answers for the questions in Part- A in the answer sheet.
3. Attach the Map to Part – A answer sheet.
4. Attach Part – B to Part A answer sheet.
5. Part – A consists of I, II, and III Sections.
6. Write the answers clearly duly following the instructions given for each section.

Part- A (Marks 60)
Section – I (6 x 2 = 12 M)

1. Answer all questions.
2. Answer each question in 3 – 4 sentences.
3. Each question carries 2 marks.

Question 1.
How were the first three general elections?
Answer:
In Independent India’s first three general elections in 1952, 1957, and 1962 the Indian National Congress won reducing other participants to almost nothing. Jawaharlal Nehru became the first Prime Minister of India. None of the other parties individually got more than 11% of the votes polled.

Question 2.
How are the environmental movements?
Answer:

1. Environmental movements are the movements demanding the rights of the local communities over the environment.
2. They aim at protecting the environment by objecting the felling down trees, and constructing dams.
3. Chipko Movement acted to prevent the cutting down of trees.
4. Narmada Bachao Andolan has stood for the rights of the people overland, forests and river.

Question 3.
What was the agreement of the Muslim League?
Answer:
The Muslim League had argued that since the majority people in many areas were Hindus, more Hindus are likely to get elected to councils and Muslims will find it difficult to protect their interests in government. But, If a certain number of seats were reserved for Muslims for which only the Muslims population of an area would vote, these Muslim members reaching the councils will be able to raise the concerns and problems of Muslims.

Question 4.
Why was it necessary for government to run schools in Himachal Pradesh?
Answer:
The rich children can get the education in private sector schools. But the majority of Indian children are enrolled in the government schools. Education has also been made free for children from 6 to 14 years of age or up to VIII class under the R.T.E. Act 2009. So it was necessary for government to run schools in Himachal Pradesh.

Question 5.
‘The geographical location of India provides its vast diversity in climate conditions Write a comment on extremes in climate conditions.
Answer:
We notice hot tropical climate in extreme southern places and severe cold in Himalayan region. Western part of Rajasthan experiences desert conditions whereas the northeast has regular rainfall conditions. All this is possible due to vast area of our country.

Question 6.
Name some non-agricultural activities of your village.
Answer:
The following are some of the non-agricultural activities in our area.

1. Dairy.
2. A small repair shop where agricultural pump sets are repaired.
3. Provision shops.
4. Small tea shops.

Section – II (6 x 3 = 18M)

1. Answer all questions.
2. Answer each question in 5 – 6 sentences.
3. Each question carries 3 marks.

Question 7.
“Formation of Telangana state is the solution for many problems of Telangana people.” Explain.
Answer:
There are many problems faced by people of Telangana like water, universities and hospitals, language, etc., are some of the incidents which Telangana people felt that they were inferior and mostly try to change their slang when they came to Hyderabad. So, that they can escape from such criticisms and situations. These are the gross situations, there are other situations also which are minor.

People from Telangana felt that because if they have enough water to cultivate 2 crops they could generate enough money to invest in Hyderabad. So formation of Telangana state is the solution for many problems of the Telangana people.

Question 8.
If the market is not linked by foreign trade, what would happen?
Answer:

1. The surplus production remains in the country.
2. The foreign exchange stagnates.
3. We lose the technical knowledge of the MNCs.
4. Imports of essential commodities also gets reduced, thereby creating scarcity.

Question 9.
Write about the NAM.
Answer:
Non-alignment was established as an international organization with an aim to promote cultural and economic cooperation among the newly independent countries of Asia, Africa and later Latin America.

The first Summit was held at Belgrade in Yugoslavia in September 1961. It was attended by 25 member countries. By 2012, the membership has grown to 120 countries with 17 observers.

The first Summit was the culmination of three major concerns:
Cooperation among the member nations of NAM most of them who had newly emerged as free countries.
Growing Cold War tensions and its impact on the world at large. Lastly, to prevent any of the newly decolonized independent countries from joining any of the military blocks.

Question 10.
How was the period between 1975 to 1985 for Indian democracy?
Answer:
The period between 19th to 1985 was a testing time for Indian democracy. It began with the state of Emergency in which basic democratic rights were denied and ended with the historic electoral victory of the Congress led by Rajiv Gandhi. Though it began and ended with the rule of the Congress. party, it saw the emergence of viable alternatives to the Congress at both the Centre and in the States. This effectively prevented India from sliding into a ‘single party democracy’.

Question 11.
What are the steps to be taken to restrict the overgrowth of population in India?
Answer:
The following steps to be taken:

1. Family planning measures should be implemented effectively by the government.
2. Child marriages must be stopped.
3. Education should be provided to all women in the country.
4. Family planning counseling centers must be maintained.
5. Newly married couples should wait at least three years to get children.
6. They should maintain minimum 3 years gap between two deliveries.

Question 12.
What is deforestation? What are its affects?
Answer:
Cutting down of the trees indiscriminately in the areas of forest or where there is a pressure of sizable number of trees like plantations is called deforestation.

Effects of deforestation:

1. It results in the lowering of the green còver.
2. It affects the ecological balance.
3. It reduces the probability of raining.
4. It affects the soil erosion, it increases the soil erosion.
5. It also affects the sustainability of green cover.

Section – III
6 x 5 = 30 M

1. Answer all questions
2. There is an internal choice for each question.
3. Answer each question in 8-10 sentences
4. Each question carries 5 marks.

Question 13.
Read the following paragraph and interpret.
The first requirement for a country is to able to produce foodgrains for the whole of its population. How do we measure whether there is enough food for all or not? Whether this food reaches families or not would be examined later. We are at first estimating what is available. This means that per person (or per capita) availability of foodgrains in the country should be sufficient and also increasing over the years. Is the increase in foodgrain availability really happening?
(OR)
What are the ways in which the Black Americans protested with the government?
Answer:
According to the paragraph, every country should produce the food grains how much it needs. Every country should examine two things. The first one is how much foodgrains are produced in the country and the second one ¡s how it is reaching to the people. The government should check whether the food grains are sufficient to the people or not.

Many countries don’t concentrate on this sensitive issue. It is very primary thing to look into the matter of foodgrain production and its availability. If sufficient foodgrain production is there in a country definitely the stock in market will be sufficient and the prices will also be at normal level. When the production is less than the need or demand, automatically the prices go up. The rich can purchase but it will be the problem for the poor people and they can’t purchase.
(OR) .

1. The Black Americans suffered a lot as the government permitted segregation in schools and buses.
2. There was discrimination against them in appointments, housing and even in voting rights.
3. They took up the Civil Rights Movement.
4. It is of non-violent in nature.
5. They gave massive demonstrationš, marches, civil disobedience and boycotts of discriminatory services.
6. They boycotted the buses for one year long.
7. More than two lakh people conducted the Washington March.
8. These are the ways in which they protested.

Question 14.
Study the following pie chart and answer the given questions:
Distribution of workers in India, by industry:
Pie Diagram:

i) What is the total percentage of female workers in agriculture?
ii) What is the total percentage of male workers in agriculture?
iii) What is the total percentage of male workers in both industry and service sectors?
iv) Who are more in industrial sector and why?
v) Who are more in agricultural sector and why?
(Or)
Read the following paragraph and write your comment on It.
Over the past few decades, groundwater has become the main source of water especially for domestic use and agriculture. This tremendous increase in the use of groundwater has significant impact on water availability and access to it.
Answer:
i) 69%
ii) 47%.
iii) 53%
iv) Male are high in industrial sector, because of various reasons.

Some of them are:
1) Illiteracy of women.
2) Lack of mobility of women.
3) More number of women engaged in unorganized and informal sectors.
v) Women are more in agriculture. The reason for this is illiteracy among women is high. Most of them are in unorganized and informal sectors.
(OR)
According to this paragraph the groundwater level is the crucial on to all the people. The groundwater is useful for both domestic purpose and for agriculture. If groundwater is not available, there will be many problems.

My opinion is that because of modernization of agriculture motor pumps of high horsepower are being used. Very deep bore wells cause for drawing out water from the ground. Water has become a source of business, many multinational companies draw water and sell in the form of bottles. Water conservation is also a major issue and it is taken as a serious one. Every individual should think about the importance of water as it is useful to all people. Actually, once it was the common property. Now it has become individual property. Hence everyone should give importance to water. Otherwise, no one can get water.

Question 15.
Compare the League of Nations with the United Nations Organisation.
(OR)
Read the following paragraph and write your opinion.
“Racism became common in the British colonial empire in late 19th and early 20th centuries. Educated Africans were excluded from the civil service and there was discrimination against African entrepreneurs. At the same time, the authorities from ruling country gave control to the tribal chiefs and elite and promoted them.
Answer:

1. Both the League of Nations and the United Nations Organisation have been formed with the aim of elementary wars and settling disputes between countries through arbitration and negotiation.
2. The league did not take the active ìnvoWement of the American Government, even though President Woodrow Wilson campaigned hard to popularise it.
3. Having 58 members only at the peak level of its functioning shows that the influence of the league was less.
4. Not inviting Germany and Russia to join the league was a big mistake.
5. The league did not have a multinational army of its own. So, it could not take any action on erring nations.
6. The UNO was more stronger than the league as its strength at formation in 1945 was 52 and reached 193 by 2013.
7. The UNO was successful in preventing many wars and took necessary action, on countries which disturbed peace by maintaining an United Nations Peace Keeping Force (UNPKF).
8. The UNO reached out the needs of the people in many countries as far as health, education and basic amenities were concerned. Thus we can say that UNO was more successful than the League of Nations.

(OR)
The colonial policy helped to promote modern education and administrative modernisation in the South while it allowed the pre-modern traditions to continue in the North. This, over the century, created much regional disparity and the North was not able to develop a modern educated social strata. in 1939 the British also separated the Yoruba and Igbo regions into Westërn and Eastern Nigeria and encouraged competition and conflict between the three major tribal groups so as to be able to ‘divide and rule’ the country.

Question 16.
Explain the code of Conduct.
(OR)
How can you say that India is a Secular State?
Answer:
Election Commission should announce code of conduct:
According to this, all the people and candidates contesting should follow the Election rules and regulations. Violation of these rules and regulations is treated as malpractices.

1. Political parties shall not make any statements pertaiñing to caste, creed, religion and regional.
2. No personal comments shall be made that are not relevant to political life.
3. No personal announcement targeting a caste or religion.
4. No candidates shall influence the voters by giving cash etc.
5. No campaigning within loo mts on the day of polling.
6. No campaigning after or before the permitted hours.
7. Taking out rallies in the residential areas and picketing is against the rules.

(OR)
The following points prove India is a secular country.

1. Secularism in the Indian context implies tolerance towards others’ beliefs and faiths.
2. In India, there is no state religion.
3. No religion is given superior status.
4. Citizens are granted complete freedom in religious matters.
5. People are free to profess, practice, and propagate any religion of their choice.
6. No religious instruction is imparted in any educational institution maintained out of public funds.
7. No discrimination is made in matters of public employment on the grounds of religion.
8. The religious tolerance is followed.

Question 17.
Read the paragraph and write your opinion.
Most of the population increase in cities and towns took place as a consequence of natural growth within the urban areas. The population of these urban areas increased over time. Some of the growth in urban settlements took place by expansion, with the inclusion of rural areas surrounding older cities and towns. Only one-fifth of the growth is due to rural-to-urban migration.
(OR)
Read the following paragraph and answer the questions that follow.
Recent data on the status of groundwater resources in India suggests that the groundwater is under serious threat of overuse in many parts of the country. Nearly one-third of the country is pumping out more groundwater than what goes in as recharge. About 300 districts have reported a water level decline of over 4 meters during the past 20 years, which points to an alarming rate of extraction. Groundwater overuse is particularly found in the agriculturally prosperous regions of Punjab and western U.P., hard rock plateau areas of central and south India, some coastal areas, and the rapidly growing urban settlements.
i) How are these regions?
ii) Where is the groundwater overused?
iii) Compare the pumping out and recharge.
iv) What does the data suggest?
v) What happened in 300 districts?
Answer:
According to the paragraph given, the natural growth within the urban areas is more as the expansion is going on around the cities and towns. When a city or town expands the surrounding villages will be submerged in the city or town. The migration from rural areas is very less.

My opinion is that it is not common in all the cities and towns. In some cities and towns, it may be correct but in many areas, the migrants are more in number. They are coming from rural areas to urban areas. They have different reasons like livelihood, employment, children’s education, medical services for their chronic patients, dejection in agriculture, and others. When all these people come to cities and towns there will be many problems.

Government should take care of these problems and find solutions. Right to life is given by the Constitution but it is not affordable to all. Agriculture is to be given priority and so villagers or farmers may stay there. It will be useful to increase the agro products also.
(OR)

• These regions are prosperous in agriculture.
• In the regions of Punjab and western ILP., hard rock plateau areas of central and south India, some coastal areas and the rapidly growing urban settlements.
• Nearly one-third ‘of the country is pumping out more groundwater than what goes in as recharge.
• Recent data on the status of groundwater resources in India suggest that the groundwater is under serious threat of overuse in many parts of the country.
• In 300 districts there was á decline of water level over 4 metres.

Question 18.
Locate the following on the map of India.
a) Maharashtra
b) Gujarat
c) Bihar
d) Uttar Pradesh
e) Jammu – Kashmir
(OR)
locate the following in the map of world.
(i) China,
(ii) Japan,
(iii) Brazil,
(iv) South Africa
(v) Spain
Answer:

(or)

Part – B
Marks 20

Instructions:

1. Answer all questions.
2. Choose the correct option from the given four Options and write the letter (A to B or C or D) in CAPITAL LETTER in the brackets.
3. Each question carries 1 mark.
4. Write the answers in the question paper itself.
5. Marks are not given to corrected, dismissed, or erased answers.

Question 1.
The deltas are developed. ( )
A) Traditionally
B) Culturally
C) Agriculturally
D) Industrially
Answer:
C) Agriculturally

Question 2.
The second requirement of a producer is – ( )
A) Land
B) Labour
C) Capital
D) None
Answer:
B) Labour

Question 3.
The Gentlemen’s Agreement signatories basically agreed points. ( )
A) 14 points
B) 10 points
C) 9 points
D) 15 points
Answer:
A) 14 points

Question 4.
Fair globalisation means. ( )
A) Ensuring better living for the people of developed countries.
B) Creating opportunities for all
C) Creating new trade barriers
D) Investing more in developing countries.
Answer:
B) Creating opportunities for all

Question 5.
The organisation of third-world countries is ( )
A) Warsaw Pact
B) NATO
C) SEATO
D) NAM
Answer:
D) NAM

Question 6.
The Congress Party was defeated at the national level for the first time In ( )
A) 1677
B) 1897
C) 1997
D) 1977
Answer:
D) 1977

Question 7.
In India, ……………….. female babies are born against 1oo male babies. ( )
A) 20
B) 103
C) 200
D) 150
Answer:
B) 103

Question 8.
Pre-monsoon showers help in the ripening of in Andhra Pradesh. ( )
A) Banana
B) Orange
C) Apple
D) Mango
Answer:
D) Mango

Question 9.
NIN means ( )
A) National Institute on Nature
B) National Institute for Nation
C) New Institute for Nation
D) National Institute of Nutrition
Answer:
D) National Institute of Nutrition

Question 10.
Vietnam is a country in the continent of ( )
A) North America
B) Africa
C) Europe
D) Asia
Answer:
D) Asia

Question 11.
G.D.P means ( )
A) Gross Domestic Product
B) National Income
C) Per Capita income
D) Total National Income
Answer:
A) Gross Domestic Product

Question 12.
The …………………… emerges from the hills of Haridwar. ( )
A) Yamuna
B) Indus
C) Ganga
D) Brahmaputra
Answer:
B) Indus

Question 13.
The Gregorian Calendar is ahead of …………………….. days Julian one. ( )
A) 10 days
B) 15 days
C) 13 days
D) 31 days
Answer:
C) 13 days

Question 14.
The founder of modern China ( )
A) Sun-Yet-Sen
B) Mao
C) Tsn-Chi
D) Kang-Yu-Vi
Answer:
A) Sun-Yet-Sen

Question 15.
E.C solves the disputes between parties, this function is under …………………….. . ( )
A) Administrative function
B) Advisory function
C) Quasijudicial function
D) None of these
Answer:
C) Quasijudicial function

Question 16.
The Constitution of India was prepared and adopted by the ( )
A) Legislators
B) Judiciary
C) Constituent Assembly
D) Executive
Answer:
C) Constituent Assembly

Question 17.
The International London Airport is in ………………….. . ( )
A) Heathrow
B) Suvarnabhoomi
C) Cairo
D) Dubai
Answer:
A) Heathrow

Question 18.
H.D.I. expands the meaning of development to include of education and health ( )
A) real estate
B) education
C) banking
D) social indicators
Answer:
D) social indicators

Question 19.
Tebhaga movement was led by ( )
A) Provincial Kisan Sabha
B) Communist Party
C) Muslim farmers
D) Congress farmers
Answer:
A) Provincial Kisan Sabha

Question 20.
The average income is also called …………………. income. ( )
A) GNP
B) GDP
C) PCI
D) None
Answer:
C) PCI

The strategic use of TS 10th Class Maths Model Papers Set 6 can significantly enhance a student’s problem-solving skills.

TS SSC Maths Model Paper Set 6 with Solutions

Time: 3 Hours
Maximum Marks: 80

General Instructions:

1. Answer all the questions under Part – A on a separate answer book.
2. Write the answers to the questions under Part – B on the question paper itself and attach it to the answer book of Part – A.

Part – A (60 Marks)
Section – I (6 × 2 = 12 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 1.
If A = {x : x is a factor of 24}, then find n(A).
Solution:
A = (1, 2, 3, 4, 6, 8, 12, 24} ; n(A) = 8
24 = 1 × 24
= 2 × 12 = 3 × 8 = 4 × 6

Question 2.
Find the roots of the Quadratic equation x² + 2x – 3 = 0.
Solution:
x² + 2x – 3 = 0
x² + 3x – x – 3 = 0
x(x + 3) – 1 (x + 3) = 0
(x + 3) (x – 1) = 0
x = – 3 (or) x = 1
Roots of Quadratic Equation are – 3, 1.

Question 3.
For what value of ‘t’ the following pair of linear equations has a no solution ?
2x – ty = 5 and 3x + 2y = 11.
Solution:
Pair of linear equations has no solution
If \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\) ⇒ \(\frac{2}{3}\) = \(\frac{-t}{2}\) ≠ \(\frac{-5}{-11}\)
– 3t = 4 ⇒ t = – \(\frac{4}{3}\)

Question 4.
In a right triangle ABC, right angled at ‘C’ in which AB =13 cm, BC = 5cm, determine the value of cos² B + sin² A.
Solution:
We have, Cos B = \(\frac{\mathrm{BC}}{\mathrm{AB}}\) = \(\frac{5}{13}\)
Sin A = \(\frac{\mathrm{BC}}{\mathrm{AB}}\) = \(\frac{5}{13}\)

Cos² B + Sin² A
= \(\frac{25}{169}\) +\(\frac{25}{169}\) = \(\frac{25+25}{169}\) = \(\frac{50}{169}\)

Question 5.
A point P is 25 cm from the centre O of the circle. The length of the tangent drawn from P to the circle is 24 cm. Find the radius of the circle.
Solution:
From right angled Δ AOP

OP² = OA² + AP²
(25)² = OA² + (24)²
625 = OA² + 576
OA² = 625 – 576 = 49 = 7²
OA = 7 cm
∴ The radius of the circle is 7 cm.

Question 6.
In a hemispherical bowl of 2.1 cm radius ice-cream is there. Find the volume of the bowl.
Solution:
Radius (r) = 2.1 cm
Volume (V) = \(\frac{1}{2}\)πr³
= \(\frac{2}{3}\) × \(\frac{22}{7}\) × (2.1)³
= 19.404 cm³

Section – II (6 × 3 = 18 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 3 marks.

Question 7.
If x² + y² = 7xy, then prove that log(\(\frac{x+y}{3}\)) = \(\frac{1}{2}\)
Given x² + y² = 7xy, now add (2xy) on both sides. We get
x² + y² + 2xy = 7xy + 2xy = 9xy
Considering square root on both sides we get
\(\sqrt{x^2+y^2+2 x y}\) = \(\sqrt{9 x y}\)
x + y = 3\(\sqrt{x y}\)
⇒ \(\frac{x+y}{3}\) = \(\sqrt{x y}=(x y)^{\frac{1}{2}}\) considering logarithm on both sides, we get
log(\(\frac{x+y}{3}\)) = log\((x y)^{\frac{1}{2}}\) = \(\frac{1}{2}\) log(xy)
log(\(\frac{x+y}{3}\)) = \(\frac{1}{2}\) (log x + log y) (∵ log mn = log m + log n)

Question 8.
“If we multiply or divide both sides of a linear equation by a non-zero number, then the roots of that linear equation will remain the same.”
Is it true ? If so, justify with an example.
Solution:
Given statement : “If we multiply or divide both sides of a linear equation by a non-zero number, then the roots of that linear equation will remain the same”.
Consider a linear equation
x + y = 5 ………….. (1)
One of the solutions for this equation (1) is (2, 3)
Now multiply equation (1) by ‘3’.
3 (x + y) = 3 × 5
3x + 3y = 15 ………….. (2)
Now substitute the point (2, 3) in the equation (2).
∴ 3(2)+ 3 (3) = 15
16 + 9= 15 ⇒ 15 = 15
∴ (2, 3) is also a solution for the equation (2).
So the given statement is true.

Question 9.
Measures of sides of a triangle are in Arithmetic Progression. Its perimeter is 30cm, and the difference between the longest and shortest side is 4cm; then find the measures of the sides.
Solution:
Let the 3 sides of given triangle = a – d, a, a + d
Then its perimeter
= a – d + a + a + d = 30 cm.
3a = 30 cm ⇒ a = \(\frac{30}{3}\) = 10 cm.
The larger side = a + d
The shorter side = a – d
The difference between the above two
= (a + d) – (a – d) = 4 cm.
a + d – a + d = 4 cm.
2d = 40 ⇒ d = \(\frac{4}{2}\) = 2 cm.
a = 10 cm, d = 2 cm
So the sides a – d = 10 – 2 = 8 cm
and a + d=10 + 2 = 12 cm.
So 8, 10, 12 cm are the sides of the triangle.

Question 10.
A bag contains balls which are numbered from 1 to 50. A ball is drawn at random from the bag, the probability that it bears a two digit number multiple of 7.
Solution:
Number of possible outcomes = 50 Number of required outcomes = 6 {14,21,28,35,42,49}
∴ Probability of getting two digit number which is a multiple of 7
= \(\frac{\text { Number of favourable outcomes }}{\text { Number of total outcomes }}\)
= \(\frac{6}{50}\) = \(\frac{3}{25}\)

Question 11.
If cot θ = \(\frac{7}{8}\) then,
Evaluate :
i) \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\)
ii) \(\frac{1+\cos \theta}{\sin \theta}\)
Solution:
i) \(\frac{(1+\sin \theta)(1-\sin \theta)}{(1+\cos \theta)(1-\cos \theta)}\)
= \(\frac{1-\sin ^2 \theta}{1-\cos ^2 \theta}=\frac{\cos ^2 \theta}{\sin ^2 \theta}\) = cot² θ
= (\(\frac{7}{8}\))² = \(\frac{49}{64}\) ………… (1)
(∵ sin² θ + cos² θ = 1)

ii) \(\frac{1+\cos \theta}{\sin \theta}\) = \(\frac{1}{\sin \theta}+\frac{\cos \theta}{\sin \theta}\) = cosec θ + cot θ
Now given cot θ = \(\frac{7}{8}\)) then we have
(1 + cot² θ) = cosec² θ
⇒ 1 + (\(\frac{7}{8}\))²
= 1 + \(\frac{49}{64}\) + \(\frac{64+49}{64}\) = \(\frac{113}{64}\)
∴ cosec θ = \(\sqrt{\frac{113}{64}}\)
∴ \(\frac{1+\cos \theta}{\sin \theta}\) = cosec θ + cot θ
= \(\frac{\sqrt{113}}{8}\) + \(\frac{7}{8}\) = \(\frac{7+\sqrt{113}}{8}\)

Question 12.
A right circular cylinder has radius 3.5 cm and height 14 cm. Find curved surface area.
Solution:
radius (r) = 3.5cm; height (h) = 14cm Curved surface area of the right circular cylinder
= 2πrh = 2 × \(\frac{22}{7}\) × 3.5 × 14
= 44 × 7 = 308 cm²

Section – III (6 × 5 = 30 Marks)

Note :

1. Answer all the following questions.
2. In this section, every question has internal choice. Answer any one alternative.
3. Each question carries 5 marks.

Question 13.
A) If two dice are thrown at the same time, find the probability of getting sum of the dots cm top is prime.
Solution:
Total possible outcomes when two dice are rolled = 36
Let E be an event to get sum of the tops is prime
Total favourable outcomes : (1, 1) (1, 2), (2, 1), (1, 4), (2, 3), (3, 2), (4, 1), (1, 6), (2, 5), (3, 4), (4, 3) (5, 2), (6, 1), (5, 6), (6, 5)
Number of total favourable outcomes = 15
P(E) = \(\frac{\text { No. of favourable outcomes }}{\text { No. of total possible outcomes }}\)
\(\frac{15}{36}\) =\(\frac{5}{12}\)

(OR)

(B) Show that \(\frac{\cos \theta}{1-\sin \theta}+\frac{1-\sin \theta}{\cos \theta}\) = 2 sec θ
Solution:

Question 14.
A) Find the ratio in which X-axis divides the line segment joining the points (2, – 3) and (5, 6). Then find the intersecting point on X-axis.
Solution:
Let X – axis divides the line segment joining points (2, – 3) and (5, 6) in the ratio m₁ : m₂
x₁ = 2 x₂ = 5
y₁ = -3 y₂ = 6
Co-ordinate of point
P = (\(\frac{m_1 x_2+m_2 x_1}{m_1+m_2}, \frac{m_1 y_2+m_2 y_1}{m_1+m_2}\))
= (\(\frac{m_1(5)+m_2(2)}{m_1+m_2}, \frac{m_1(6)+m_2(-3)}{m_1+m_2}\))
But this is a point on X-axis, so its y co-ordinate is zero.
\(\frac{m_1(6)+m_2(-3)}{m_1+m_2}\) = 0
6m₁ – 3m₂ = 0
6m₁ = 3m₂
\(\frac{\mathrm{m}_1}{\mathrm{~m}_2}\) = \(\frac{3}{6}\) = \(\frac{1}{2}\)
∴ Required ratio = 1 : 2

(OR)

B) DWACRA is supplied cuboidal shaped wax block with measurements 88 cm × 42 cm × 35 cm. From this how many number of cylinderical candles of 2.8 cm diametre and 8 cm of height can be prepared ?
Solution:
Shape of wax block = cuboid
Its length (l) = 88 cm ;
breath (b) = 42 cm ; height (h) = 35 cm
Then the volume of wax present in block = lbh
= 88 × 42 × 35 cm³ …………… (1)
Shape of candle = cylinder
Diameter of candle = (d) = 2.8 cm 2.8
⇒ radius = r = \(\frac{2.8}{2}\) = 1.4 cm
height (h) = 8 cm
Volume of wax required to make one candle = V = πr²h
= \(\frac{22}{7}\) × 1.4 × 1.4 × 8 cm³
∴ Total number of candles that can be
made = \(\frac{\text { Total volume of block }}{\text { Volume of each candle }}\)
= \(\frac{88 \times 42 \times 35}{\frac{22}{7} \times 1.4 \times 1.4 \times 8}\) = 2625
So 2625 candles can be made with given measurements.

Question 15.
A) Two trains leave a railway station at the same time. The first train travels towards west and the second train towards north. The first train travels 5 km/hr faster than the second train. If after two hours they are 50 km. apart, find the average speed of each train.
Solution:
Let the speed of the slower train = x kmph
then speed of the faster train = x + 5 kmph.

Distance = Speed × Time
∴ Distance travelled by the first train = 2(x + 5) = 2x+ 10
Distance travelled by the second train = 2.x = 2x
By Pythagoras Theorem
(hypotenuse)² = (side)² + (side)²
⇒ (2x)² + (2x + 10)² = 50²
⇒ 4x² + (4x² + 40x + 100) = 2500
⇒ 4x² + 4x² + 40x + 100 = 2500
⇒ 8x² + 40x – 2400 = 0
= x² + 5x – 300 = 0
⇒ x² + 20x – 15x – 300 = 0
⇒ x(x + 20) – 15(x + 20) = 0
⇒ (x + 20) (x – 15) = 0
∴ x – 15 = 0 (or) x + 20 = 0
⇒ x = 15 (or) -20
But x can’t be negative.
∴ Speed of the slower train x = 15kmph.
Speed of the faster train
x + 5 = 15 + 5 = 20 kmph.

(OR)

B) In a right angle triangle, the hypotennse is 10 cm more than the shortest side. If third side is 6 cm less than the hypotenuse, find the sides of the right angle triangle.
Solution:
Let the shortest side of right angled triangle be x cm,
Hypotenuse = (x + 10) cm (given)
Third side = (x + 10 – 6) cm
= (x + 4) cm (given)
AC = (x + 10) cm, AB = x cm,
BC = (x + 4) cm
In a right angled triangle ABC

AC² = AB² + BC²
(x + 10)² = x² + (x + 4)²
x² + 20x + 100 = x² + x² + 8x + 16
⇒ x² – 12x – 84 = 0

⇒ x = 6 + 2\(\sqrt{30}\) cm (∵ x < 0)
x + 4 = 10 + 2\(\sqrt{30}\) cm
x + 10 = 16 + 2\(\sqrt{30}\) cm

Question 16.
A) Show that √5 – √3 is an irrational number.
Solution:
Suppose √5 – √3 is not an irrational number. √5 – √3 is a rational number.
Let √5 – √3 = \(\frac{p}{q}\) where q ≠ 0 and p, q e ∈ Z squaring on both sides
5 + 3 – \(2 \sqrt{15}=\frac{p^2}{q^2}\)
\(\sqrt{15}=\frac{8 q^2-p^2}{2 q^2}\)
∴ p, q ∈ Z & q ≠ 0
8q² – p² & 2q² ∈ Z and also 2q² ≠ 0.
So \(\frac{8 q^2-p^2}{2 q^2}\) JL is a rational number.
but \(\sqrt{15}\) is an irrational number.
An irrational number never be equal to a rational number.
So our supposition that √5 – √3 is not an irrational number is false.
∴ √5 – √3 is an irrational number.

(OR)

(B) Prove that :
(1 + tan² θ) + ( 1 + \(\frac{1}{\tan ^2 \theta}\)) = \(\frac{1}{\sin ^2 \theta-\sin ^4 \theta}\)
Solution:

Question 17.
A) Draw the graph of the polynomial p(x) = x² – 7x + 12, then find its zeroes from the graph.
Solution:
p(x) = x² – 7x + 12


zeroes of the polynomial is 3, 4

(OR)

B) Find the solution of x + 2y = 10 and 2x + 4y = 8 graphically.
Solution:
x + 2y = 10 ………… (1)

x	0	2	4	6
y	5	4	3	2
(x, y)	(0, 5)	(2, 4)	(4, 3)	(6, 2)

2x + 4y = 8 ……….. (2)

x	0	2	4	6
y	2	1	0	-1
(x, y)	(0, 2)	(2, 1)	(4, 0)	(6, -1)

The lines are parallel
∴ No solution for the given pair of equations.

Question 18.
A) Construct a triangle of sides 4.2 cm, 5.1 cm and 6 cm. Then construct a triangle similar to it, whose sides are 2/3 of corresponding sides of the first triangle.
Solution:

Construction Steps :

1. Draw a triangle ABC, with sides AB = 4.2 cm, BC = 5.1 cm, CA = 6 cm.
2. Draw a ray BX making an acute angle with BC on the side opposite to vertex A.
3. Locate 3 points B₁, B₂, B₃ on BX so that BB₁ = B₁B₂ = B₂B₃.
4. Join B₃, C and draw a line through B₂ parallel to B₃C intersecting BC at C’.
5. Draw a line through C’ parallel to CA intersect AB at A’.
6. ΔA’BC’ is required triangle.

(OR)

B) Draw a circle of radius 6 cm and construct two tangents to the circle so that angle between the tangents is 60°.
Solution:
To begin let us consider a circle with centre ‘O’ and radius 6 cm.
Let PA and PB are two tangents draw from a point ‘P’ outside the circle and the angle between them is 60°.
In this ∠APB = 60°. Join OP.

As we know, OP is the bisector of ∠APB, then
∠OAP = ∠OPB = \(\frac{60^{\circ}}{2}\) = 30° (∵ ΔOAP≅ΔOBP)
Now in ΔOAP
sin 30° = \(\frac{\text { Opposite side }}{\text { Hypotenuse }}=\frac{\mathrm{OA}}{\mathrm{OP}}\)
\(\frac{1}{2}=\frac{6}{\mathrm{OP}}\) (From trigonometric ratio)
OP = 12 cm
Now we can draw a circle of radius 6 cm with centre ‘O’. We then mark a point at a distance of 12 cm from the centre of the circle. Join OP and complete the construction.

Hence PA and PB are the required pair of tangents to the given circle.

Part – B (20 Marks)

Note :

1. Answer all the questions.
2. Each question carries 1 mark.
3. Answers are to be written in the Question paper only.
4. Marks will not be awarded in any case of over writing, rewriting or erased answers.

Note : Write the capital letters (A, B, C, D) showing the correct answer for the following questions in the brackets provided against them. (Marks: 20 × 1 = 20)

Question 1.
If both roots are common to the Quadratic equations
x² – 4 = 0 and x² + px – 4 = 0, then p =
A) 2
B) 0
C) 4
D) 1
Answer:
B) 0

Question 2.
The distance of the point p(x, y) from Y-axis is
A) |x|
B) |y|
C) |x + y|
D) |x – y|
Answer:
A) |x|

Question 3.
The exponential form of log_a\(\sqrt{x^4}\) = y is
A) a^y = x⁴
B) y^a = 4
C) a^y = x²
D) x^y = a²
Answer:
C) a^y = x²

Question 4.
If A ⊂ B, then A – B =
A) A
B) B
C) B – A
D) Φ
Answer:
D) Φ

Question 5.
If (a, b), (b, c) and (c, a) art the vertices of a triangle and the centroid of triangle is origin, then a³ + b³ + c³ =
A) abc
B) a + b + c
C) 3abc
D) 0
Answer:
C) 3abc

Question 6.
If \(\frac{5}{x-1}+\frac{1}{y-2}\) = 2, \(\frac{6}{x-1}+\frac{-3}{y-2}\) = 1 then x = …………..
A) 4
B) 7
C) -1
D) 3
Answer:
A) 4

Question 7.
The last (unit place) digit of 6²⁰¹⁹ in its standard form
A) 6
B) 4
C) 9
D) 19
Answer:
A) 6

Question 8.
If α, β are the zeroes of the polynomial x² + 5x + k and α – β = 3, then the value of k.
A) 6
B) 9
C) 5
D) 4
Answer:
D) 4

Question 9.
The 25^th term of -300, -290, -280, is ………
A) -60
B) -80
C) 60
D) 80
Answer:
A) -60

Question 10.
If A {x : x² – 16 = 0, x ∈ R} and
B – {x : x² – 5x + 6 = 0, x∈ R}, then A∪B is a ………..
A) Singleton set
B) Infinite set
C) Null set
D) Finite set
Answer:
D) Finite set

Question 11.
What change will be observed in the angle of elevation as we move away from the object?
A) increase
B) decrease
C) can’t be determined
D) no change
Answer:
A) increase

Question 12.
Let x₁, x₂, x₃, x₄,……. x_n be the n observations and \(\overline{\mathbf{x}}\) be the mean of n observations, then \(\sum_{i=1}^n\left(x_1-\bar{x}\right)\) = ……..
A) 0
B) n\(\overline{\mathbf{x}}\)
C) \(\frac{\bar{x}}{n}\)
D) \(\frac{2 \bar{x}}{n}\)
Answer:
A) 0

Question 13.
A 20 m long ladder is placed on a pole of 10 m height Shaking ‘α’ angle with the ground, then α =
A) 60°
B) 45°
C) 30°
D) 0°
Answer:
C) 30°

Question 14.
Tangents PA and PB inclined at an angle 60° as shown in the figure, the ratio of lengths of OA, OP and AP is

A) 1 : 2 : 3
B) 3 : 2 : 1
C) √3 : 2 : 1
D) 1 : 2 : √3
Answer:
D) 1 : 2 : √3 (Add Score)

Question 15.
ABC is a right angle triangle and ∠C = 90°, Let BC = a, CA = b, AB = c and p be the length of the perpendicular from C on AB, then ………………
A) \(\frac{1}{\mathrm{p}^2}=\frac{1}{\mathrm{a}^2}-\frac{1}{\mathrm{~b}^2}\)
B) \(\frac{1}{\mathrm{p}^2}=\frac{1}{\mathrm{~b}^2}-\frac{1}{\mathrm{a}^2}\)
C) \(\frac{1}{\mathrm{p}^2}=\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}\)
D) \(\frac{2}{p^2}=\frac{1}{a^2}+\frac{1}{b^2}\)
Answer:
C) \(\frac{1}{\mathrm{p}^2}=\frac{1}{\mathrm{a}^2}+\frac{1}{\mathrm{~b}^2}\)

Question 16.
Let r, h had l be the radius, height and slant height of a cone respectively, then express l in terms of r and h is ……………
A) \(\sqrt{h^2-r^2}\)
B) \(\sqrt{\mathrm{r}^2+\mathrm{h}^2}\)
C) \(\sqrt{\mathrm{r}^2-\mathrm{h}^2}\)
D) \(\sqrt{4 r^2+h^2}\)
Answer:
B) \(\sqrt{\mathrm{r}^2+\mathrm{h}^2}\)

Question 17.
Number of circles passing through 3 collinear points in a plane is
A) 1
B) 0
C) 9
D) 12
Answer:
B) 0

Question 18.
Choose the correct figure for which sin A = \(\frac{5}{13}\)

Answer:

Question 19.
A letter is choosen from the word “BAHUBALI”, the probability that it was not a vowel is
A) \(\frac{1}{2}\)
B) \(\frac{3}{2}\)
C) \(\frac{4}{3}\)
D) \(\frac{3}{4}\)
Answer:
A) \(\frac{1}{2}\)

Question 20.
Which of the following statement is true ?
A) All acute angle triangles are similar.
B) All obtuse angle triangles are similar.
C) All right angle triangles are similar.
D) All isosceles right triangles are similar.
Answer:
D) All isosceles right triangles are similar.

Thoroughly analyzing TS 10th Class Social Model Papers Set 4 with Solutions helps students identify their strengths and weaknesses.

TS 10th Class Social Model Paper Set 4 with Solutions

Time: 3 hours
Max. Marks: 80

Instructions:

1. Read the questions carefully, understand them, and answer.
2. Write the answers for the questions in Part – A in the answer sheet.
3. Attach the Map to Part – A answer sheet.
4. Attach Part – B to Part A answer sheet.
5. Part – A consists of I, II, and III Sections.
6. Write the answers clearly duly following the instructions given for each section.

Part – A (Marks 60)
Section – I (6 x 2 = 12 M)

1) Answer all questions.
2) Answer each question in 3 -4 sentences.
3) Each question carries 2 marks.

Question 1.
Imagine and write the main reasons for the continuation of anti-Hindi movement in Tamil Nadu till today.
Answer:

1. DMK in Tamil Nadu believed the passage of Official Languages Act, 1963 was an attempt to foist Hindi on the rest of the country.
2. They started a statewide campaign protesting the imposition of Hindi.
3. They organised strikes, dharnas, burning effigies, Hindi books as well as pages of the Constitution.
4. Still, there is same feeling in Tamil Nadu.

Question 2.
What are the disadvantages of projects or dams?
Answer:
The disadvantages of dams are:

1. Displacement of local people.
2. Submerging of low-lying areas,
3. Destroying fertile land.
4. Harming human life and bio-diversity.
5. Causing ecological imbalance, etc.

Question 3.
Write about the Muslim League.
Answer:
This was a party formed in 1906. Till the 1930, it mainly represented the interests of Muslim landlords of UP and did not have much mass support. It had demanded that the British should create separate seats in all councils for which only Muslims would vote.

Question 4.
‘Money cannot buy all the goods and services that one needs to live well.’ Explain.
Answer:

1. Even though per capita income is high in many states, education and health ‘Facilities are still lacking. ,
2. Money or high per capita income cannot buy a pollution-free environment or good health.
3. Money cannot buy peace and democracy.

Question 5.
Observe the picture and write about it.

Answer:

1. It is a remote village covered with trees.
2. It is on the Brahmaputra valley in Assam.
3. The river is noted for floods.

Question 6.
“Labour is an essential item for production.” Read the statement and interpret it.
Answer:

1. Labour means people who do the work either highly trained and educated or who can do manual work.
2. Each worker is providing necessary labour for production.
3. Skilled or semiskilled or unskilled labour – all are providing labour for production.

Section-II
6 x 3 = 18 M

1. Answer all questions.
2. Answer each question in 5 – 6 sentences.
3. Each question carries 3 marks.

Question 7.
Read the following paragraph and write your opinion.
“Even in the overall educational attainment, Telangana region remained behind Coastal Andhra region. The literacy rate in 2001 in Telangana region was 53% but in Andhra region, it was 63% During the same period, literacy rates were further less among the poor and socially deprived sections of Telangana region.
Answer:
The total number of colleges in Telangana region were 159 if Hyderabad is excluded only 160 but in Andhra region there are 181 colleges for the same number of youth. In a similar fashion, the grant for college education was about Rs. 93 crores in Tel angana region and it was Rs. 224 crores in Andhra region.

In addition to uneven development, the people of Telangana region also felt that they were being culturally discriminated against. After the merger, the language and culture of Coastal Andhra region was promoted as the ideal language and culture and those of Telangana region were treated as being backward. The history, culture and leaders of Telangana region were not adequately represented in the school textbooks. The folk dieties and festivals of Telangana region were being ignored while the festivals and Sanskritised cultural practices of the Coastal regions were given prominence. The films too depicted the people of Telangana region as backward arid crude.

Question 8.
Read the following paragraphs and answer the questions that follow.
In recent years, the central and state governments in India have been taking special steps to attract foreign companies to invest in India. Industrial zones, called Special Economic Zones (SEZs), are being set up. SEZs are to have world-class facilities: electricity, water, roads, transport, storage, recreational and educational facilities. Companies who set up production units in the SEZs do not have to pay taxes for an initial period of five years.

Government has also allowed flexibility in the labour laws to attract foreign investment. Instead of hiring workers on a regular basis, companies hire workers ‘flexibly’ for short periods when there is intense pressure of work. This is done to reduce the cost of labour for the company. However, foreign companies are demanding further flexibility in labour laws.
i) What are world class facilities?
ii) What are foreign companies demanding?
iii) Why did government allow flexibility in the labour laws?
iv) What are industrial zones called?
v) What are the state and central governments in India taking special steps for?
Answer:
i) Electricity, water, roads, transport, storage, recreational and educational facilities.
ii) Foreign companies are demanding further flexibility in labour laws.
iii) To attract foreign investment, government allowed flexibility in the labour laws.
iv) Industrial zones are. called Special Economic Zones.
v) In recent years, the central and state governments in India are taking special steps to attract foreign companies to invest in India.

Question 9.
Explain the organs of the UNO.
Answer:
The UNO works through six different organs. Each of these organs has specific functions like maintaining peace and security, improving education and health facilities, alleviating poverty, providing justice in the context of international crimes and so on. Some bodies responsible for these functions include International Court of Justice located in Hague; The World Health Organisation located at Geneva, The United Nations Educational, Scientific and Cultural Organisation functioning from Paris, and United Nations Children’s Emergency Fund functioning from New York.

Question 10.
Observe the following table and answer the questions given below.

Often we have listed only those parties that had more S or MPs
A) When was the first coalition government formed in India?
B) Which party was a partner of Government in all the three Coalition Governments?
C) To which State Trinamool Congress belongs to?
D) What is the difference between political parties becoming partners in the Coalition Governments and supporting the Governments?
Answer:
A) The first coalition government was formed in India in the year 1989.
B) Jammu and Kashmir National Conference (JKNC).
C) Trinamool Congress bêlongs to West Bengal state.
D) If the political parties become partners in the coalition governments they will frame the government and If they support the government they can withdraw their support arid collapse the government.

Question 11.
Give a brief account of history in census in India.
Answer:
In India, the first census was taken in 1872. The first complete census however was taken in 1881. Since then census have been regularly every tenth year India’s population as of 2011 is 12,10,193,422. These 1.21 billion people are unevenly distributed over our country’s vast land area of 3.28 million square km.

Question 12.
Study the following climograph and answer the questions that follow.

i) Where is Hyderabad located?
ii) What s the mean maximum temperature recorded in Hyderabad?
iii) In which month does it rain maximum in Hyderabad? .
iv) Which is the coldest month in Hyderabad?
Answer:
i) Hyderabad is located on the 17.4° North latitude and 78.5° East longitude.
ii) 38°C.
iii) In August.
iv) December.

Section-III
6 x 5 = 30 M

1. Answer all questions.
2. There is an internal choice for each question.
3. Answer each question In 8-10 sentences.
4. Each question carries 5 marks.

Question 13.
What would be the impact of availability of other food items and food security?
(OR)
Narmada Bachao Andolan-organised people’s movement in the Narmada Valley against dam Estimates its impact.
Answer:

1. It is said that there is a change in consumption pattern with people demanding more fruits, vegetables, milk, meat, poultry and fisheries.
2. This is a good sign for the consumers as well as producers.
3. Farmers producing foodgrains can go in for crop diversification in order to increase their incomes.
4. Farmers require support in terms of inputs and market opportunities for diversification to other food items.
5. Over the years, although there has been increase in production of other food items, it is not sufficient to meet the minimum dietary requirements.
6. The policies should aim at increasing food crop production and other food items simultaneously.
7. It will fill the gap and make food security more viable.

(OR)

1. Government proposed to build a series of major and minor dams across the Narmada River.
2. The leaders of the Narmada Bachao Andolan movement decided to oppose the very construction of the dams.
3. Initially, World Bank was ready to fund this project.
4. After intense protests, World Bank decided to withdraw its funding.
5. The government has built Sardar Sarovar Dam.
6. it forced everyone to think about the nature of development in the interest of poor or of the rich.
7. It forced governments to consider giving adequate and respectable compensation.
8. It combined many strands of movements like indigenous people, against neo-liberal policies, struggle of farmers who lost land to dams, urbanisation, industries, mines, and forests.

Question 14.
Observe the below table and answer the following questions.

Organized Sector	Unorganized Sector
1. An Employee in steel plant	Laundry
2. Job in Army	Tailoring Shop
3. Banking Sector	Beedi Making
4. Automobiles	Agarbathi Making
5. Chemicals	Khadi and village industries
6. Machine Tools	Hand paper Manufacturing
7. Engineering Goods	Candle Making
8. Textiles	Book Binding
9. TV Manufacturing	Potter
10. Computers	Beauty Parlours

i) What are the two main differences between the organized sector and the unorganized sector?
ii) Banking and Financial Institutions will come under which sector of economy?
iii) Write any four household activities that come under unorganized sector.
iv) Hand Paper manufacturing will come under which sector of economy? ,
v) All state and central government employees will come under which sector?
(OR)
Read the following paragraph and state your opinion on it.
Encroachment of public lands for cultivation is common. It results in more land being brought under cultivation at the expense of tree cover. Rampant felling of trees and mining activity is resulting in forest degradation, along with the destruction of the habitat of highly threatened flora and fauna. Inflows of groundwater depend on the tree cover in the catchment areas Inadequate tree cover leads to water run-off as surface flow without getting a chance to recharge the underground system. Moreover, this also causes flash floods. If we wish to be fair to both the rainfed and canal irrigated regions, we must adopt a different plan for water conservation and a system of sharing water.
Answer:
i) The two main differences are 1) Working hours, 2) Salaries.
ii) Banking and Financial Institutions will come under the organized sector of economy.
iii)

• Laundry,
• Tailoring Shop,
• Agarbathi Making,
• Beedi Making.

iv) Hand Paper manufacturing will come under unorganized sector of economy.
v) All state and central government employees will come under organized sector of economy.
(OR)

1. In recent years public land is brought under cultivation at the expense of tree cover.
2. The felling of trees and other mining activities threatened flora and fauna.
3. Inadequate free cover leads to water runoff.
4. There is less chance for recharging groundwater.
5. It causes flash floods.
6. The felling of trees threatened flora and fauna.
7. Hence we must be alert and adopt a different plan for water conservation.

Question 15.
What steps would you suggest to prevent these World Wars among the countries?
(OR)
Read the given paragraph and write your opinion.
The coastal environment of Nigeria has been disturbed because of reckless oil extraction by foreign oil companies. Oil spillage from oil wells has a major impact on the ecosystem.
Answer:
To prevent World Wars, all the countries on the earth must follow the following steps:

1. The countries one and all should give up their attitude of aggressive nationalism.
2. Every country should be ready to disarmament action of itself.
3. All the countries should promise to stop the usage of nuclear and chemical weapons.
4. Every country should respect the sovereignty and integrity of all other countries.
5. Every country, should pledge not to interfere in the internal affairs of other countries.
6. Countries must negotiate or go to International Court of Justice in case of disputes, but not to resort to wars.

(OR)
In my opinion oil spillage from oil wells has a major impact on the ecosystem large tracts of the mangrove forests, which are especially susceptible to oil have been destroyed. An estimated 5 – 10% of Nigerian mangrove ecosystems have been wiped out either by clearing or oil. Spills destroy crops and aquaculture through contamination of groundwater and soils. Drinking water is also frequently contaminated and a sheen of oil is visible in many local bodies of water.

If the drinking water is contaminated, even if no immediate health effects are apparent, it can cause in long-term cancer. Offshore spills, which are usually much greater in scale contaminate coastal environments and cause a decline in local fish production.

Question 16.
What are the recommendations of T.N. Seshan?
(OR)
How is the President of India under the Draft Constitution?
Answer:
Mr.T.N.Seshan was the one of the prominent election commissioners in India. He was recommended some reforms in the election commission.

1. 14-day time limit of campaigning after the date of withdrawal of nominations.
2. One candidate should not contest from more than two constituencies at a time.
3. If any candidate is punished for 2 years, he/she is barred from contesting elections for the next 6 years.
4. If the contesting candidate expires, the election shall be postponed not to be but abolished.
5. After completion of campaign time, sale of liquor shall be banned for 48 hours.

(OR)
Under the Draft Constitution, the President occupies the same position as the King under the English Constitution. He is the head of the State but not of the Executive. He represents the Nation but does not rule the Nation. He is the symbol of the nation. His place in the administration is that of a ceremonial device or a seal by which the nation’s decisions are made known. President of the United States is not bound to accept any advice tendered to him by any of his Secretaries. The President of the Indian Union will be generally bound by the advice of his Ministers. He can do nothing contrary to their advice nor can he do anything without their advice. The President of the Indian Union has no power to do so long as his Ministers command a majority in Parliament.

Question 17.
Write briefly about urbanization in India.
(OR)
Read the following paragraph and write your opinion.
For most rural communities, the link between the environment and the lives of the people is very strong. Access to environment serves a large number of their needs (like food, firewood, fodder, economically valuable articles, etc.,) which otherwise they would have to pay for. As they lose this access to environment either because of displacement or because the environment is destroyed and polluted, the poor are the greatest sufferers. The question of environment and sustainability is intimately connected to the issue of equity.
Answer:
In India, nearly 350 million, i.e., one-third of population lives in cities and towns. People have been increasingly taking up non agricultural work and living in cities and towns, this is called urbanisation. A considerable section of population in the 1950s lived in 5.6 lakh villages and there were only 5 cities that had a population of more than I million each and the number of cities with 1 lakh population was about 40. Today the number of villages has increased to 6.4 lakhs and about 850 million people live in these villages. There are more than 50 cities that have a population of 1 million.
(OR)
According to the paragraph given here, the rural people are attached with environment for their food and other cçmmodities. When there is a displacement they don’t have this facility of getting commodities. These poor people suffer a lot when the environment is destroyed and polluted.

My opinion on this paragraph is that many a time it is happening in many places. When the placement takes place, the forest dwellers have to face many problems. They don’t have sufficient food and land for cultivation. They don’t get loans as they are new to the money lenders of that place. The banks also don’t give loans as they have no collateral. They are forced to vacate the place and so they don’t have access to their commodities. They have to pay money for everything. Most of these people are very poor. Their relation between forest and livelihood is inseparable. The rural women go to forest areas or nature and collect their firewood and fodder for their regular use.

The government should think about the troubles of these people when they are asked to move from their living places. I am not opposing to construct dams and projects but the displacement should not lead to troubles. Alternate arrangements should be made keeping their problems in mind.

Question 18.
Locate the following in the political map of India.
a) Kashmir
b) Hyderabad
c) Junagadh
d) Bengal
e) Travancore
(OR)
Locate the following on the map of the world.
a) Nepal
b) Japan
c) Delhi
d) USA
e) Europe
Answer:

(or)

Part – B (Marks 20)

Instructions:

1. Answer all questions.
2. Choose the correct option from the given four Options and write the letter (A to B or C or D) in CAPITAL LETTER in the brackets.
3. Each question carries 1 mark.
4. Write the answers in the question paper itself.
5. Marks are not given to corrected, dismissed or erased answers.

Question 1.
The River Yamuna is the tributary of …………………… .( )
A) Mahanadi
B) Godavari
C) Ganges
D) Sindhu
Answer:
C) Ganges

Question 2.
In villages across India …………………. is the main production activity. ( )
A) Fishing
B) Farming
C) Pottery
D) None
Answer:
B) Farming

Question 3.
The topography of Telangana is ………………… . ( )
A) Plain
B) Plateau region
C) Coastal region
D) Mountainous region
Answer:
B) Plateau region

Question 4.
Removing barriers or restrictions set by the government is known as ( )
A) Liberalisation
B) Privatisation
C) Industrialisation
D) Nationalisation
Answer:
A) Liberalisation

Question 5.
The “Zionist Movement” was developed by ( )
A) Jews
B) Arabs
C) Nazis
D) Christians
Answer:
A) Jews

Question 6.
The significance of 1990s is ………………. . ( )
A) Coalition governments
B) Majority governments
C) Uniparty democracy
D) None of these
Answer:
A) Coalition governments

Question 7.
The …………………… shows that in the age group 0-5, the number of girls who survive is much lower than boys. ( )
A) census
B) directory
C) literacy rate
D) voter list
Answer:
A) census

Question 8.
Cyclone depressions coming from Mediterranean Sea called ………………… and cause low to moderate rainfall over northern India. ( )
A) Jet Stream
B) Easterly winds
C) Western Disturbances
D) Trade winds
Answer:
C) Western Disturbances

Question 9.
These cause regeneration of body tissues ( )
A) Carbohydrates
B) Proteins
C) Vitamins
D) Minerals
Answer:
B) Proteins

Question 10.
The famous speech ‘’I have a Dream’’ was given by ( )
A) George Washington
B) John E. Kennedy
C) George Bush
D) Martin Luther King Jr.
Answer:
D) Martin Luther King Jr.

Question 11.
The period of a financial year is from ………………… to …………………. . ( )
A) March April
B) April – March
C) February – March
D) March – February
Answer:
B) April – March

Question 12.
The Krishna is the second largest ……………………. flowing peninsular river. ( )
A) West
B) North
C) South
D) East
Answer:
D) East

Question 13.
The biggest nation …………………… could not be the member of League of Nations. ( )
A) France
B) U.K
C) USA
D) None
Answer:
B) U.K

Question 14.
At the turn of 20th century China was ruled by emperors of this dynasty. ( )
A) King
B) Manchu
C) Ziang
D) Tung
Answer:
B) Manchu

Question 15.
What is time duration for Indian general election? ( )
A) 4 years
B) 6 years
C) 2 years
D) 5 years
Answer:
D) 5 years

Question 16.
First President of independent India is: ( )
A) Nehru
B) Dr. Babu Rajendra Prasad
C) Radhakrishnan
C) Gandhiji
Answer:
B) Dr. Babu Rajendra Prasad

Question 17.
Professionals migrate from India to ……………………. . ( )
A) UAE
B) USA
C) Saudi Arabia
D) Kuwait
Answer:
C) Saudi Arabia

Question 18.
Not a primary sector activity ( )
A) Mining
B) Quarrying
C) Agriculture
D) Factory
Answer:
D) Factory

Question 19.
Separate electorates were implemented from ( )
A) 1919
B) 1908
C) 1907
D) 1909
Answer:
D) 1909

Question 20.
It is a material thing. ( )
A) Food
B) Freedom
C) Security
D) Discrimination
Answer:
A) Food

Thoroughly analyzing TS 10th Class Social Model Papers Set 3 with Solutions helps students identify their strengths and weaknesses.

TS 10th Class Social Model Paper Set 3 with Solutions

Time: 3.00 hours
Max. Marks:80

Instructions

1. Read the questions carefully, understand them, and answer.
2. Write the answers for the questions in Part – A in the answer sheet.
3. Attach the Map to Part – A answer sheet.
4. Attach Part – B to Part A answer sheet.
5. Part – A consists of I, II, and III Sections.
6. Write the answers clearly duly following the instructions given for each section.

Part-A (Marks 60)
Section – I (6 x 2 = 12M)

1. Answer all questions.
2. Answer each question in 3 -4 sentences.
3. Each question carries 2 marks.

Question 1.
Write about the S.R.C. and its work.
Answer:

1. In August 1953, the States Reorganisation Commission (SRC) was appointed with Fail All, K.M. Panikkar and Hridaynath Kunzru as members. They had to address the issue of formation of states on the basis of the linguistic principle.
2. On the basis of its report in 1956 the States of Reorganisation Act was passed in Parliament.
3. This led to the creation of 14 States and 6 Union Territories.
4. Only languages like Tamil or Telugu spoken by dominante were considered.

Question 2.
What are the important and urgent environmental issues before us now?
Answer:
The important and urgent environmental issues before us now are:

1. Soil erosion,
2. Depletion of groundwater,
3. Mining,
4. Industrial emissions,
5. Deforestation,
6. Global warming,
7. Pressure on grazing land,
8. Climate change.

Question 3.
Why did all Congress ministries resign in October 1939?
Answer:
The Congress was upset at the obstinacy of the British and decided to walk out of the provincial governments. All Congress ministers resigned in October 1939 after having come to power in 1937.

Question 4.
‘India cannot achieve the real and sustainable development unless the role of women is much fostered’. Assess the role of women in this regard.
Answer:

1. In India, half of its population are nothing but women.
2. But they are not producing half of the share in Gross Domestic Product.
3. This is mainly because many women are limited their potentialities only to their houses.
4. If all women are educated and allowed to work outside, this definitely turns the composition of GDP.

Question 5.
Write about Himadri (Greater Himalayas).
Answer:

1. Greater Himalayas (Himadri) are composed of snow and ice cover.’
2. This range is the most continuous consisting of the highest peaks with an average elevation of about 6100 mts above the mean sea level.
3. The glaciers of Himadri are the sources of perennial rivers.
4. Mt. Everest, Nandadevi, and Kanchenjunga are some of the important peaks located here.

Question 6.
Briefly explain the factors of production in dairy activity.
Answer:
The production factors of dairy activity are briefly described here:
Land: Own shed in the village.
Labour: Family labour, especially women to look after the buffaloes.
Physical capital: Buffaloes purchased at the cattle fair.
Working capital: Feed from their land, some medicines are purchased.

Section-II
6 x 3 = 18M

1. Answer all questions.
2. Answer each question in 5 – 6 sentences.
3. Each question carries 3 marks.

Question 7.
Read the following paragraph and interpret it.
“Rich people from the Coastal Andhra Pradesh outside the state began investing in a big way in purchasing land in Telangana, especially in and around Hyderabad city. While this brought investment into the region, the local people did not benefit much from this development and were in fact losing control over their own land to real estate developers”.
Answer:
According to the given paragraph, the people from Coastal Andhra and outside the state came to Hyderabad and invested for development. The investment came to Hyderabad but local people couldn’t get any sort of benefit. As real estate business improved in and around Hyderabad, the Telangana people lost their lands and the outsiders of Hyderabad and Telangana got no benefits.

The Telangana people have low literacy rate and so they are poor. They have no opportunities for jobs. Many rich people came to Hyderabad and they earned much money, Along with the rich people from Andhra and other states, ordinary people of their respective areas came to Hyderabad and settled in and around the city. A few companies brought people from entire villages and formed colonies on their names. Industrial areas are developed in Patancheru area. Thousands of watchmen, guards, salesboys, representatives, receptionists, and hoteliers are from Andhra area. There was a comment from Union leaders of Telangana, that the Telangana people are working as tea servers, attenders, and servers in the Andhra Companies.

There is another criticism that company benefits are for the rich company owners. Andhra people work in A/C rooms and menial jobs are given to local people. They are not permanent employees. Either they are contract or daily wage labourers. The Andhra people also humiliated the language and culture of Telangana. They exploited the resources of Telangana. In the names of Specially Economic Zones, the lands of local people were purchased and no jobs were given to them.

Now the two states are separated. They are developing by themselves. With new plans, they are moving forward. The two Chief Ministers declared that all the issues can be solved with negotiations. Irrespective of regions, rich and poor, all people in both the states should be developed. In a democracy, all people have equal rights. The landless Dalit families are being given three acres of land in Telangana. The deprived groups are also going to be developed.

Question 8.
Justify the statement -“Globalisation by connecting countries results in greater competition among producers”.
Answer:

1. Globalization is a major change that occurred across the globe in the late 20th century. This has political, cultural as well as economic dimensions.
2. An MNC does different operations related to its business at different locations across the globe.
3. An MNC is able to take advantage of cost benefits and also of easier access to important markets.
4. There is a greater choice before the consumers who now enjoy improved quality and lower prices for several products.
5. Competition is held between local producers and foreign companies.

Question 9.
How was the USA after the World War – II?
Answer:
The USA suffered less as the war was not fought on its territories. In fact, the Second World War helped the USA grow out of its economic misery caused by the Great Depression. Far from the theatres of war, the industries and agriculture of the USA prospered. This ensured full employment and high productivity in the US during the Second World War. In March 1945, the US President, Harry Truman, said, “We have emerged from this War the most powerful nation in the world – the most powerful nation, perhaps, in all history”.

Question 10.
a) Who was the leader of Congress government in 1980?
b) When was Indira Gandhi assassinated?
c) Who were the Prime Ministers of India that nm the coalition governments after emergency?
d) What was the reason for elections within 5 years in 1980?

End of Emergency and formation of Janata Party. Government under Moraiji Desai and Charan Singh.	1977
Formation of Congress Government led by Indira Gandhi.	1980
Formation of TDP	1982
Operation Blue Star and Assassination of Indira Gandhi.	1984
Gandhi accords with H.S. Longowal on Punjab and AASU on Assom	1985

Answer:
a) Indira Gandhi.
b) 1984.
c) Morarji Desai, Chowdary Charan Singh.
d) The elections after lifting up of emergency gave a chance to form non – Congress government at center.

This was a coalition government. Due to internal conflicts, the self-driven interest of parties, Prime Ministers were changed. As government has no majority in house, the house was dissolved and moved for elections to the Parliament in 1980.

Question 11.
“Overpopulation creates many problems”. Do you support this statement? Write in your own words.
Answer:

1. The number of non-working people increases.
2. Per capita income decreases with increase in population.
3. Production has to be increased to provide facilities like houses, educational institutions, health centres, transport, etc., to the increasing population.
4. There is a danger of occurrence of famine if sufficient food is not produced.

Question 12.
Write the effect of Jet Streams on India.
Answer:
The climate of India is also affected by the movement of upper air currents known as Jet Streams”. These are fast-flowing air currents in a narrow belt in the upper atmosphere above 12,000 m. The speed varies from about 110 km / h in summer to about 184 km / h in winter. Jet Streams causes the neighbouring atmosphere to cool. This cooling effect of the easterly Jet Stream causes rain from clouds.

Section-III
6 x 5 = 30 M

1. Answer all questions
2. There is an internal choice for each question.
3. Answer each question in 8-10 sentences.
4. Each question carries 5 marks.

Question 13.
Classify the food that we consume normally.
(OR)
Anti-nuclear and anti-war movements gained momentum during these days of intensive Cold War-Comment.
Answer:
Food is required by the body for all of its functions – for energy, growth and the capacity to remain healthy and fight illness. The food that we consume is normally classified as:

• Carbohydrates: That provide energy through wheat, flee, ragi, jowar, oils, sugar, fats, etc.
• Proteins: These help growth and regeneration of body tissues through beans, dais, meat, eggs, rice, wheat, etc.
• Vitamins: That provide protection and ensure the working of many vital systems of the body, through foods such as fruits, leafy vegetables, sprouts, unpolished rice, etc.
• Minerals: That are required in small quantities for many important functions such as iron for blood formation. This is provided through green leafy vegetables, ragi, etc.

(OR)

1. The 1970 and 1980 saw a new kind of movement. The movement against war and nuclear arms.
2. Superpowers like U.S.A, U.S.S.R, Britain, France began building arsenals of nuclear weapons justifying it as a means of deterring the other powers from using them.
3. The entire world was constantly in fear of the outbreak of another World War.
4. It was feared that if a war broke out and nuclear weapons were used then entire mankind would be wiped out.
5. Scientists and intellectuals across the world campaigned for abolishing nuclear weapons.
6. Massive protests swept across America against the Vietnam War.
7. Thus, the U.S. ended war with Vietnam, and this inspired peace movements across the world.

Question 14.
Read the given information and answer the following questions.
Narasimha works in a government office. He attends his office from 9.30 a.m.. to 5.30 p.m. He uses his motorbike to travel from this house to office which is about 5 kilometers away. He gets his salary regularly at the end of every month, deposited in his bank account. In addition to the salary, he also gets provident fund as per the rules laid down by the government. He also gets medical and other allowances. Narasimha does not go to office on Sundays. This is a paid holiday. When he joined work, he was given an appointment letter stating all the terms and conditions of work.

i) Who are employed in organised sector?
ii) Where does Narasimha works?
iii) When does Narasimha attend his office?
iv) When does he get his salary?
v) What is P.F.?
(OR)
Read the paragraph and answer the given questions.
Water flowing out via surface flows and groundwater: Imagine a region such as a village. Some amount ofwater would flow out of the village as surface flows through streams. During monsoon months, this surface flow would increase substantially. A portion of the rainfall percolates into the soil and travels to the underground strata and recharges the aquifers. Some of it flows into and becomes available for use through wells and borewells and a portion of it goes, into very deep aquifers that do not become available. Some of the underground water becomes part of flows that eventually appear in streams or rivers.
1) Some of the underground water becomes part of ………………… .
2) How does the rainfall recharge the aquifers?
3) Some of its flows into and becomes available for use through ……………… and ……………….. .
4) When would this surface flow increase? ‘
5) Give an example for surface flow.
Answer:
Narasimha.
Narasimha works in government office.
He attends his office from 9.30 a.m. to 5.30 p.m.
He gets his salary regularly at the end of every month.
Provident Fund.
(OR)

1. Flows.
2. A portion of the rainfall percolates into the soil and travels to the underground strata and recharges the aquifers.
3. Wells; borewells.
4. This surface flow would increase substantially during monsoon months.
5. Streams.

Question 15.
Which things led to the rise of Hitler and his Nazy Party? And what did the Nazis want?
(OR) .
“Environmental pollution is one of the important problems of the World countries”. Write any four causes and four consequences of the
Answer:

1. After the defeat of Germany at the end of the First World War in 1919, the victorious allies wanted to punish Germany for starting the war and also cripple it so that it cannot rise again.
2. For the Germans, the provisions enforced on them by the Treaty of Versailles were Slavish.
3. This created a reaction in Germany which led to the rise of Hitler and his Nazi Party.
4. They wanted to recover the territories lost by them in the Treaty of Versailles, restore
   German dominance over central Europe and end the restrictions on German armaments.
5. Germany reindustrialized itself furiously under the Nazis and developed a massive army and armament industry which could only be served by a war.

(OR)
The causes of environmental pollution:

1. The negligence in extraction of oil.
2. The destruction of mangrove forests leads to disturbed ecosystem.
3. Contaminated water by spillage of oil caused environmental pollution.
4. Lack of control over oil companies by the local government.

Consequences of environmental pollution:

1. The spillage of oil caused degradation of mangroves and contaminated coastal environments.
2. Spills destroy crops and aquaculture, through contamination of the groundwater and soils.
3. Drinking water also gets contaminated.
4. This causes long-term effects like cancer etc.

Question 16.
What are the challenges to free and fair Elections?
(OR)
The Constitution of India is the biggest written Constitution in the world. Elucidate.
Answer:
Elections in India are basically free and fair manner. The party that aims an election and forms government does so because people have chosen it over its rival.

Challenges to free and fair Elections:

1. Candidates and parties with a lot of money may not be sure of their victory.
2. Unfair advantage over smaller parties and independents.
3. Some candidates with criminal connections have been able to push others out of the electoral race.
4. Some families tend to dominate political parties.
5. Tickets are distributed to relatives from the same family.
6. Very often elections offer little choice to ordinary citizens.
7. Smaller parties and independent candidates suffer a huge disadvantage compared to bigger parties.
   That is why citizens, social activists, and organizations have been demanding reforms in our electoral system.

(OR)

1. The Constitution of India has many unique and outstanding features.
2. One among them is that it is the biggest written Constitution in the world.
3. Each and every detail of our Constitution was written extensively and in detail, making ‘the biggest written Constitution.
4. At the time of adoption of it in 1949, it had 395 articles and eight schedules.
5. The Drafting Committee took 2 years, 11 months, and 18 days to draft our Constitution.
6. At present, we have 470 articles and 12 schedules.
7. The documents can be changed to suit the needs of the people of the country from time to time.

Question 17.
Read the passage and answer the following questions.
Though there has been an increase in urbanisation, the necessity of providing basic infrastructure that can support this growth is missing. You require roads, drainage, electricity, water, and other public facilities. Government intervention is making some headway in improving the urban infrastructure particularly those associated with road transport. However, the provision of electricity water, and health infrastructure is not sufficient. For poorer people in the cities and towns, this situation is even worse.
i) What do we require?
ii) Which is not sufficient?
iii) For whom this situation is even worse?
iv) What is missing?
(OR)
What is the relationship between development and environmental issues?
Answer:
i) We require roads, drainage, electricity, water, and other public facilities.
ii) The provision of electricity, water, and health infrastructure is not sufficient.
iii) For poorer people in the cities and towns, this situation is even worse.
iv) Though there has been an increase in urbanization, the necessity of providing basic infrastructure that can support this growth is missing.
(OR)

1. Development has to be achieved at any cost.
2. Growth in GDP and modern industrial development are necessary, for raising the living.
3. Since, modern industrial and agricultural development are intensive in use of natural resources, including energy.
4. It is a sacrifice that has to be born for higher growth. Once high economic growth and prosperity is achieved, pollution and environmental degradation can be handled.

Question 18.
Locate the following in the map of India.
a) Chennai
b) Bengaluru
c) Delhi
d) Hyderabad
e) Kolkata
(OR)
Locate these places in the given map of world.
a) Russia
b) Bangladesh
c) Bandung
d) The country that started Second World War.
e) U.S.A
Answer:

(or)

Part – B (Marks 20)

Instructions:

1. Answer all questions.
2. Choose the correct option from the given four Options and write the letter (A to B or C or D) in CAPITAL LETTER In the brackets.
3. Each question carries 1 mark.
4. Write the answers in the question paper itself.
5. Marks are not given to corrected, dismissed or erased answers.

Question 1.
The longest canal in India is ( )
A) Rajiv Gandhi canal
B) Indira Gandhi canal
C) Mahatma Gandhi canal
D) Jawaharlal Nehru canal
Answer:
B) Indira Gandhi canal

Question 2.
Common non-farming activity in Rampur families ( )
A) Dairy activity
B) shops
C) Transport
D) Manufacture
Answer:
A) Dairy activity

Question 3.
There were ………………….. distinctive regions which spoke Telugu. ( )
A) 3
B) 4
C) 5
D) 2
Answer:
A) 3

Question 4.
The main destination of Indian indentured migrants is ………………… . ( )
A) Fiji
B) Malaya
C) Both (A) and (B)
D) None
Answer:
C) Both (A) and (B)

Question 5.
U.S.S.R put the first satellite Sputnik and the first human …………………… in space. ( )
A) Yuri Gagarin
B) Churchill
C) Harry Truman
D) William Greg
Answer:
A) Yuri Gagarin

Question 6.
The revolution with which Rajiv Gandhi’s name associated is ( )
A) Green revolution
B) White revolution
C) Blue revolution
D) Telecom revolution
Answer:
D) Telecom revolution

Question 7.
……………………. is a pivotal element in social studies. ( )
A) population
B) finance
C) vote
D) academic
Answer:
A) population

Question 8.
Bursting of monsoon in ……………………… . ( )
A) March
B) October
C) November
D) June
Answer:
D) June

Question 9.
……………………… need a diverse food basket and a balanced diet. ( )
A) Consumers
B) Investors
C) Buyers
D) Sellers
Answer:
A) Consumers

Question 10.
A major issue of 20th century was the end of the ( )
A) I World War
B) China War
C) French War
D) II World War
Answer:
D) II World War

Question 11.
This is not an example for an Intermediate good.
A) Petrol
B) Metals
C) Wood pulp
D) All of these
Answer:
D) All of these

Question 12.
The river Sindhu flows through
A) Pakistan
B) China
C) Delhi
D) Chennai
Answer:
A) Pakistan

Question 13.
Hitler decided to attack in ………………….. 1941. ( )
A) U.S.S.R
B) U.S.A
C) U.K
D) Italy
Answer:
C) U.K

Question 14.
The People’s Republic of China was based on the principles of ( )
A) New Democracy
B) Three principles
C) Four virtues
D) 4 great needs
Answer:
A) New Democracy

Question 15.
Which organ revises the voter’s list? ( )
A) Panchayat Raj
B) Mandai Parishat
C) Judiciary
D) Election Commission
Answer:
D) Election Commission

Question 16.
A Constituent Assembly was formed in …………………… following the election to the provincial as assemblies. ( )
A) 1947
B) 1949
C) 1956
D) 1946
Answer:
D) 1946

Question 17.
Delhi has grown in this manner ( )
A) Unplanned
B) Meticulously planned
C) Planned
D) Unknown
Answer:
A) Unplanned

Question 18.
“Right to life” is laid down in Article ( )
A) 15
B) 16
C) 21
D) 18
Answer:
C) 21

Question 19.
In the elections held in 1937, Congress won ……………….. provinces. ( )
A) 8 out of 11
B) 11 out of 11
C) 10 out of 12
D) 9 out of 11
Answer:
A) 8 out of 11

Question 20.
Schooling Revolution. ( )
A) Bihar
B) Andhra Pradesh
C) Himachal Pradesh
D) Punjab
Answer:
C) Himachal Pradesh

The strategic use of TS 10th Class Maths Model Papers Set 5 can significantly enhance a student’s problem-solving skills.

TS SSC Maths Model Paper Set 5 with Solutions

Time: 3 Hours
Maximum Marks: 80

General Instructions:

1. Answer all the questions under Part – A on a separate answer book.
2. Write the answers to the questions under Part – B on the question paper itself and attach it to the answer book of Part – A.

Part – A (60 Marks)
Section – I (6 × 2 = 12 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 1.
Is x (2x + 3) = x² + 5 a Quadratic equation ? Justify.
Solution:
x (2x + 3) = x² + 5
2x² + 3x = x² + 5
2x² + 3x – x² – 5 = 0
x² + 3x – 5 = 0
It is in the form of a x² + bx + c = 0.
So, the given equation is a quadratic equation.

Question 2.
Find the distance between the points (sec θ, 0) and (0, tan θ), when θ = 45°.
Solution:
Given points A(sec θ, 0) and B (0, tan θ) If θ = 45°,
then A(sec 45°, 0) and B (0, tan 45°)
A(√2,0) and B(0, 1)
∴ Distance between A, B
= \(\sqrt{\left(x_2-x_1\right)^2+\left(y_2-y_1\right)^2}\)
AB = \(\sqrt{(0-\sqrt{2})^2+(1-0)^2}\)
= \(\sqrt{2+1}\) = √3 units.
∴ Distance between (sec 45°, 0) and (0, tan 45°), when θ = 45° is √3 units

Question 3.
The solutions of the linear equation x + y = 8 are (1, 7), (2, 6) and (3, 5). The solutions of another linear equation 3x + 3y = 12 are (1, 3), (3, 1) and (0, 4). Plot these points on a graph sheet and draw lines.
Solution:

Question 4.
If the ratio of base radii of two right circular cylinder is 1 : 2 and the ratio of their heights is 2 : 3, then find the ratio of their volumes.
Solution:

∴ V₁ : V₂ = 1 : 6
∴ The ratio of the volumes of two cylinders = 1 : 6

Question 5.
In the given figure, if \(\frac{\mathrm{AD}}{\mathrm{DB}}\) = \(\frac{2}{3}\), AE = 6 cm and AC = 15 cm, then is DE || BC ? Justify.

Solution:
Given \(\frac{\mathrm{AD}}{\mathrm{DB}}\) = \(\frac{2}{3}\),
AE = 6, and AC =15
∴ EC = AC – AE = 15 – 6 = 9
Now \(\frac{\mathrm{AE}}{\mathrm{EC}}\) = \(\frac{6}{9}\) = \(\frac{2}{3}\)
\(\frac{\mathrm{AD}}{\mathrm{DB}}\) = \(\frac{\mathrm{AE}}{\mathrm{EC}}\)
(By converse of BPT)
∴ DE//BC.

Question 6.
A circle is inscribed in ΔABC touching the sides AB, BC and CA at points D, E and F respectively. If AD = 3 cm, BE = 4 cm, CF = 5 cm, then find the perimeter of the triangle.

Solution:
Given AD = 3 cm, BE = 4 cm, CF = 5 cm AD = AF = 3 cm
BD = BE = 4 cm [Lengths of tan gents are equal]
CF = AF = 5 cm
∴ AB = AD + BD = 3 + 4 = 7 cm
BC = BE + EC = 4 + 5 = 9 cm
AC = AF + FC = 3 + 5 = 8 cm
∴ Perimeter of the
ΔABC = 7 + 9 + 8= 24 cm

Section – II (6 × 3 = 18 Marks)

 

Note :

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 7.
Solve : 3x + 2y = 11 and 2x + 3y = 4.
Solution:
3x + 2y = 11 ……….. (1)
2x + 3y = 4 …………. (2)

∴ x = \(\frac{25}{5}\) = 5
Substitute x = 5 in (1)
3(5) + 2y = 11
15 + 2y = 11
2y = 11 – 15
2y = -4
y = \(\frac{-4}{2}\) = -2
∴ Solution x = 5, y = -2

Question 8.
3, 6, 9, 12, ….. is an arithmetic progression. Find the sum of first 20 terms of the progression.
Solution:
Given A.P 3, 6, 9, 12, ……….
a = 3, d = a₂ – a₁ = 6 – 3 = 3, n = 20 S_n = ?
S_n = \(\frac{n}{2}\)[2a + (n – 1)d]
∴ Sum of 20 terms
S₂₀ = \(\frac{20}{2}\) [2(3) + (20 – 1)3]
= 10 [6 + 57] = 10 × 63 = 630
∴ Sum of 20 terms S₂₀ = 630.

Question 9.
If A = {4, 8, 12, 16, 20},
B = {6, 12, 18, 24, 30}, then show that n(A∪B) = n(A) + n(B) – n(A∩B).
Solution:
A = {4, 8, 12, 16, 20},
B = {6, 12, 18, 24, 30}
n(A) = 5, n(B) = 5
A∪B = {4, 8, 12, 16, 20}∪{6, 12, 18, 24, 30} = {4, 6, 8, 12, 16, 18, 20, 24, 30}
n(A∪B) = 9
A∩B = {4, 8, 12, 16, 20} ∩{6, 12, 18, 24, 30} = {12}
n(A∩B) = 1
n(A) + n(B) – n(A∩B)
= 5 + 5 – 1 = 10 – 1 = 9 = n(A∩B)
∴ n(A∪B) = n(A) + n(B) – n(A∩B)

Question 10.
Write the formula for median of a grouped data and explain each term of it.
Solution:
Median = l + \(\left[\frac{\frac{n}{2}-c f}{f}\right]\) × h
where,
l – lower boundary of median class.
n – number of observations.
cf – cumulative frequency of class preceding the median class.
f – frequency of median class.
h – size of the median class.

Question 11.
A bag contains 5 red, 8 white, 4 green colour balls. If a ball is selected randomly from the bag, then find the probability that selected ball is (i) a green ball, (ii) not a white ball.
Solution:
Red colour balls n(R) = 5
White colour balls n(W) = 8
Green colour balls n(G) = 4
∴ Total balls = 17
∴ The number of all possible outcomes n(S) = 17

i) The number of favourable outcomes to selected a green ball n(G) = 4
∴ P(G) = \(\frac{\mathrm{n}(\mathrm{G})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{4}{17}\)

ii) The number of favourable outcomes to selected not a white ball
= n((\(\overline{\mathbf{W}}\))) = 5 + 4 = 9
P((\(\overline{\mathbf{W}}\))) = \(\frac{\mathrm{n}(\overline{\mathrm{W}})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{9}{17}\)

Question 12.
The statue stands on the top of a 3 metre tall pedestal. From a point on the ground angle of elevation of the top of the statue is 60° and from the same point the angle of elevation of the top of the pedestal is 45°. Find the height of the statue.
Solution:

BC = Height of the pedestal = 3m
DC = Height of the statue
In ΔABC,
Tan 45° = \(\frac{\mathrm{BC}}{\mathrm{AB}}\)
1 = \(\frac{3}{\mathrm{AB}}\)
∴ AB = 3 m
In ΔABD,
Tan 60° = \(\frac{\mathrm{BD}}{\mathrm{AB}}\) ⇒ 3 = \(\)
∴ BD = 3√3
3 + CD = 3
CD = 3√3 – 3
3(√3 – 1) = 3(1.732 – 1)
= 3 × 0.732 = 2.196 m
∴ Height of the statue CD = 2.196 m

Section – III (6 × 5 = 30 Marks)

Note :

1. Answer all the following questions.
2. In this section, every question has internal choice. Answer any one alternative.
3. Each question carries 5 marks.

Question 13.
A) Find the mode for the following data.

Solution:


= 30 + 2.5 = 32.5
∴ Mode of the given data = 32.5

(OR)

B) A man observes top of a tower at an angle of elevation of 30°. When he walked 40 m towards the tower, the angle of elevation is changed to 60° Find the height of the tower and dis-tance from the first observation point to the tower.
Solution:
Given height of the tower we will find BC = 40 m; CD = x m

From figure tan 30° = \(\frac{h}{x+40}\)
\(\frac{1}{\sqrt{3}}=\frac{h}{x+40}\)
x + 40 = √3h
x = √3h – 40 ………….. (1)
tan 60° = \(\frac{h}{x}\)
√3 = \(\frac{h}{\sqrt{3} h-40}\) [∵ from (1)]
3h – 40√3 = h
2h = 40√3 ⇒ h = 20√3 m
∴ Height of the tower = 20√3 m.
x = √3h – 40 = √3 × 20√3 – 40
= 3 × 20 -40 = 60 – 40 = 20m.
Distance from the first observation point to the tower.
BD = x + 40 = 20 + 40 = 60m.

Question 14.
A)Prove that √3 + √7 is an irrational number.
Solution:
Let us assume that √3 + √7 is a rational number.
Lut us √3 + √7 = \(\frac{\mathrm{a}}{\mathrm{b}}\), where a, b are coprimes and b ≠ 0
∴ √7 = \(\frac{\mathrm{a}}{\mathrm{b}}\) – √3
(√7)² = (\(\frac{\mathrm{a}}{\mathrm{b}}\) – √3)² (S.O.B.S)
7 = \(\frac{a^2}{b^2}\) – 2\(\frac{\mathrm{a}}{\mathrm{b}}\)√3 + 3
2\(\frac{\mathrm{a}}{\mathrm{b}}\)√3 = \(\frac{a^2}{b^2}\) + 3 – 7
2\(\frac{\mathrm{a}}{\mathrm{b}}\)√3 = \(\frac{a^2}{b^2}\) – 4
⇒ √3 = \(\frac{a^2-4 b^2}{b^2} \times \frac{b}{2 a}\)
∴ √3 = \(\frac{a^2-4 b^2}{2 a b}\)
Since, a, b are integers \(\frac{a^2-4 b^2}{2 a b}\) is a rational number.
So, √3 is also a rational number.
This contradicts the fact that √3 is irrational number.
Hence √3+ √7 is an irrational number.

(OR)

B) Prove that \(\frac{1+\sin \theta}{\cos \theta}+\frac{\cos \theta}{1+\sin \theta}\) = 2 sec θ.
Solution:
LHS = \(\frac{1+\sin \theta}{\cos \theta}+\frac{\cos \theta}{1+\sin \theta}\)


= 2 sec θ = RHS
∴ LHS = RHS

Question 15.
A) From the given Venn-diagram, write the sets A∪B, A∩B, A – B and B – A.

Solution:
i) A∪B = {2, 3, 4, 6, 8, 9, 10, 12, 15}
ii) A∩B = {6, 12}
iii) A – B = {2, 4, 8, 10}
iv) B – A = {3, 9, 15}

(OR)

B) A metallic vessel is in the shape of a right circular cylinder mounted over a hemisphere. The common diameter is 42 cm and the height of the cylindrical part is 21 cm. Find the capacity of the vessel. (Take π = \(\frac{22}{7}\))
Solution:
Common diameter of the cylinder and hemisphere d = 42 cm.
Common radii r = 21 cm
Height of the cylinder h = 21 cm.

∴ Capacity of the vessel = Volume of cylinder + Volume of Hemisphere.
= πr²h + \(\frac{2}{3}\)πr³
= \(\frac{22}{7}\)(21)² × 21 × \(\frac{2}{3}\) × \(\frac{22}{7}\) (21)³
= \(\frac{22}{7}\) × 21³[1 + \(\frac{2}{3}\)]
= \(\frac{22}{7}\) × 21³ × \(\frac{5}{3}\) = \(\frac{22 \times 21^3 \times 5}{21}\)
= 22 × 21² × 5 = 48,510 cm³
∴ Capacity of the vessel = 48,510 cm³

Question 16.
A) A train travels 360 km at a uniform speed. If the speed had been 5 km/h more, it would have taken 1 hour less for the same journey. Find the speed of the train.
Solution:
The distance travelled = 360 km
Let the speed of the train = x kmph
Time taken to complete a journey = \(\frac{\text { distance }}{\text { speed }}\)
By problem (\(\frac{360}{x}-\frac{360}{x+5}\)) = 1
360(\(\frac{1}{x}-\frac{1}{x+5}\)) = 1
360(\(\frac{x+5-x}{x(x+5)}\)) = 1
\(\frac{5}{x^2+5 x}=\frac{11}{360}\)
x² + 5x = 1800
x + 5x – 1800 = 0
x + 45x – 40x – 1800 = 0
x (x + 45) – 40 (x + 45) = 0
(x + 45) (x – 40) = 0
x + 45 = 0 (or) x – 40 = 0
x = -45 or x = + 40
But x can’t be negative.
∴ The speed of the train = 40 kmph

(OR)

B) Show that the distance of the points (5, 12), (7, 24) and (35, 12) from the origin are arranged in the ascending order, forms an arithmetic progression, Find the common difference of the progression.
Solution:
i) Distance of the point (5, 12) from the origin (0, 0)
∴ Distance of the point (x, y) from origin (0, 0) = \(\sqrt{x^2+y^2}\)
= \(\sqrt{5^2+12^2}\) = \(\sqrt{25+144}\) = \(\sqrt{169}\)
= 13 units.

ii) Distance of the point (7, 24) from the origin (0, 0)
= \(\sqrt{7^2+24^2}\) = \(\sqrt{49+576}\)
= \(\sqrt{625}\) = 25 units.

iii) Distance of the point (35, 12) from the origin (0, 0)
= \(\sqrt{35^2+12^2}\) = \(\sqrt{1225+144}\)
= \(\sqrt{1369}\) = 37 units.
Above distance in ascending order.
13, 25, 37
a₁, a₂, a₃
a₂ – a₁ = 25 – 13 = 12
a₃ – a₂ = 37 – 25 = 12
a₂ – a₁ = a₃ – a₂
∴ 13, 25, 37 are in an A.P
Common difference d = a₂ – a₁ = 12

Question 17.
A) Draw the graph of the polynomial P(x) = x² – x – 2 and find the zeroes of the polynomial from the graph.
Solution:
Let y = x² – x – 2

∴ Zeroes of the polynomial are 2, -1

(OR)

B) Draw the graph of x + y = 11 and x – y = 5. Find the solution of the pair of linear equations.
Solution:
Given x + y = 11 and x – y = 5
a₁x + b₁y + c₁ = 0; a₂x + b₂y + c₂ = 0
\(\frac{\mathrm{a}_1}{\mathrm{a}_2}\) = \(\frac{1}{1}\); \(\frac{\mathrm{b}_1}{\mathrm{b}_2}\) = \(\frac{1}{-1}\) ∴ \(\frac{\mathrm{a}_1}{\mathrm{a}_2}\) ≠ \(\frac{\mathrm{b}_1}{\mathrm{b}_2}\)
Hence the linear equations are consistent.

x + y = 11
x	y	(x, y)
0	11	(0, 11)
11	0	(11, 0)

x – y = 5
x	y	(x, y)
0	-5	(0, -5)
5	0	(5, 0)

∴ The lines intersecting at a point (8, 3)

Check Method: Intersect at a point (8, 3)
x + y = 11
8 + 3 = 11
11 = 11

x – y = 5
8 – 3 = 5
5 = 5

Question 18.
A) Draw a circle of radius 4 cm. from a point 9 cm away from it’s centre, construct a pair of tangents to the circle.

Solution:
OA = 4 cm, OP = 9 cm

Steps of construction:

1. Draw a circle with a radius 4 cm and “O” as centre.
2. Take a point such that OP = 9 cm. Join OP.
3. Draw a perpendicular bisector to OP which is bisects OP at M.
4. Draw a circle M as centre and PM as radius.
5. Let the circle intersects the given circle at ‘A’ and ‘B’,
6. Join P to A and B.
7. PA, PB are the required pair of tan-gents.

(OR)

B) The following table gives the marks obtained by 100 students in SA – 1 exams in Mathematics subject.
Draw Ogive graph of less than and greater than.

Solution:
The given data is to be changed to more than frequency distribution type.

Part – B (20 Marks)

Note :

1. Answer all the questions.
2. Each question carries 1 mark.
3. Answers are to be written in the Question paper only.
4. Marks will not be awarded in any case of over writing, rewriting or erased answers.

Note : Write the capital letters (A, B, C, D) showing the correct answer for the following questions in the brackets provided against them. (Marks : 20 × 1 = 20)

Question 1.
If A = {x : x is a day of a week}, then the value of n(A) is …………..
A) 6
B) 4
C) 5
D) 7
Answer:
D) 7

Question 2.
The degree erf the polynomial p(x) = 3x³ + 0.x⁴ + 0x – 2x² + 4 is …………
A) 1
B) 2
C) 3
D) 4
Answer:
C) 3

Question 3.
The midpoint of the line segment joining the points (3, 5), (x, 3) is (4, 4), then the value of x is …………..
A) 3
B) 4
C) 5
D) 7
Answer:
C) 5

Question 4.
The decimal form of \(\frac{3}{4}\) is …………….
A) 0.75
B) 0.50
C) 0.25
D) 0.075
Answer:
A) 0.75

Question 5.
If 3x + 2y = 6, 9x + ky = 7 represents two inconsistent equations, then the value of k is ………………
A) 5
B) 6
C) 8
D) 7
Answer:
B) 6

Question 6.
The total cost of 4 pencils and 5 note books is Rs.180. The linear equation representing this data is …………….
A) x + y = 180
B) 4x + 5y = 180
C) 9x + y = 180
D) 4x + 5y = 20
Answer:
B) 4x + 5y = 180

Question 7.
If the sum of first n terms of an arithmetic progression is \(\frac{n^2+n}{2}\), then the sum of first 10 terms is ………………….
A) 55
B) 110
C) 50
D) 45
Answer:
A) 55

Question 8.
The sum of the roots of the Quadratic equation 2x² + 6x + 4 = 0 is ………………
A) 3
B) -3
C) 2
D) -2
Answer:
B) -3

Question 9.
The nature of roots of the Quadratic equation x² + 10x + 24 = 0 is ……………
A) Real and distinct.
B) Real and equal.
C) No real roots.
D) One root is positive and the other root is negative.
Answer:
A) Real and distinct.

Question 10.
In an arithmetic progression n^th term is a_n = a + (n – 1) d. In this formula ‘d’ represents …………..
A) Number of terms
B) n^thterm
C) First term
D) Common difference
Answer:
D) Common difference

Question 11.
From the given Ogive curve, the value of the median of the data is …………….

A) 20
B) 25
C) 15
D) 30
Answer:
D) 30

Question 12.
The curved surface area of a right circular cone is CSA = πrl. In this ‘l’ represents ………………..
A) Height
B) Radius
C) Slant height
D) Diameter
Answer:
C) Slant height

Question 13.
Among the following, the value which is not possible for the probability of an event is …………….
A) \(\frac{1}{3}\)
B) 0.5
C) 25%
D) \(\frac{4}{3}\)
Answer:
D) \(\frac{4}{3}\)

Question 14.
In ΔABC, DE || BC, AD = 6 cm, DB = 2 cm, DE = 9 cm and BC = x cm, then the value of x ,is ……………..

A) 6
B) 8
C) 9
D) 12
Answer:
D) 12

Question 15.
In the given figure, PA and PB are tangents drawn to the circle and AB is a chord. If PA = 6 cm and ∠PAB = 60°, then the length of the chord AB is ……………..

A) 5 cm
B) 6 cm
C) 7 cm
D) 4 cm
Answer:
B) 6 cm

Question 16.
In ΔABC, ∠B = 90°, AB = 100 cm and BC = 100 √3 cm, then the value of angle θ is ……………

A) 30°
B) 60°
C) 45°
D) 25°
Answer:
B) 60°

Question 17.
If θ = 45°, then the value of \(\frac{1-\cos 2 \theta}{\sin 2 \theta}[latex] is …………….
A) 2
B) infinity
C) 1
D) 0
Answer:
C) 1

Question 18.
If one letter is selected randomly from the letters of the word “EXAMINATION”, then the probability of getting a vowel is …………..
A) [latex]\frac{5}{12}\)
B) \(\frac{6}{11}\)
C) \(\frac{4}{9}\)
D) \(\frac{5}{11}\)
Answer:
B) \(\frac{6}{11}\)

Question 19.
Which of the following is not true?
A) sin θ = \(\sqrt{1-\cos ^2 \theta}\)
B) sec²θ – tan²θ = 1
C) cos θ • cosec θ = 1
D) tan θ • cot θ = 1
Answer:
C) cos θ • cosec θ = 1

Question 20.
In the given figure, ‘O’ is the centre of the circle, OA and OB are radii. PA and PB are the tangents to the circle at points A and B. If ∠AOB = 120°, then the value of ∠APB is ……………

A) 60°
B) 30°
C) 90°
D) 45°
Answer:
A) 60°

Thoroughly analyzing TS 10th Class Social Model Papers Set 2 with Solutions helps students identify their strengths and weaknesses.

TS 10th Class Social Model Paper Set 2 with Solutions

Time:3.00 hrs
Max. Marks: 80

Instructions:

1. Read the questions carefully, understand them, and answer.
2. Write the answers for the questions in Part – A in the answer sheet.
3. Attach the Map to Part- A answer sheet.
4. Attach Part – B to Part A answer sheet.
5. Part – A consists of, II and III Sections.
6. Write the answers clearly duly following the instructions given for each section.

Part – A (Marks 60)
Section-I (6 x 2 = 12 M)

1. Answer all questions.
2. Answer each question in 3 -4 sentences.
3. Each question carries 2 marks.

Question 1.
Write about the first five-year plan.
Answer:
The first five-year plan focussed on agriculture and stressed on the need for increasing food production, development of transportation and communications and provision of social services.

Question 2.
What are the advantages of dams?
Answer:
The advantages of dams are:

1. Providing irrigation,
2. Generating hydroelectricity,
3. Controlling floods,
4. Conservation of soil fertility,
5. Promoting tourism.

Question 3.
What is the significance of the year 1946?
Answer:
The year 1946 was a year of strikes and work stoppages in factories and mills in many parts of the country. CPI and the Socialist parties were active in these movements. The countryside was also on the boil.

Question 4.
Write about
a) Life expectancy at birth
b) Mean ‘ears of schooling
Answer:
a) Life expectancy at birth: Denotes the average expected length of life of a person at the time of birth.
b) Mean years of schooling: Average number of completed years of education of a country’s population aged 25 years and older, excluding years spent repeating individual grades.

Question 5.
Observe the following pictures and describe them.

Answer:
A) Nicobar pigeons live in Nicobar Islands.
B)

1. They are called coral reefs.
2. Coral is often used in jewelry
3. They also help marine creatures.

Question 6.
How is land distributed in Rampur?
Answer:
In Rampur, about /3rd i.e., 150 families are landless. There are 60 families are medium and large farmers, who cultivate 2 hectares of land. 240 Families cultivate small plots of land less than 2 hectares in size.

Section-II
6 x 3 = 18 M

1. Answer all questions.
2. Answer each question in 5 – 6 sentences.
3. Each question carries 3 marks.

Question 7.
Read the following information and answer the questions.
Total Cropped Area – in million hectares

Region	1955-56	2006-07	Growth %
Andhra Region	4.2	5.3	20
Telangana Region	4.8	5	5

Net irrigated area in lakh hectares

Region	1955-56	2006-07	Growth %
Andhra Region	17	23	135
Telangana Region	7	19	257

Net irrigated area in lakh hectares 2007

Region	Wells	Canals	Tanks	Others
Andhra Region	5	13	2.5	2.5
Telangana Region	14	2.5	2	0.5

i) What is the main irrigation method of Telangana region?
Answer:
In Telangana, wells are dug and used as main irrigation method in 14 lakh hectares.

ii) Which region showed a less net irrigated area?
Answer:
Telangana showed a less net irrigated area of 19 lakh hectares when compared with Andhra’s net irrigated area of 23 lakh hectares.

iii) What type of irrigation is followed mainly in Andhra?
Answer:
Canal irrigation is followed mainly in Andhra. Canal irrigation is carried out in 13 lakh hectares.

iv) What percentage of’ increase was the total cropped area recorded in both the regions?
Answer:
Andhra region recorded an increase of 20% in total cropped area. And Telangana region recorded an increase of only 5%.

v) Which region showed a higher growth rate of net irrigated area? And how much?
Answer:
Telangana region recorded higher growth rate in net irrigated area. And the growth rate was 257%. Net irrigated area rose from 7 lakh hectares to 18 lakh hectares.

Question 8.
Read the following paragraph and answer the question that follows.
We read earlier that the liberalisation of foreign trade and investment in India was supported by some very powerful international organizations. These organizations believe that barriers to foreign trade and investment are harmful. Trade between countries should be ‘free’ without any barriers. World Trade Organisation (WTO) is one such organisation whose aim is to liberalise international trade. Started at the initiative of the developed countries, WTO establishes rules regarding international trade and sees that these rules are obeyed. Nearly 164 countries of the world are currently members of the WTO.
Q) What is the WTO?
Answer:
The WTO is the only global international organisation dealing with the rules of trade between nations. The goal of WTO is to help producers of goods and services, exporters and importers conduct their business. Nearly 164 countries of the world are currently members of the WTO (As on 29-7-2016).

Question 9.
Write about the military alliances.
Answer:
Both the USA and the USSR were in the possession of nuclear weapons but knew very well neither would be the winner in a nuclear war. Yet, they formed military and strategic alliances – the West formalised its alliances in an organisation known as North Atlantic Treaty Organisation (NATO) in 1949. To counter this, Communist nations made similar alliances and signed the Warsaw Pact. In addition to this, the US established regional military and strategic alliances like South East Asian Treaty Organisation (SEATO) and Central Treaty Organization (CENTO).

Question 10.
What was meant by liberalisation?
Answer:

1. Liberalisation means a lot of things put together like drastic reduction of government expenditure, reducing restrictions and taxes on imports, etc.
2. It proved for reducing restrictions on foreign investments in India and allowed foreign countries to set up companies in India.
3. It is required to the opening of many sectors of the economy to private investors.
4. It brought in foreign goods and Indian businessmen were forced to compete with them.
5. It had many positive and negative impacts on India.

Question 11.
Describe the categories of working population.
Answer:
The Census of India groups the working population into four categories. Cultivators are farmers, who farm or supervise the land that they own or take on rent. Agricultural labourers are those who work on another’s farm for wages in cash or kind. Workers in household industries would be those who are manufacturing or repairing some product at home such as dehusking of paddy, bidi workers, potters, weavers, repair of footwear, manufacture of toys, matches, etc. Other workers would be those who are employed ¡n factories, trading, casual labour and all other occupations.

Question 12.
explain the land and water relationship.
Answer:
The amount of sunlight that is first absorbed and then radiated back or directly reflected depends on the nature of the surface. Darker areas, such as heavily vegetated regions, tend to be good absorbers; lighter areas such as snow and ice-covered regions tend to be good reflectors. The ocean absorbs and loses heat more slowly than land. This affects climate in many ways.

Section – III
6 x 5 = 30 M

1. Answer alt questions.
2. There is an internal choice for each question.
3. Answer each question in 8-10 sentences.
4. Each question carries 5 marks.

Question 13.
What are the salient features of food security bill?
(OR)
‘Denial of equal rights was the root cause of many social movements”. Elucidate.
Answer:

1. The Indian government came out with a new law in 2013 called the ‘National Food Security Act’ to legalise people’s Right to Food.
2. Every person of low-income family is entitled to 5 kgs of foodgrains per month at subsidised rates.
3. The poorest families are entitled to 35 kgs of food grains.
4. For a few years, the central government supply rice, wheat and millets for ‘ ₹ 3 ₹ 2, and ₹ 1 respectively.
5. If government is not able to arrange food grains, it will give cash for the people to buy food grains.
6. Providing free cooked meals for pregnant women, lactating mothers, children aged 1-6 coming to Anganwadis and mid-day meals for children aged 6 -14 years in schools are also the features of the bill.

(OR)

1. Many social movements have fought for equal rights for the deprived classes.
2. Black Americans suffered from segregation in schools, buses and in public places.
3. They were also discriminated in appointments housing and even voting rights.
4. Many Eastern European countries did not allow free multiparty elections, free uncensored press, freedom of expression, movement of ordinary people.
5. Many movements for equal treatment of women, equal rights, wages, and opportunities, justice are also organised.
6. Thus, we can say that denial of equal rights was the root cause of many social movements.

Question 14.
Read the para and answer the given questions. Rajeshwari is working as a construction worker. She goes for work at 7 a.m. and returns home at 7 p.m. She travels about 8 to 10 kilometers daily for work by bus. Construction workers get one hour lunch break between 1 pm and 2 p.m. She gets, work only for 10 to 12 days a month. In the remaining days, she has no work, and she does not get any wage. She gets 150 per day as wages. Mostly, she is paid the wages on the spot in the evening. When she works for three or four days at the same day, she is paid after the work is completed.

She gets more work from February to June. July to January is unseasonal. Rajeshwari is a member of a Self Help Group
in her locality. The government will pay some compensation in case of death or major injury while she is at work. There is no help from the government for the treatment in accidents while working. She is also a part of a group that works under a mason. There are 6 to 10 workers under each mason.
i) Where is Rajeshwari working?
ii) What are the working hours of Rajeshwari?
iii) How much money does she earn every day?
iv) Which months does Rajeshwari get more work?
v) In which group Rajeshwari is a member?
(OR)
Write about peninsular rivers.
Answer:
i) Rajeshwari is working at a construction worker.
ii) She works from 7 a.m. to 7 p.m. every day.
iii) She earns ‘ ₹ 150 every day.
iv) She gets more work from February to June.
v) Rajeshwari is a member of Self Help Group in her locality.
(OR)
1. The Western Ghats are the water divide between the major peninsular rivers, discharging their water in the Bay of Bengal and as small rivulets joining the Arabian Sea.
2. Most of the major peninsular rivers except Narmada and Tapti flow from West to East.
3. The Chambal, Sind, Betwa, Ken, and Son originating in the northern part of the peninsular belongs to the Ganga river system.
4. The other major river systems of the peninsular drainàge are the Mahanadi, the Godavari, the Krishna, and the Cauveri.
5. Peninsular rivers are characterized by fixed course, absence of meanders, and largely perennial flow of water.

Question 15.
How far were secret alliances the cause for the World War — I ? (Or) “Secret alliances laid the first road map to world war – I”. Comment.
(OR)
Why does the oil spillage from oil wells have a major impact on the ecosystem?
Answer:

1. After defeating France in 1870, Bismarck, the German Chancellor decided to isolate it.
2. To achieve this end, he entered into secret alliances with Austria and Italy thus formed ‘Triple Alliance’ in 1882.
3. The French broke their isolation by striking a mutual alliance with Russia.
4. Again they resolved their irritants with Britain.
5. Thus Russia, France, and Britain formed their Triple Entente in 1907.
6. These European countries formed secret alliances to safeguard their freedom, economic and commercial interests.
7. These secret alliances made European powers jealous and suspicious of one another.
8. Instead of real peace, these alliances created an atmosphere of fear and armed peace in Europe.
9. Thus we can say secret alliances were a justifiable cause for the World War I.

(OR)

1. Oil spillage from oil wells has a major impact on the ecosystem.
2. Large tracts of the mangrove forests, which are especially susceptible to oil (this is mainly because it is stored in the soil and re-released annually with inundation), have been destroyed.
3. As estimated 5-10% of Nigerian mangrove ecosystems have been wiped out either by clearing or oil.
4. Spills destroy crops and aquaculture through contamination of the groundwater and soils.
5. Drinking water is also frequently contaminated and a sheen of oil is visible in many local water bodies.
6. Offshore spills, which are usually much greater in scale, contaminate coastal environment and cause a decline in local fish production.

Question 16.
What makes an election democratic?
(OR)
Describe the features of Indian Federalism.
Answer:
Elections can be held in many ways. All the democratic countries held elections, but really some countries only conducted in fair manner.
Minimum conditions of a democratic election:

1. Everyone should be able to choose.
2. Everyone should have one vote one person and one value.
3. Parties and candidates should be free contest elections and should offer some real choice to the voters.
4. The choice should be offered at regular intervals.
5. The candidate preferred by the people should get elected.
6. Elections should be conducted in free and fair manner.

(OR)
The features of Indian Federalism:

1. Supremacy of the Constitution: The suprçmacy of the Constitution means that both the Union and State governments shall operate within the limits set by the Constitution.
2. Written constitution: The constitution of India is the largest and most elaborate one, which discusses on several issues.
3. Division of powers: The Indian constitution clearly described administrative powers into three lists viz The Union List, The State List, and The Concurrent List.
4. Supremacy of the Judiciary: As per the Constitution of India, Judiciary is Independent and supreme. It can declare a contrivances law as unconstitutional.

Question 17.
What are the problems of overpopulation?
(OR)
What is Organic fanning?
Answer:
The problems of overpopulation are:

1. Resource crisis
2. Water and Energy crisis
3. Traffic problems
4. Inflation
5. Pollution problems
6. Unemployment crisis
7. Slum areas increases
8. Dearth of housing
9. Anti-social activities
10. Rise of poverty levels
11. Corruption, Mafia
12. Violence extends etc.

(OR)

1. Organic farming is to forego the use of chemical fertilizers and pesticides.
2. It rely mainly on natural techniques such as crop rotation, natural compost, and biological pest control in farming.
3. Farms can be bio-diverse.
4. Farmers can produce a variety of crops.
5. Organic farming use local resources like on-farm biological process.
6. It protects the environment from pollution.

Question 18.
Locate the following on the physical map of India on the raised relief Map:
1) Malwa Plateau
2) Bundelkhand
3) Bhagelkhand
4) Rajmahal Hills
5) Chotanagpur plateau
(OR)
Locate the following in the map of the world.
1) Germany
2) Italy
3) Austria
4) U.S.A
5) Britain
Answer:

or

Part – B (Marks 20)

Instructions:

1. Answer all questions.
2. Choose the correct option from the given four Options and write the letter (A to B or C or D) in CAPITAL LETTER in the brackets.
3. Each question carries 1 mark.
4. Write the answers in the question paper itself.
5. Marks are not given to corrected, dismissed or erased answers.

Question 1.
……………….. is the highest peak in South India. ( )
A) Dodabetta
B) Anaimudi
C) Everest
D) Annamalai Hills
Answer:
B) Anaimudi

Question 2.
All human efforts put In production is ( )
A) casual labour
B) manual labour
C) capital
D) labour
Answer:
D) labour

Question 3.
Nationalists from Coastal Andhra also supported this Telangana movement in ( )
A) 1960s
B) 1970s
C) 1940s
D) 1980s
Answer:
C) 1940s

Question 4.
This is playing vital role in deciding the value of a currency. ( )
A) Government
B) Reserve Bank of India
C) Market forces
D) People
Answer:
C) Market forces

Question 5.
World Health Organisation is located at ( )
A) Hague
B) New York
C) Geneva
D) Paris
Answer:
C) Geneva

Question 6.
This party led anti-Hindi agitation in South. ( )
A) AIADMK
B) DMK
C) TDP
D) TRS
Answer:
B) DMK

Question 7.
The idea of equality is also based on the ………………. . ( )
A) country
B) religion
C) region
D) people
Answer:
A) country

Question 8.
The least temperature and rainfall is recorded at ………………… . ( )
A) Leh
B) Delhi
C) Chennai
D) Jaipur
Answer:
A) Leh

Question 9.
Public Distribution System is associated with ( )
A) Ration shops
B) Co-operative stores
C) Super Bazaars
D) General stores
Answer:
A) Ration shops

Question 10.
Alcohol prohibition in Andhra Pradesh was imposed in ( )
A) 1991
B) 1992
C) 1993
D) 1995
Answer:
D) 1995

Question 11.
This is not an example for a final good. ( )
A) Car
B) Notebook
C) TV
D) Tyre
Answer:
D) Tyre

Question 12.
Second largest peninsular river is ( )
A) Krishna
B) Mahanadi
C) Godavari
D) Cauvery
Answer:
A) Krishna

Question 13.
Mussolini belonged to ‘( )
A) Italy
B) Germany
C) France
D) Russia
Answer:
A) Italy

Question 14.
Nigeria was the colony of this country. ( )
A) Britain
B) France
C) Germany
D) Spain
Answer:
A) Britain

Question 15.
In which part of the constitution Election Commission’s functions are mentioned ( )
A) 14
B) 16
C) 15
D) 20
Answer:
C) 15

Question 16.
The Constitution of India is ( )
A) Flexible
B) Only women
C) Partly flexible and Partly rigid
D) Discrimination on women
Answer:
C) Partly flexible and Partly rigid

Question 17.
The largest city in population is ( )
A) Chennai
B) Kolkata
C) Delhi
D) Mumbai
Answer:
D) Mumbai

Question 18.
“Chipko Andolan” started in ( )
A) Uttarakhand
B) Kerala
C) Tripura
D) U.P.
Answer:
A) Uttarakhand

19. The Second World War was started in ( )
A) 1944
B) 1938
C) 1937
D) 1939
Answer:
D) 1939

Question 20.
Gender bias. ( )
A) Men and women
B) Rigid
C) Only men
D) None of these
Answer:
D) None of these.

Thoroughly analyzing TS 10th Class Social Model Papers Set 1 with Solutions helps students identify their strengths and weaknesses.

TS 10th Class Social Model Paper Set 1 with Solutions

Time: 3.00 hrs.
Max. Marks: 80

Instructions:

1. Read the questions carefully, understand them, and answer,
2. Write the answers for the questions in Part – A in the answer sheet.
3. Attach the Map to Part – A answer sheet.
4. Attach Part – B to Part A answer sheet.
5. Part – A consists of I, II, and III Sections.
6. Write the answers clearly duly following the Instructions given for each section.

Part – A (60 Marks)
Section – I (6 x 2 = 12 M)

1. Answer all questions.
2. Answer each question in 3-4 sentences.
3. Each question carries 2 marks.

Question 1.
Identify the differences between Bhabar and Terai.
Answer:

Bhabar	Terai
1) Bhabar comprises pebble-studded rocks in the shape of porous beds.	1) Terai is composed of comparatively finner alluvium and is covered by forest.
2) It is 8-16 kms wide.	2) It is 20-30 kms wide
3) Due to porosity of the rocks,the streams disappear and flow underground.	3) The underground streams of the Bhabar reemerge on the surface and give birth to marshy area.
4) This region is not much suitable for agriculture.	4) Most parts of the Terai area are suitable for agriculture.

Question 2.
Why did the League of Nations fail?
Answer:
Failures of the League of Nations: Though the League was an international organisation, it failed in many issues.

1. It could not bring out the disarmament.
2. The League failed in controlling the evil plans of Hitler.
3. The League did not have armed forces of its own.
4. Rise of dictatorships in Germany and Italy contributed to its failure.
5. Some countries joined late and some countries which joined the League withdrew from it.

Question 3.
Write any two slogans to create awareness on the importance of voting.
Answer:
Slogans:

1. If you don’t cast your vote now, a few people with a lot of power and money in their hands will control your life for the next few years.
2. Your vote, Your voice.
3. Vote, It’s your Right and Responsibility.
4. Your vote can change the way things are.
5. Voting is your Right. Try to do it Right.

Question 4.
Write suggestions for the improvement of Indian foreign policy.
Answer:
Suggestions:

1. Prioritizing an integrated neighbourhood.
2. Our country should maintain co operation with neighbours on disaster management.
3. We should maintain our foreign policy on the Gandhian principles of peace and non-violence.
4. Friendship should be enhanced through cultural exchange. Thus it built bridges of Friendship through trade, sports, films, tourism, etc.

Question 5.
Draw the outline map of Telangana.
Answer:

Question 6.
Observe the given table below and answer the following questions.

State	IMR per 1000 (2016)	Literacy Rate (%) (2011)	Net Attendance Ratio for Secondary Stage (2013-14)
Haryana	33	77	61
Himachal Pradesh	25	84	67
Bihar	38	64	43

a) As per the above table, which state is in a better position in terms of IMR, Literacy rate, and Net attendance ratio?
b) Give one reason, why Bihar has a low literacy rate?
Answer:
a) Himachal Pradesh is in a better position in terms of IMR, Literacy rate, and Net attendance ratio.
b)

1. The spending of Bihar Government on education has been very low.
2. Teachers are very few and resources are not available.
3. Not much job opportunities are encouraged to women

Section – II
6 x 3 = 18 M

1. Answer all questions.
2. Answer each question In 5-6 sentences.
3. Each question carries 3 marks.

Question 7.
Read the paragraph and interpret.
We often hear people talk of population growth in alarming tones. These people are often literate and talk about others not benefitting because there are many people who have to share very few resources.
Answer:
According to the given paragraph the population growth affects many ways. People should aware of this and the literate people talk about the benefits share of resources is not balancing. Very few people are using more resources whereas many people are using less resources. Countries like USA are using more natural resources though its population is less than 5% of the world population. In India, it is less than 16% of the world population is using less natural resources.

In India population in steadily increasing. If population increases in this way, one day India would be the first in world population. Population is not a curse to the country development, it is a boon for the development of country. People in any country can be divided into three categories. They are skilled, semi-skilled, and unskilled.

The Government has to utilise the services of the skilled for the nation’s development. The semi-skilled should be made skilled. the unskilled should be provided with some training and so they would be doing some sort of productive work which would be strengthening GP. Equal distribution of resources should be the target of the government. The underdeveloped countries should focus on improving qualities of the workforce. So population is not a problem. It is a boon.

Question 8.
What were the problems faced by the people during the partition of India?
Answer:

1. With the creation of Muslim nation, Pakistan, a painful and imaginable situation arose before many people.
2. Most of the Hindus living on one side of the newly drawn border became insecure and felt forced to leave and vice-versa.
3. They felt hatred against each other for being forced to move out of their homes, villages and cities.
4. Around 1.5 crore people, both Hindu and Muslim, were displaced.
5. They killed looted and burnt.
6. Between 2 to 5 lakh people both Muslim and Hindu were killed.
7. They became refugees, lived in relief camps, moved out on trains to find new homes.

Question 9.
Prepare a pamphlet on the prohibition of Liquor.
Answer:
Prohibition of liquor
Liquor consumption is actually the most bad for human body. Nowadays we see many of the people having addiction towards such unusual things. But we have to stop doing it. I don’t say, that it has only bad effects but should be consumed in a limit. It affects so badly on our lives and also causes to different cancers. This consumption is like killing ourselves without hands.

The directive principles to state policy in the Constitution of India state that the state shall endeavour to bring about prohibition of the consumption except for medicinal purposes of intoxicating drinks and drugs which are injurious to health. But I wish all our country means to stop doing it. Please stop liquor consumption, If prohibition implemented it led to lower rates of drinking among men, as well as a decreased incidence of violence against women.

Question 10.
What is the role of technology in Globalization?
Answer:

1. Rapid growth of technology has been one major factor that has stimulated the globalisation process.
2. The developments in information and communication technology have even more remarkable and rapid.
3. Telecommunication facilities like telegraph, telephone, mobile phones, and fax are used to contact one another around the world to access information instantly and to communicate from remote areas.
4. It is the globalisation which has created new opportunities for companies providing services like data entry, accounting other administrative tasks are now being done cheaply in India and are exported to the developed countries.

Question 11.
Observe the given map and answer the questions a, b, a c.

a) Name the shaded area in the map.
b) Name the state shown with lines.
c) Write any one eastern border sharing country with India.
Answer:
a) The area is Ganga river drainage area of the states Uttarakhand, Uttar Pradesh, Bihar, West Bengal, and the Ganga plain area also.
b) Karnataka state.
c) Myanmar and Bangladesh.

Question 12.
Observe the given table and analyse it.
Total cropped Area – in million hectares.

Region	1955-56	2006-2007	growth %
Andhra Region	4.2	5.3	20
Telangana Region	4.8	5	5

Answer:
The above table explained the total cropped area in Telangana Region and Andhra Region in the years of 1955-56 and 2006-07 and its growth also. In 1955-56 in Andhra Region, only the crops are grown 4.2 million hectares only. But in Telangana Region 4.8 million hectares area used.

In 2006-07 in Andhra Region the total cropped area increases from 4.2 millions to 5.3 millions. But in Telangana just 0.2 millions hectares only brought under cultivation. But in Andhra Region 1.1 million hectares land brought under cultivation.
The reasons for low cropped area in Telangana are:

1. Changing weather conditions creating a situation of severe drought,
2. lack of groundwater irrigation sources,
3. digging borewells for water and failures,
4. extreme indebtedness,
5. insufficient public investment for agrarian development and inadequate access to institutional credit apart frequent droughts and floods.

Section – III
6 x 5 = 30 M

1. Answer all questions.
2. There is an internal choice for each question.
3. Answer each question in 8-10 sentences.
4. Bach’s question carries 5 marks.

Question 13.
Classify the Himalayan river system and write about any one of the river systems.
(OR)
What are the reasons for the rise of regional parties after 1967?
Answer:
The Himalayan Rivers belong to the three principal system:

1. The Indus
2. The Ganga and
3. The Brahmaputra

These rivers originate from almost the same region within few kilometers of each other separated by water divides. The Himalayan Rivers are perennial.
The Indus system:

1. The Indus originates in the northern slopes of the Kailash range in Tibet near Lake Mana Sarovar.
2. It enters Indian Territory in Jammu and Kashmir (Ladakh).
3. The main tributaries of the Indus in India are Jhclum, Chenab, Ravi, Beas and Sutlej.
4. They covers Jammu and Kashmir, Punjab and Himachal Pradesh states of India.

(OR)
The main reasons for the rise of regional parties after 1967 are historical reasons, cultural reasons and linguistic reasons.

1. To protect the regional interest and aspirations of the people.
2. Protecting of their natural resources without exploiting by others.
3. A political desire for greater regional autonomy of states.
4. Failure of national politics to meet the regional aspirations.
5. Centralising tendencies of the Congress party.
6. Economic disparities and regionál imbalances in development.
7. The frequent change of Chief Ministers by the Central Congress party.
8. The local people felt that they would lose their cultural roots and soon be outnumbered by the ‘outsiders.
9. They want to protect their language etc.

Question 14.
What are the differences between the organised sector and the unorganised sector?
(OR)
How did the main features of the Gentlemen’s Agreement become a point of distrust between two regions of Telangana and Andhra?
Answer:

Organised Sector Centre	Unorganised Sector Centre
1) It has some formal processes and procedures.	1) It has small and scattered units largely outside the control of government.
2) It gives security of employment.	2) Rules and regulations are not enforced here.
3) It has fixed number of work hours, overtime will be paid by the employer.	3) Jobs here are low-paid and non regular.
4) It provides paid leave, payment during holidays, provident fund, medical benefits, etc.	4) There is no provision of overtime, paid leave, holidays, leave due to sickness etc.
5) It also ensures pensions.	5) When there is less work, some people are asked to leave.
6) It has workers of government, companies and large establishment.	6) A lot also depends on the whims of the employer or changes in the market situation.

(OR)
Introduction: On the initiative of the Union Government, the leaders of both sides signed on an agreement on 20th February 1958 which was known as Gentleman’s Agreement.

Main points: Main points in the agreement were

1. Expenditure on Administration was to be borne proportionately by the two regions and surplus revenue from Telangana region would be spent only for the development of Telangana.
2. The existing educational facilities in Telangana would be reserved for the students of Telangana only.
3. It was agreed to continue the Mitiki ria les.
4. It was agreed to set up a Regional Council to oversee the needs and development of Telangana.
5. Sale of agricultural land in Telangana would be controlled by the Regional Cocuncil.
6. The Andhra Pradesh ministry will consist of 40% members from Telangana and 60% members frorn Andhra.
7. The Chief Minister was from A.R, the Deputy Chief Minister would be from Telangana and vice versa. “But the governments never implemented the Gentlemen’s Agreement. Hence people started agitation in 1969 in Telangana and a counter-movement started in A.P. in 1972, i.e. ‘Jai Andhra Movement.’.

There were three main causes for this:

1. Discontent diversion of surplus revenue from Telangana to other regions of the state.
2. Discrimination in employment in government sector.
3. And granting of domicile status to Coastal Andhra persons working in Telangana region in violation of the Mulki rule.

Question 15.
Read the given paragraph and interpret.
The coastal environment of Nigeria has been disturbed because of reckless oil extraction by foreign oil companies. Oil spillage from oil wells has a major impact on the ecosystem.
(OR)
The Taliban’s, which took over Afghanistan after the withdrawal of Soviet troops, similarly established an extremist Islamic state. These states tried to force all the people to strictly follow the rules laid down in religious texts.
Answer:
The given paragraph emphasises that the coastal environment of Nigeria has been disturbed because the oil companies extracted more than their share. It is talking about the consequences of over-spillage of oil.

Overspillage of oil has various negative consequences:
Oil spillage from oil wells has a major impact on the ecosystem. Large areas of the mangrove forests, which are especially susceptible to oil, have been destroyed. This is mainly because oil is stored in the soil and re-released annually. Around 5-10% of Nigerian mangrove ecosystems have been destroyed either by clearing or oil. Spills destroy crops arid aqua culture through contamination of the groundwater and soil. Drinking water is also frequently contaminated, and sheen of’ oil is visible in many local bodies of water. Even if there is no immediate health efffect of this water contamination, it can cause cancer in the long term. Offshore spills, which are usually much bigger in scale, contaminate the coastal environments and cause a decline in the local fish production.

If the same is continued the whole world be affected. Oil is a natural resource. so natural resources are to be saved.
(OR)

1. The given paragraph says that an extremist Islamic state was formed in Afghanistan.
2. This forced all the people to strictly follow the rules mentioned in religious texts.
3. The women were not treated as equals, their basic freedom was denied.
4. The Taliban are extremists in Afghanistan.
5. Once they fired a girl named Malala for voice for education.
6. She was rescued and later on given Nobel Prize.
7. The Talibans insisted everyone to follow the rules laid down in religious texts. My opinion is that one should follow the religious rules with understanding them and they should follow heartfully. Religion is personal – No one can force anyone to follow some rules or not ot follow the same.
8. The Talibans do not allow women to have basic freedom. And they do not have equal rights.
9. In modern society all the men and women are equal in getting opportunities.

Conclusion:

1. There should be no denial of basic freedom and equality of opportunity to women and religious minorities.
2. International Human Rights commission should intervene and solve the problems of Taliban women.

Question 16.
Nowadays, in which economic sector, the job opportunities are increasing? Give reasons.
(OR)
Mention the challenges of present-day urbanisation and suggest remedies.
Answer:

• Now a days employment opportunities are available more in secondary and service sectors.
• Last 50 years onwards the changes are occurred in GDP in all sectors, but employment is not increased. Yet, employment opportunities are increased in secondary and service sectors.

Reasons:

1. Establishment of industries in public and private sectors.
2. Increasing of technological methods.
3. Increasing of educational facilities.
4. Due to globalisation, Multi-National Companies are entered and industrial and service sectors are developed.
5. Transportation facilities are developing.
6. Migrations are increased.
7. Increasing of local foreign investment.

(OR)
Urbanization: The migration of people from rural areas to urban areas is called urbanisation.

Causes of urbanisation:

1. Natural growth
2. Inclusion of rural areas and
3. Migrations

Challenges of urbanisation:

1. The rapid inflows of rural population to urban places give rise to housing problem and thus slums are developed in these places.
2. The decrease in rural population affects the agricultural production due to shortage of workers in rural areas.
3. Due to use of more vehicles, air, water, sound pollutions are increased.
4. Traffic problem will arise.
5. Proper drainage facilities are not expanded.
6. Using of plastic covers are increased.
7. The unemployment increases in urban areas.
8. Due to this, various criminal activities, corruption, etc. increase affecting the law and order system.

Remedies:

1. Controlling of migrations from villages to towns and cities.
2. Recycling of waste materials.
3. Providing more employment opportunities in villages.
4. Eradicating the use of plastic.

Question 17.
Observe the given graph and analyse.

(OR)
Observe the given table and analyse.
Table 1:
Distribution of Workers in India. 2017 – 2018 (%)

Answer:

1. The given graph is a climograph.
2. It says about maximum and minimum temperatures and mean rainfall of Leh City.
3. As we observe the data, we come to know that in July and August, the mean rainfall is very high. It is more than 14 mm.
4. Temperature is very high in the months of June and July. It is up to 25°C.
5. We observe the above graph rainfall is very high and temperature is also very high in the same month only.

Why this is happen in Leh because it is situated at an elevation of 3,520mts. It is surrounded by the towering peaks of the Ladakh range, south eastern extension of the Karakoram range.
The people of Leh traditionally lead a nomadic pastoral life.
Their lifestyle is very simple and they prefer to remain close to the nature.
(OR)

1. The above table explains about distribution of workers in India in 2017-18 in different sectors.
2. Most of the rural workers are employed in agriculture.
3. Most of the urban workers are employed in service sector.
4. Most of the agricultural labourers are women.
5. Female workers are very less in industrial sector.
6. Agriculture sector offers the largest employment on the whole.
7. The industrial sector offers the least employment.

Due to the above table we should understand employment opportunities in the secondary and service sectors are gradually increasing.

Question 18.
Locate the following places in the map of India.
1. Deccan plateau
2. Thar Desert
3. Malabar coast
4. One west-flowing river
5. Dodabetta
(OR)
Locate the following places in the world map.
1. Britain
2. Austria
3. India
4. Egypt
5. A country associated with Nazism.
Answer:

(OR)

Part – B
Marks: 20

Instructions:

1. Answer all questions.
2. Choose the correct option from the given four Options and write the letter (A to B or C or D) in CAPITAL LETTER in the brackets.
3. Each question carries 1 mark.
4. Write the answers in the question paper itself.
5. Marks are not given to corrected, dismissed, or erased answers.

Question 1.
Puna Pact was signed by ( )
A) Gandhi – Ambedkar
B) Gandhi – Nehru
C) Nehru – Ambedkar
D) Ainbedkar – Vallabhai Patel
Answer:
A) Gandhi – Ambedkar

Question 2.
An idea which promotes the unity of all African peoples irrespective of country or tribe. ( )
A) Democracy
B) Secularism
C) Pan-Africanism
D) Republic
Answer:
C) Pan-Africanism

Question 3.
The ‘New Deal’ promise was a relief to the victims of ( )
A) World wars
B) Economic depression
C) Partition of India
D) Flood-affected people
Answer:
B) Economic depression

Question 4.
An example of MNC ( )
A) Indian Railways
B) BSNL
C) TATA motors
D) Indian postal service
Read the given text and answer the following 5 & 6 questions:
Underground water tables have fallen rapidly across the country. Even in regions with bountiful rains and favourable natural systems of recharge, the water tables have reached dangerously low levels. As the water tables decline, farmers have to drill deeper tube wells than before. The use of diesel/electricity for irrigation rises accordingly.
Answer:
C) TATA motors

Question 5.
Drilling deeper tube wells leads to the increase in: ( )
A) The yield of the crop
B) Cultivated area
C) The use of electricity
D) Soil fertility
Answer:
C) The use of electricity

Question 6.
Identify the TRUE statement. ( )
A) The groundwater level is good in regions with bountiful rains.
B) There is fall in the water tables where there is favourable natural system of recharge
C) There is no change in the underground water tables in India.
D) Farmers do not use groundwater to cultivate crops.
Answer:
B) There is fall in the water tables where there is favourable natural system of recharge

Question 7.
The present Chief Election Commissioner of India is ( )
A) Rajiv Kumar
B) Susheel Chandra
C) Anup Chandra Pandey
D) Y.V. Chandrachud
Answer:
A) Rajiv Kumar

Question 8.
The present President of India is ( )
A) Ramnath Kovind
B) Narendra Modi
C) Draupadi Murmu
D) Tamilisai Soundara Rajan.
Answer:
C) Draupadi Murmu

Question 9.
Which of the following is NOT an example of a public facility ( )
A) Safe drinking water
B) Electricity
C) Education
D) Airport
Answer:
D) Airport

Question 10.
These are considered while estimating GDP ( )
A) The value of all goods and services
B) The value of all final goods and services
C) The value of all goods only
D) The value of all services only.
Answer:
B) The value of all final goods and services

Question 11.
The reason for ban in growing sugarcane and banana in HiWare Bazar is ( )
A) The prices are very low
B) The production is very less
C) These crops consume moved water
D) There is no demand for these crops.
Answer:
C) These crops consume moved water

Question 12.
Match the following and choose the correct option. ( )

1) Mega Cities	a) Population between 1 million and 10 million
2) Metropolitan	b) Population above 10 million
3) Class 1 Towns	c) Population between 5000 and I Lakh
4) Towns	d) Population between 1 lakh and 1 million

A) 1-a, 2-b, 3-c, 4-d
B) 1-d, 2-c, 3-b, 4-a
C) 1-c, 2-d, 3-a, 4-b
D) 1-b, 2-a, 3-d, 4-c
Answer:
D) 1-b, 2-a, 3-d, 4-c

Question 13.
Most of the unskilled and semi-skilled workers are migrating to these countries ( )
A) European countries
B) USA
C) African countries
D) Oil Exporting countries
Answer:
D) Oil Exporting countries

Question 14.
Hill stations-Simla, Nainital, Mussorie are in ………………. . ( )
A) Greater Himalayas
B) Lesser Himalayas
C) Shiwaliks
D) Nilgiris
Answer:
B) Lesser Himalayas

Question 15.
The slogan ‘do or die’ is related to this. ( )
A) Non-cooperation Movement
B) Quit India Movement
C) Khilafat Movement
D) Civil disobedience
Answer:
B) Quit India Movement

Question 16.
One of the following is not related to Telangana. ( )
A) Gentleman agreement
B) Mulki rules
C) Regional council
D) Silent Valley movement
Answer:
D) Silent Valley movement

Question 17.
Identify the correctly matched pair. ( )
A) Green peace movement – New York
B) Treaty of Versailles – Paris
C) Sardar Sarovar dam – Ganga River
D) Non-Alignment Movement – London
Answer:
B) Treaty of Versailles – Paris

Question 18.
Arrange the following in the chronological order. ( )
1. Direct Action Day
2. Quit India Movement
3. Individual Satyagraha
4. Cripps Mission
A) 1,2,3,4
B) 1,3,4,2
C) 3,4,2,1
D) 2,3,4,1
Answer:
C) 3,4,2,1

Question 19.
Among the following, choose the correct statement. ( )
A) The President of U.S.A. is elected directly by the people
B) The president of India is elected directly by the people
C) Indian people have dual citizenship
D) Concurrent list cannot be amended by the states.
Answer:
A) The President of U.S.A is elected directly by the people

Question 20.
The reform that was not related to Jawaharlal Nehru. ( )
A) Land reforms
B) Abolition of privy purse
C) Agricultural cooperatives
D) Local self-government
Answer:
D) Local self-government

The strategic use of TS 10th Class Social Model Papers and TS 10th Class Social Question Paper April 2023 can significantly enhance a student’s problem-solving skills.

TS 10th Class Social Question Paper April 2023

Time:3 hours.
Max. Marks: 80

Introduction

1. Read the questions carefully and understand them.
2. Write the answers for the questions in Part – A in the answer sheet.
3. Attach the Map to the Part – A answer sheet.
4. Attach Part B to Part A answer sheet.
5. Part A consists of I, II, and III Sections.
6. Write the answers clearly duly following the instructions given for each section.

Part – A (Marks: 60)
Section – I (6 x 2 = 12 M)

Instructions:

• Answer all questions.
• Answer each question in 3 – 4 sentences.
• Each question carries 2 marks.

Question 1.
What are the factors that affect the density of the population in India?
Answer:
Factors that affect the density of population in India include:

1. Topography and geography: Physical features influence habitable areas. ‘
2. Economic opportunities: Urban centers attract higher population density.
3. Infrastructure and amenities: Availability of resources affects settlement patterns.

Question 2.
What are the main objectives of the National Food Security Act?
Answer:
The main objectives of the National Food Security Act in India are to provide food and nutritional security by ensuring access to adequate food at affordable prices for all eligible beneficiaries.

Question 3.
Which quality of Dr. B.R. Ambedkar do you like the most? Give reasons.
Answer:
The quality of Dr. B. R. Ambedkar that I admire the most is his relentless pursuit of social justice and equal rights for marginalized communities. His commitment to empowering the oppressed through education, advocacy, and constitutional reforms is commendable and has left a lasting impact on India’s social fabric.

Question 4.
What are the consequences of frequent violation of election code of conduct by political parties at present?
Answer:
Frequent violations of the election code of conduct by political parties can lead to an erosion of democratic values, electoral integrity, and fair representation, potentially resulting in electoral malpractices and public distrust in the electoral process.

Question 5.
Draw the outline map of Telangana.
Answer:

Question 6.
Observe the following table and answer the questions A & B.

A) What does the above table show?
B) Why the share of employment in the agriculture sector has not decreased?
Answer:
A) The above table shows the Distribution of Workers in India.
B) The share of employment in the agricultural sector has not decreased significantly due to a lack of alternative employment opportunities in other sectors and the continued reliance on traditional farming practices in many regions.

Section – II
(6 x 4 = 24 M)

‘Instructions:

• Answer all questions.
• Answer each question in 5 – 6 sentences.
• Each question carries 4 marks.

Question 7.
What are the basic concepts that contribute to an area becoming a Settlement? Explain them.
Answer:
The basic concepts that contribute to an area becoming a settlement are:
1. Availability of Resources: Settlements form where essential resources such as water, fertile land, and natural resources are available for šustenance and economic activities.

2. Accessibility: Proximity to transportation routes, trade networks, and communication facilities enhances connectivity and fosters settlement growth.

3. Social Factors: Cultural, religious, and historical factors can influence the establishment of settlements as centers of community Life.

4. Economic Opportunities: The presence of job opportunities, markets, and economic activities attracts people to settle in a particular area.

5. Defense and Security: Strategic locations with natural barriers or defensive advantages often lead to the development of settlements for protection.

6. Government Policies: Supportive policies and infrastructure development by authorities can encourage settlement growth in certain regions.

7. Topography: Favorable terrain and climate contribute to the suitability and desirability of an area for settlement.

Question 8.
What changes occurred in Indian democracy between 1975-85?
Answer:
Between 1975 and 1985, India witnessed significant changes in its democracy, including:
1. Emergency (1975-1977): A period of suspended civil liberties, censorship, and political repression declared by then Prime Minister Indira Gandhi.

2. Return to Democracy: The end of the Emergency in 1977 led to free and fair elections, with the Janata Party forming the government.

3. Political Shifts: The Janata Party government’s collapse in 1979 and the re-emergence of the Congress Party under Indira Gandhi in 1980.

4. Economic Reforms: Economic liberalization measures were introduced in the 1980s to boost the economy and attract foreign investment.

5. Punjab Conflict: The rise of Sikh separatist movement in Punjab, leading to escalating violence and the Operation Blue Star in 1984.

6. Assassination of Indira Gandhi: Prime Minister Indira Gandhi was assassinated in 1984 by her Sikh bodyguards, resulting in anti-Sikh riots.

7. Rajiv Gandhi’s Leadership: Rajiv Gandhi took over as Prime Minister after his. mother’s assassination, bringing in a new era of leadership.

8. Assam Agitation: The movement against illegal immigrants in Assam demanding the updation of the National Register of Citizens. These changes had a profound impact on India’s political landscape and shaped the course of its democracy during the given period.

Question 9.
Prepare a pamphlet explaining the need for organic farming.
Answer:
Pamphlet on Needt of Organic Farming:
Need of Organic Farming
Nowadays many people consume the food grains grown by using chemical fertilizers. There is no usage of organic food. Governments and Non-governmental agencies are concentrating various awareness programmes but there is no concentration on farming and. consuming Organic Food grains.

Due to chemicals, there are many diseases and people suffer a lot with health problems. Whenever the farmers sprinkle some chemical spray in plants, the remains of chemicals join with water when there is a rain and the remains mix with water and reach any tank. The fish consume the water and the chemical enters the fish. When the humans consume the fish it affects them. Sometimes it leads to cancer.

My appeal to the farmers and government is that everyone should give priority to Organic Food which has no side effects; It is healthy food. Natural manure like animal dung, dry leaves and grass, humus, etc., are to be used in farming. Government should encourage cow-based agriculture instead of chemical farming Including maintaining grain banks for next season so that the side effects will not be there. Healthy society can be seen.

No. of copies: 3000

Published by: Welfare Society

Question 10.
Read the given paragraph and interpret it.
Most small farmers have to borrow money to arrange for the working capital. They borrow from large farmers or the village moneylenders or the traders who supply various inputs for cultivation. The rate of interest on such loans is very high.
Answer:
The paragraph suggests that small farmers often need to borrow money for their farming operations. They typically borrow from large farmers, village money lenders, or input suppliers. The interest rates on these loans are exorbitantly high.

Question 11.
Locate the following on the outline map of the World.
1. Washington
2. Japan
3. Congo
4. Italy.
Answer:

Question 12.
Observe the given table and analyse it.
Net Irrigated_area in lakh hectares

Region	1955-56	2006-07	Growth %
Andhra Region	17	23	135
Telangana Region	7	19	257

Answer:
The table provides data on population growth in two regions of India: the Andhra Region and Telangana Region, over a period of 51 years from 1955-56 to 2006-07.
1. Andhra Region:

• Population in 1955-56:17 million
• Population in 2006-07: 23 million
• Growth %: 135% Growth %: 257%

2. Telangana Region:

• Population in 1955-56: 7 million
• Population in 2016-07: 19 million

Analysis:

• Both regions experienced significant population growth over the 51-year period.
• Telangana Region had a higher rate of population growth (257%) compared to Andhra Region (135%).
• The higher growth rate in Telangana may indicate factors such as better economic opportunities, infrastructure development, or natural population increase.
• However, it’s important to note that this data alone may not provide a complete understanding of the underlying factors contributing to the population growth in each region.

Section – III
(4 x 6 = 24 M)

Instructions:

• Answer any 4 questions.
• Answer each question in 8 – 10 sentences.
• Each question carries 6 marks.

Question 13.
Classify the Himalayas and explain.
Answer:
The Himalayas can be classified based on their geographical features and their location within the mountain range. They are categorized into three main subdivisions:
1. Greater Himalayas (Himadri):

• This is the northernmost and highest subdivision of the Himalayas.
• It consists of some of the world’s highest peaks, including Mount Everest and K2.
• The Greater Himalayas are primarily composed of snow-capped peaks and glaciers.

2. Middle Himalayas (Himachal or Lesser Himalayas):

• The Middle Himalayas lie south of the Greater Himalayas and run parallel to them,
• This region is characterized by densely forested hills and valleys.
• The elevation of the Middle Himalayas is lower than the Greater Himalayas.

3. outer Himalayas (Shiwalik or Sub-Himalayas):

• The Outer Himalayas are the southernmost and outermost subdivision of the Himalayas.
• They are composed of relatively lower hills and foothills, known as the Shiwalik Range.
• The Outer Himalayas act as the transition zone between the mountains and the plains.

Explanation: The Himalayas are a vast and formidable mountain range in South Asia, stretching across several countries, including India, Nepal, Bhutan, China, and Pakistan. They are the result of the collision between the Indian tectonic plate and the Eurasian plate, which began around 50 million years ago and continues to this day.

The Greater Himalayas form the majestic northern barrier, with towering peaks that are snow-clad throughout the year. These peaks are a testament to the immense forces of nature and attract mountaineers and trekkers from around the world.

The Middle Himalayas, Lying south of the Greater Himalayas, are characterized by lush green valleys and are home to a variety of flora and fauna. The hill stations of Shimla, Mussoorie, and Nainital are part of the Middle Himalaýas, making this region a popular tourist destination.

The Outer Himalayas, the southernmost subdivision, mark the transition between the mountainous terrain and the plains below. These foothills provide a natural buffer and help in regulating water flow into the river systems that sustain the vast population living in the Indo-Gangetic plains.

The Himalayas are not only a spectacular geographical feature but also hold immense cultural, religious, ahd ecological significance for the people living in the region. They act as a crucial water source, supply essential resources, and influence weather patterns, making them an indispensable part of life in South Asia.

Question 14.
Explain the relations between India and China.
Answer:
India and China, being two major Asian powers with ancient civilizations, have a complex relationship that has evolved over centuries and continues to be a significant factor ¡n regional and global geopolitics. Here is a brief overview of the key aspects of their relations:
1. Historical ties: India and China have historical ties dating back thousands of years, with interactions in trade, culture, and religious exchanges. However, there have also been periods of conflict and territorial disputes.

2. Border Disputes: The most significant point of contention between India and China is their unresolved border dispute, which led to a war in 1962. The border issues continue to be a sensitive and contentious topic.

3. Geopolitical Rivalry: India and China are both emerging as major economic and geopolitical powers in the 21st century. As a result, there is an element of competition for regional influence and resources, leading to occasional tensions.

4. Economic Relations: Despite political differences, India and China have substantial economic ties. They are significant trade partners, with bilateral trade volumes reaching billions of dollars. However, there is a trade imbalance in China’s favor, which is a matter of concern for India.

5. Strategic Cooperation and Rivalry: Both countries are part of various regional and international forums and organizations. They cooperate on issues like climate change and multilateral platforms. However, they also have competing interests in areas like the Indian Ocean region and the Belt and Road Initiative (BRI).

6. Diplomatic Engagements: India and China engage in high-level diplomatic dialogues, including bilateral summits and meetings between their leaders. These interactions aim to manage and address differences and find common ground on various issues.

7. Security Concerns: Both countries share concerns over terrorism, regional stability, and maintaining peace along their borders. They sometimes collaborate on security issues while remaining vigilant about each other’s military activities.

8. Cultural Exchanges: Cultural exchanges and people-to-people interactions between India and China help build understanding and goodwill between the two nations.

9. International Relations: India and China’s stances on global issues often differ, but they also cooperate on certain international platforms, such as BRICS (Brazil, Russia, India, China, and South Africa) and the Shanghai Cooperation Organization (SCO).

Overall, India-China relations are characterized by a mix of cooperation, competition, and occasional tensions. Managing their differences and finding common ground is crucial for regional stability and prosperity.Both nations recognize the importance of engaging with each other constructively while safeguarding their respective national interests.

Question 15.
Why are the working conditions of workers in unorganised sector not improving even today? Suggest suitable measures.
Answer:
The working conditions of workers in the unorganized sector often do not improve due to various reasons:
I. Lack of Regulation: The unorganized sector operates outside formal labor regulations, making it challenging to enforce labor standards and ensure better working conditions.

2. Informal Nature: Many unorganized sector jobs lack formal contracts and social security benefits, leaving workers vulnerable to exploitation and, uncertain employment.

3. Limited Skill Development: Workers in the unorganized sector often have, limited access to skill development and training programs, hindering their ability to seek higher-paying and safer jobs.

4. Inadequate Awareness: Many workers in the unorganized sector are unaware of their rights and labor laws, making them susceptible to unfair treatment and low wages.

5. Market Pressures: The informal nature of the unorganized sector makes it susceptible to market fluctuations, affecting wages and job stability.

6. Lack of Collective Bargaining Power: Individual workers in the unorganized sector often lack the bargaining power to demand better working conditions and wages.

Suggested Measures to Improve Working Conditions:
1. Legal Reforms: Strengthen labor laws and regulations to cover workers in the unorganized sector, ensuring minimum wages, social security, and safe working conditions.

2. Skill Development: Invest in skill development programs to enhance the employability of unorganized sector workers and provide opportunities for better-paying jobs.

3. Social Security Nets: Introduce social ‘security schemes tailored for unorganized sector workers to provide them with health benefits, insurance coverage, and old-age pensions.

4. Awareness Campaigns: Conduct awareness campaigns to educate unorganized sector workers about their rights and entitlements.

5. Worker Organizations: Facilitate the formation of worker cooperatives and associations to enhance collective bargaining power and negotiate for better working conditions.

6. Microfinance and Access to Credit: Promote microfinance initiatives and improve access to credit for workers in the unorganized sector to help them start and expand their own enterprises.

7. Corporate Social Responsibility (CSR): Encourage private companies to engage in CSR activities that support the welfare and skill development of unorganized sector workers.

8. Monitoring and Enforcement: Strengthen enforcement mechanisms to ensure compliance with labor laws and penalize violators.

9. Government Schemes: Extend government welfare schemes to cover unorganized sector workers and ensure their inclusivity.

Improving the working conditions of workers in the unorganized sector requires a multi-faceted approach involving legal reforms, social policies, and public-private partnerships. It demands a collective effort from the government, employers, workers, and civil society to create a more equitable and sustainable work environment for all.

Question 16.
Read the following paragraph and write your opinion.
Land reforms were however implemented in a halfhearted manner across India. While the Zamindari system was abolished, redistribution of land to the landless did not take place. The rich and powerful in the rural areas continued to control most of the land.
Answer:
Opinion: The paragraph highlights a significant issue With land reforms in India. While the abolishment of the Zamindari system was a positive step, the failure to effectively redistribute land to the landless population is concerning. This lack of proper implementation allowed the rich and powerful in rural areas to retain control over the majority of the land. Land reforms are essential to address historical íncqualities empower marginalized communities and promote equitable development. Without meaningful and comprehensive land redistribution, the benefits of land reforms may not reach those who need it the most. It is crucial for policymakers to prioritize effective implementation and ensure that land reforms are carried out in a more equitable and impactful manner to create a fairer and more inclusive society.

Question 17.
Locate the following on the outline map of India.
1) Maiwa plateau
2) River Godavari
3) Circar coast
4) The state with the lowest density of population
5) Chandigarh
6) Bihar.
Answer:

Question 18.
Observe the following graph and analyse it.

(Germany, Austria-Hungary, Great Britain, Russia, Italy and France 1880 – 1914)
(Source: The Times Atlas of World History, London 1978)
Answer:

1. The graph shows that the military expenditure of the great countries has been increasing since 1880.
2. During 1914, the weapons were prepared in large scale.
3. Military expenditure increases for every 10 years because of armament race.
4. Countries like Germany, Great Britain, Russia, Italy, and France are some countries that spend more money on weapons.
5. Money spent on military expenditure in 1914 was 397 million pounds.

Part – B (20 Marks)

Instructions:

1. Answer all questions.
2. Each question carries 1 mark.
3. Write the answers in the question paper itself.
4. Marks are not given to corrected, dismissed, or erased answers.

Choose the correct option from the given four options and write the letter (A, B, C, and D) in CAPITAL LETTER in the brackets.

Question 1.
Match the following. ( )

1) Loo winds	A) Temperate zone
2) North-East monsoons	B) Heavy rainfall to Coromandel coast
3) The region to the north of the Tropic of Cancer	C) Hot winds blow in the northern plains
4) South-West monsoons	D) Heavy rainfall along the West coast.

A) 1 – A, 2-B, 3-C, 4-D
B) 1 – D, 2 C, 3-B, 4-A
C) 1-C, 2-B, 3-A, 4-D
D) 1-C, 2-B, 3-D, 4-C
Answer:
C) 1-C, 2-B, 3-A, 4-D

Question 2.
This is not an environmental movement. ( )
A) Chipko Movement
B) Greenpeace Movement
C) Meira Paibi Movement
D) Silent Valley Movement
Answer:
C) Meira Paibi Movement

Question 3.
There is a dispute between these two countries regarding the distribution of Ganga river waters. ( )
A) India – Pakistan
B) India – Bangladesh
C) India – Sri Lanka
D) India – Myanmar
Answer:
B) India – Bangladesh

Question 4.
Liberalization leads to ………….. . ( )
A) Trade barriers
B) Free Trade
C) Trade restrictions
D) More taxes
Answer:
B) Free Trade

Question 5.
The main allegation made by Punjab during the Punjab agitation was ………………… . ( )
A) Ignoring the role of the state in the development of the country.
B) Declaring Chandigarh as a Union Territory.
C) Claiming less water from Bhakranangal dam.
D) Recruiting fewer Sikhs into the army.
Answer:
A) Ignoring the role of the state in the development of the country.

Question 6.
Match the following. ( )

1) Hamlets	A) A group of houses within the revenue village.
2) Class – 1 cities	B) Villages with defined borders.
3) Metropolitan cities	C) Urban areas having population between 1 lakh and one million.
4) Revenue villages	D) Cities having population between one million and 10 million.

A) 1-ii. 2-i, 3-iii, 4-iv
B) 1-iii, 2-ii, 3-iv, 4-i
C) 1-i, 2-iv, 3-ii, 4-iii
D) 1-i, 2-iii, 3-iv, 4-ii
Answer:
D) 1-i, 2-iii, 3-iv, 4-ii

Question 7.
This is not the cause for reducing fertility of the soil. ( )
A) Unscientific use of chemical fertilisers
B) Excessive use of fertilisers and pesticides
C) Improper utilisation of natural resources
D) Use of organic fertilisers
Answer:
D) Use of organic fertilisers

Question 8.
The northern edge of Deccan plateau is ( )
A) Nilgiri mountains
B) Satpura mountains
C) Himalayan mountains
D) Western Ghats
Answer:
B) Satpura mountains

Question 9.
The Election Code of Conduct will come into force ……………… . ( )
A) After the announcement of election result.
B) At the time of commencement of election schedule.
C) After the submission of nominations.
D) On the day of polling.
Answer:
B) At the time of commencement of election schedule.

Question 10.
In China, the Communist Party of China worked for land reforms and …………………… . ( )
A) Encouraging the rich.
B) To participate landlords in the politics.
C) Discouraging the poor peasants.
D) Spreading literacy.
Answer:
D) Spreading literacy.

Question 11.
The first Five Year Plan gave priority to ………………. . ( )
A) Agriculture
B) Industries
C) Railways
D) Aviation
Answer:
A) Agriculture

12. The following is not the working capital. ( ).
A) Seeds
B) Pesticides
C) Machines
D) Chimicals fertilisers
Answer:
C) Machines

Question 13.
The Commission formed to study the developments in Andhra Pradesh and submit the report to the Centre is ……………….. . ( )
A) Justice Sri Krishna Commission
B) Dr. Fazal Mi Commission
C) Mandai Commission
D) Kothari Commission.
Answer:
A) Justice Sri Krishna Commission

Question 14.
Find Out the odd one regarding services. ( )
A) Brokers
B)’ Saving accounts
C) Banks
D) Handicrafts
Answer:
D) Handicrafts

Question 15.
This is a tributary of river Ganga. ( )
A) Dihang
B) Beas
C) Tapati
D) Chambal
Answer:
D) Chambal

Question 16.
As per 2011 Census, the male literacy is …………………. . ( )
A) 82%
B) 65%
C) 74%
D) 12%
Answer:
A) 82%

Question 17.
Match the following.

1) Announcement of partition of country	A) M.S. Khan
2) A Naval Central Strike Committee	B) Mahammed Iqbal
3) Need for North-West Muslim State	C) Jawaharlal Nehru
4) A resolution on the rights of minorities	D) Lord Mount Batten

A) 1-D, 2-A, 3-B, 4-C
B) 1-C, 2-A, 3-B, 4-D
C) 1-D,2-A,3-C,4-B
D) 1-B,2-D,3-A,4-C
Answer:
A) 1-D, 2-A, 3-B, 4-C

Question 18.
Imposing taxes on imported goods leads to ……………….. . ( )
1) Imported goods are cheaper.
2) Beneficial to domestic producers.
3) Prices of imported goods rise.
A) 1 and 2
B) 2 and 3
C) 1 and 3
D) 1,2 and 3
Answer:
B) 2 and 3

Question 19.
The present President of India is …………………. . ( )
A) Ramnath Kovind
B) Droupadi Murmu
C) Venkaiah Naidu
D) Chandra Shekhar Rao
Answer:
B) Droupadi Murmu

Question 20.
The present Secretary General of UNO is ……………… . ( )
A) Kofi Annan
B) U Thant
C) Ban Ki-Moon
D) Antonio Guterres
Answer:
D) Antonio Guterres

The strategic use of TS 10th Class Maths Model Papers Set 4 can significantly enhance a student’s problem-solving skills.

TS SSC Maths Model Paper Set 4 with Solutions

Time: 3 Hours
Maximum Marks: 80

General Instructions:

1. Answer all the questions under Part – A on a separate answer book.
2. Write the answers to the questions under Part – B on the question paper itself and attach it to the Part – A

Part – A (60 Marks)
Section – I (6 × 2 = 12 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 1.
If A = {x : x ∈ N, x < 5} and B = {x : x ∈ N, 2 < x < 7}, then draw Venn diagram for A∪B.
Solution:
A = {1, 2, 3, 4}
B = {3, 4, 5, 6}
A∪B Venn diagram

A∪B {1, 2, 3, 4, 5 , 6}

Question 2.
Check whether the given pair of linear equations x + 2y – 4 = 0 and 2x + 4y – 12 = 0 is intersecting lines or parallel lines.
Solution:
Given pair of linear equations
x + 2y – 4 = 0
a₁ = 1, b₁ = 2, c₁ = -4
2x + 4y – 12 = 0
a₂ = 2, b₂ = -4, c₂ -12
\(\frac{a_1}{a_2}\) = \(\frac{1}{2}\), \(\frac{b_1}{b_2}\) = \(\frac{2}{4}\) = \(\frac{1}{2}\), \(\frac{c_1}{c_2}\) = \(\frac{-4}{-12}\) = \(\frac{1}{3}\)
\(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\)
∴ Given lines are parallel lines.

Question 3.
Give one example each for an Arithmetic progression and a Geometric progression.
Solution:
Examples for an Arithmetic progression and Geometric progression
A.P. : 3, 5, 7, 9, 11, ……………
G.P. : 3, 6, 12, 24, 48, ………….

Question 4.
Find the probability of getting a ‘vowel’ if a letter is chosen randomly from English alphabet.
Solution:
Total number of alphabets in English n(S) = 26
Number of Vowel in English alphabets n(V) = 5
∴ P(V) = \(\frac{\mathrm{n}(\mathrm{V})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{5}{26}\)

Question 5.
Find the volume of a hemispherical bowl whose radius is 2.8 cm.
Solution:
Radius of hemispherical bowl r = 2.8 cm
Volume of the hemispherical bowl

Question 6.
In ΔABC, DE||BC. If AO : DB = 2 : 3, AE = 3x + 1 and EC = 5x, then find the value of ‘x’.

Solution:
Given in ΔABC, DE||BC, AD : DB = 2 : 3, AE = 3x + 1, EC = 5x
∴ \(\frac{\mathrm{AD}}{\mathrm{DB}}\) = \(\frac{\mathrm{AE}}{\mathrm{EC}}\)(BPT)
\(\frac{2}{3}\) = \(\frac{3 x+1}{5 x}\)

10x = 3(3x + 1)
10x = 9x + 3
10x – 9x = 3
∴ x = 3

Section – II (6 × 3 = 18 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 3 marks.

Question 7.
If log (1 + tan θ + sec θ) + log (1 + cot θ – cosec θ) = log k (0°< θ < 90°), then find the value of k.
Solution:
Given
log (1 + tan θ + sec θ) + log (1 + cot θ – cosec θ) = log k
= log (1 + tan θ + sec θ) log (1 + cot θ – cosec θ) = log k (∵ log x + log y = log xy)
∴ (1 + tan θ + sec θ) (1 + cot θ – cosec θ) = k
Now

Question 8.
Write the formula for mode of a grouped data and explain each term of it.
Solution:
Mode = l + \(\left[\frac{\mathrm{f}_1-\mathrm{f}_0}{2 \mathrm{f}_1-\mathrm{f}_0-\mathrm{f}_2}\right]\) × h
l = lower boundary of mode class
f₁ = frequency of mode class
f₀ = frequency of preceding class to the mode class
f₂ = frequency of succeeding class to the mode class
h = size of class

Question 9.
Prove that 2 + 3√5 is an irrational number.
Solution:
Let us assume that 2 + 3√5 is a rotational number.
∴ 2 + 3√5 = \(\frac{a}{b}\), (b ≠ 0) and a, b are co-primes.
3√5 = \(\frac{a}{b}\) – 2 = \(\frac{a-2 b}{b}\)
∴ √5 = \(\frac{a-2 b}{3 b}\)
Since a, b are integers \(\frac{a-2 b}{3 b}\) is rational number. So √5 is rational number.
This contradicts the fact that √5 is an irrational number.
Hence 2 + 3√5 is an irrational number.

Question 10.
Prove that x² + 2x + 1 divides x⁴ – 2x³ – 4x² + 2x + 3 exactly.
Solution:

Remainder (x) = 0
∴ x² + 2x + 1 divides x⁴ – 2x³ – 4x² + 2x + 3.

Question 11.
In a circle of radius 3.5cm, a chord subtends a right angle at the centre. Find the area of the corresponding
major segment. (Take π = \(\frac{22}{7}\))
Solution:
Radius of the circle r = 3.5 cm
Sector angle at centre x° = 90°

Area of minor segment AXB = Area of Sector AOBXA – Area of ΔAOB

= 12.25 × \(\frac{22-14}{28}\)

= 3.5 cm²
∴ Area of major segment AYB = Area of circle – Area of minor segment
= \(\frac{22}{7}\) × (3.5)² – 3.5 [Area of Circle = πr²]

= 38.5 – 3.5 = 35cm²
Another Method:
Area of Major segment = Area of Major sector AYBOA + Area of ΔAOB
= \(\frac{270^{\circ}}{360}\) × πr² + \(\frac{1}{2}\)bh
= \(\frac{3}{4}\) × \(\frac{22}{7}\) × 3.5 × 3.5 + \(\frac{1}{2}\) × 3.5 × 3.5

= 3.5 × 3.5 × (\(\frac{33}{7}\) + \(\frac{1}{2}\))
= 3.5 × 3.5 × \(\frac{33+7}{14}\)

= 35 cm²
∴ Area of major segment = 35 cm²

Question 12.
Find the area of the triangle whose vertices are (5, 2) (3, -5) and (-3, -4).
Solution:
Let A (5, 2), B(3, -5) and C(-3, – 4)
Area of ΔABC
= \(\frac{1}{2}\)|x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)|
= \(\frac{1}{2}\)|5[- 5 – (- 4)] + 3[- 4 – 2] + (- 3) [2 – (- 5)]
= \(\frac{1}{2}\)|5(- 1) + 3(- 6) – 3(7)|
= \(\frac{1}{2}\)|- 5 – 18 – 21 | = \(\frac{1}{2}\)|- 44|
= \(\frac{1}{2}\) × 44 = 22
∴ Area of ΔABC = 22 sq. units.

Section – III (6 × 5 = 30 Marks)

Note :

1. Answer all the following questions.
2. In this section, every question has internal choice. Answer any one alternative.
3. Each question carries 5 marks.

Question 13.
A) Find mean for the following data.

Solution:

a = 95, Σf_i = 100, Σf_iu_i = 40
Mean \(\overline{\mathrm{x}}\) = a + \(\frac{\Sigma f_i u_i}{\Sigma f_i}\) × h

= 95 + 4 = 99
Mean \(\overline{\mathrm{x}}\) = 99

(OR)

B) The angle of elevation of the top of a building from the foot of the tower is 30° and the angle of elevation of the top of the tower from the foot of the building is 60°. If the tower is 100m high, then find the height of the building.
Solution:
AB = Height of the tower = 100 m
CD = Height of the building

In ΔABC,
tan 60° = \(\frac{\mathrm{AB}}{\mathrm{BC}}\)
√3 = \(\frac{100}{B C}\) ⇒ BC = \(\frac{100}{\sqrt{3}}\) ……….. (1)
In ΔDCB,
tan 30° = \(\frac{\mathrm{CD}}{\mathrm{BC}}\)
\(\frac{1}{\sqrt{3}}\) = \(\frac{\mathrm{CD}}{\mathrm{BC}}\) ⇒ √3 CD = BC
√3 CD = \(\frac{100}{\sqrt{3}}\) [From (1))]
CD = \(\frac{100}{\sqrt{3} \times \sqrt{3}}=\frac{100}{3}\)
∴ Height of the building CD = \(\frac{100}{3}\)m = 33\(\frac{1}{3}\)m

Question 14.
A) Prove that \(\frac{\tan \theta+\sec \theta-1}{\tan \theta-\sec \theta+1}=\frac{1+\sin \theta}{\cos \theta}\)
Solution:

(OR)

B) Show that the quadrilateral obtained by joining the points (-2, 4) (-6, -2) (-2, -8) and (2, -2) is a Rhombus.
Solution:
Let A(-2, 4), B(-6, -2), C(-2, -8) and D(2, -2)

∴ AB = BC = CD = DA
ABCD is a Rhombus.

Question 15.
A) Solve \(\frac{2}{x-1}+\frac{3}{y+1}\) = 2 and \(\frac{3}{x-1}+\frac{2}{y+1}\frac{3}{x-1}+\frac{2}{y+1}\) = \(\frac{13}{6}\) where x ≠ 1, y ≠ 1.
Solution:
Given
\(\frac{2}{x-1}+\frac{3}{y+1}\) = 2 and \(\frac{3}{x-1}+\frac{2}{y+1}\frac{3}{x-1}+\frac{2}{y+1}\) = \(\frac{13}{6}\)
Let \(\frac{1}{x-1}\) = a and \(\frac{1}{y+1}\) = b then the given equations
2a + 3 b = 2 …………… (1)
3a + 2b = \(\frac{13}{6}\) = 18a + 12b = 13 …………. (2)

10 a = 5
a = \(\frac{5}{10}\) = \(\frac{1}{2}\)
a = \(\frac{1}{2}\) substitute in (1)
2(\(\frac{1}{2}\)) + 3b = 2
1 + 3b = 2
3b = 1
∴ b = \(\frac{1}{3}\)
But a = \(\frac{1}{x-1}\) = \(\frac{1}{2}\),
∴ x – 1 = 2
x = 3

b = \(\frac{1}{y+1}\) = \(\frac{1}{3}\)
∴ y + 1 = 3
y = 3 – 1
y = 2
∴ Solutions x = 3, y = 2

(OR)

B) Cards marked with numbers 2 to 101 are placed in a box. They are mixed thoroughly and one card is selected randomly from the box. Find the probability that the number on the selected card is
(i) an even number
(ii) a number less than 14
(iii) a number which is a perfect square
(iv) a prime number less than 20
Solution:
Total number of cards in a box = 100
∴ Number of total outcomes n(S) = 100

i) Number of even number marked cards = 50
∴ Number of favourable outcomes to select an even number n(E) = 50
∴ The probability to select an even number card P(E) = \(\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{50}{100}\) = \(\frac{1}{2}\)

ii) Number of favourable outcomes to select a number less than 14
n(F) = 12
F = (2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13}
∴ The probability to select a number less than P(F) = \(\frac{\mathrm{n}(\mathrm{F})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{12}{100}\) = \(\frac{3}{25}\)

iii) Number of favourable outcomes to select a number which is a perfect square n(G) = 9
G = {4, 9, 16, 25, 36, 49, 64, 81, 100}
∴ The probability to select a perfect square number P(G) = \(\frac{\mathrm{n}(\mathrm{G})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{9}{100}\)

iv) Number of favourable outcomes to select a prime number less than 20
n(H) = 8
H = (2, 3, 5, 7, 11, 13, 17, 19}
∴ The probability to select a prime number less than 20
P(G) = \(\frac{\mathrm{n}(\mathrm{H})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{8}{100}\) = \(\frac{2}{25}\)

Question 16.
A) A metallic vessel is in the shape of a right circular cylinder mounted over a hemisphere. The common diameter is
56 cm and the height of the cylindrical part is 21cm. Find the capacity of the vessel. (Take π = \(\frac{22}{7}\))
Solution:
Common diameter of cylinder and hemisphere d = 56 cm

∴ Common radius r = 28 cm
Height of the cylinder h = 21 cm
∴ Volume the vessel = Volume of cylinder + Volume of hemisphere.

∴ Volume the vessel = \(\frac{293216}{3}\)
= 97738.66 cm²

(OR)

B) A motor boat travels a distance of 18 km upstream and travels back to reach the starting point. Fôr up and down
trip, It takes 12 hours. If the speed of the stream is 2 kmph, then find the speed of the boat in still water. (Assume that the motor boat maintains a constant speed)
Solution:
Let the speed of the boat in still water = x km/h
Speed of the stream = 2 km/h
Now the speed of the boat in upstream = x – 2 km/h
Speed of the boat in downstream = x + 3 km/h
Distance d = 18 km
By the problem total time for the trip = 12 hours

∴ x² – 4 = 3x
x² – 3x – 4 = 0
x² – 4x + x – 4 = 0
x(x – 4) + 1(x – 4) = 0
(x – 4)(x + 1) = 0
∴ x – 4 = 0 (or) x + 1 = 0
x = 4 (or) x = -1
But x > 0
∴ x = 4
Speed of the boat in still water = 4 km/h

Question 17.
A) Draw the graph of the polynomial p(x) = x² – x – 6 and then find its zeroes from the graph.
Solution:
Given that y = x² – x – 6


Result : From the graph we observe that 3 and -2 are the intersecting points of X – axis.
So, the zeroes of given quadratic polynomial are 3 and -2.

(OR)

B) Solve the equations graphically
3x + 4y = 10 and 4x – 3y = 5.
Solution:
Given two equations 3x + 4y = 10 and 4x – 3y = 5
3x + 4y = 10
4y = 10 – 3x
y = \(\frac{10-3 x}{4}\)

4x – 3y = 5
– 3y = 5 – 4x
3y = 4x – 5
y = \(\frac{4 x-5}{3}\)


Given two lines intersect at (2, 1)
So the solution is x = 2, y = 1

Question 18.
A) Construct a triangle PQR, in which PQ = 4 cm, QR = 6 cm and ∠PQR = 60°. Construct another triangle similar to ΔPQR, with its sides equal to \(\frac{4}{3}\) times of the corresponding sides of the triangle PQR.
Solution:

Construction Steps:

1. Construct a triangle PQ R with the given measurements PQ = 4 cm, QR = 6 cm, ∠PQR = 60°
2. Draw a ray \(\overrightarrow{\mathrm{PQ}}\) making an acute angle with PQ,
3. Locate 4 points P₁, P₂, P₃, P₄ on PX. So that P₁P₂ = P₂P₃ = P₃P₄ = P₄P₁.
4. Join P₃ to Q, Draw a line form P₄ parallel to QP₃. It intersect PQ at Q’.
5. Draw a line through Q’ parallel to QR intersect PR at R’
6. ΔPQ’R’ is required triangle.

(OR)

B) Draw a circle of radius 5 cm. From a point 9 cm away from its centre, construct a pair of tangents to the circle.
Solution:

1. Construct a circle with a radius of 5 cm.
2. Trace the point ‘P’ in the exterior of the circle.
3. Construct a perpendicular bisector to OP which meets at M.
4. Draw a another circle with a radius of MP or MO and M as centre. It intersect previous circle at the points A and B.
5. Join P, A and P B.
6. PA, PB are the required tangents.

Part – B (20 Marks)

Note :

1. Answer all the questions.
2. Each question carries 1 mark.
3. Answers are to be written in the Question paper only.
4. Marks will not be awarded in any case of over writing, rewriting or erased answers.

Note : Write the capital letters (A, B, C, D) showing the correct answer for the following questions in the brackets provided against them. (Marks : 20 × 1 = 20)

Question 1.
The value of k for which the system of equations 4x + y = 3 and 8x + 2y = 5k has infinite solutions is
A) \(\frac{-5}{6}\)
B) \(\frac{-6}{65}\)
C) \(\frac{5}{6}\)
D) \(\frac{6}{5}\)
Answer:
D) \(\frac{6}{5}\)

Question 2.
Among the following, a statement that is NOT true is
A) sin θ = \(\sqrt{1-\cos ^2 \theta}\)
B) sec² θ – tan² θ = 1
C) cos θ. cosec θ = 1
D) tan θ. cot θ = 1
Answer:
C) cos θ. cosec θ = 1

Question 3.
The logarithmic form of 7 = 3^x is
A) log₃x = 7
B) log₇3 = x
C) log₇x = 3
D) log₃7 = x
Answer:
D) log₃7 = x

Question 4.
The decimal form of \(\frac{3}{8}\) is
A) 3.75
B) 0.365
C) 0.375
D) 0.0375
Answer:
C) 0.375

Question 5.
If 72, 63, 54,………… is an Arithmetic progression, then the terhithat becomes zero in it
is
A) 11^th
B) 10^th
C) 9^th
D) 8^th
Answer:
C) 9^th

Question 6.
The equal set of A = {x : x is a letter of the word “FOLLOW”} is
A) {f, o, l, l, o, w}
B) {f, o, l, l, w)
C) {f, l, o, w}
D) (f, o, l, o, w}
Answer:
C) {f, l, o, w}

Question 7.
If n(A – B) = 5, n(B – A) = 7 and n(A∩B) = 3, then n(A ∪B) is
A) 9
B) 12
C) 10
D) 15
Answer:
D) 15

Question 8.
Among the following, the value which is not possible for the probability of an event is
A) \(\frac{1}{3}\)
B) 0.5
C) 25%
D) \(\frac{4}{3}\)
Answer:
D) \(\frac{4}{3}\)

Question 9.
Among the following, a linear polynomial is
A) 3x² + 2x – 4
B) 2x + 3
C) 5
D) x³ – 3x² + 7
Answer:
B) 2x + 3

Question 10.
IF p(x) = x² – 2x + 2, then the value of p(0) is
A) 4
B) 0
C) 2
D) -2
Answer:
C) 2

Question 11.
The value of Discriminent of x² + x + 1 = 0 is
A) 3
B) 4
C) -4
D) -3
Answer:
D) -3

Question 12.
A quadratic equation whose roots are -2 and -3 is
A) x² – 5x – 6 = 0
B) x² + 5x + 6 = 0
C) x² + 5x – 6 = 0
D) x² – 5x + 6 = 0
Answer:
B) x² + 5x + 6 = 0

Question 13.
If the product of the first 5 terms of a Geometric progression is 243, then its third term is
A) 9
B) 27
C) 3
D) 1
Answer:
C) 3

Question 14.
LCM of numbers 2⁷ × 3⁴ × 7 and 2³ × 3⁴ × 11 is
A) 2³ × 3⁴
B) 2⁷ × 3⁴
C) 2⁷ × 3⁴ × 7 × 11
D) 2³ × 3⁴ × 7 × 11
Answer:
C) 2⁷ × 3⁴ × 7 × 11

Question 15.
In an Arithmetic progression n^th term is a_n = a + (n – 1 )d. In this formula “d” represents
A) Number of terms
B) n^th term
C) First term
D) Common difference
Answer:
D) Common difference

Question 16.
In ΔABC, if ∠C = 30°, AB = 1 unit, then AB : AC : BC is

A) 1 : 2 : 3
B) 3 : 2 : 1
C) √3 : 2 : 1
D) 1 : 2 : √3
Answer:
D) 1 : 2 : √3

Question 17.
If the radius of a cylinder is doubled and its height is halved, then the volume of the new cylinder formed is
A) 4 times the volume of the first cylinder
B) 3 times the volume of the first cylinder
C) 2 times the volume of the first cylinder
D) Volume remains the same
Answer:
C) 2 times the volume of the first cylinder

Question 18.
E and \(\overline{\mathbf{E}}\) are two complementary events in a random Experiment. If P( \(\overline{\mathbf{E}}\)) = 0.07, then the value of P(E) is
A) 0.3
B) 0.93
C) 0.03
D) 0.83
Answer:
B) 0.93

Question 19.
The mean of 9 observations is 45. In doing so, if an observation was wrongly taken as 42 for 24, then the correct mean of the data is
A) 34
B) 43
C) 37
D) 45
Answer:
B) 43

Question 20.
Base radii and heights of a cylinder and a cone are equa}. If the volume of cone is 9 cubic units, then the volume of the cylinder is
A) 27 cubic-units
B) 18 cubic-units
C) 9 cubic-units
D) 36 cubic-units
Answer:
A) 27 cubic-units

The strategic use of TS 10th Class Maths Model Papers Set 3 can significantly enhance a student’s problem-solving skills.

TS SSC Maths Model Paper Set 3 with Solutions

Time: 3 Hours
Maximum Marks: 80

General Instructions:

1. Answer all the questions under Part – A on a separate answer book.
2. Write the answers to the questions under Part – B on the question paper itself and attach it to the the answer book of Part A.

Part – A (60 Marks)
Section – I (6 × 2 = 12 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 1.
Check whether A = {x : x² = 25 and 6x = 15} is an empty set or not ? Justify your answer.
Solution:
x² = 25 . ∴ x = \(\sqrt{25}\) = ± 5
6x = 15 ∴ x = \(\frac{15}{6}\) = \(\frac{5}{2}\)
Any value of x is not satisfying the above two equations. So, A is empty set.

Question 2.
Find two numbers whose sum is 27 and product is 182.
Solution:
Let the first number = x
∴ Second number = 27 – x
Product of two numbers = 182
x(27 – x) = 182
27x – x² = 182
⇒ x² – 27x + 182 = 0
⇒ x² – 13x – 14x + 182 = 0
⇒ x(x- 13) – 14(x – 13) = 0
⇒ (x – 13) (x – 14) = 0
⇒ x – 13 = 0 (or) x – 14 = 0
⇒ x = 13 (or) x = 14
∴ If first number =13, then second number = 27 – 13 = 14
If first number =14, then second number = 27 – 14 = 13
∴ Required numbers = 13 and 14.

Question 3.
Verify that the points (1, 5), (2, 3) and (-2, -1) are collinear are not.
Solution:
Let A(1, 5), B(2, 3), C(-2, -1)
Area of ΔABC
= \(\frac{1}{2}\)|x₁(y₂ – y₃) + x₂(y₃ – y₁) + x₃(y₁ – y₂)|
= \(\frac{1}{2}\)|1[3 – (- 1)] + 2[- 1 – 5] + (- 2) [5 – 3]|

= \(\frac{1}{2}\) × 12 = 6 sq.units
Area of ΔABC ≠ 0
∴ Given points (1, 5), (2, 3) and (-2,-1) are not collinear.

Question 4.
A person from the top of a building of height 25 m has observed another building top and bottom at an angle of elevation 45° and at an angle of depression 60° respectively. Draw a diagram for this data.
Solution:

Question 5.
Find the area of required cloth to cover the heap of grain in conical shape, of whose diameter is 8m and slant height of 3m.
Solution:
Diameter of conical shape (heap of grain) (d) = 8m
Radius (r) = \(\frac{8}{2}\) = 4 m
Slant height l = 3m
L.S.A of the conical shape (heap) = πrl
= \(\frac{22}{7}\) × 4 × 3
= \(\frac{264}{7}\) = 37.71 m²
∴ Area of required cloth to cover the heap of grain = 37.71 m²

Question 6.
ΔABC ~ ΔDEF and their areas are respectively 64 cm² and 121 cm².
If EF = 15.4 cm., then find BC.
Solution:
\(\frac{{ar}(\triangle \mathrm{ABC})}{{ar}(\triangle \mathrm{DEF})}\) = \(\left(\frac{B C}{E F}\right)^2\)
\(\frac{64}{121}\) = \(\left(\frac{B C}{15.4}\right)^2\)
= \(\frac{8}{11}\) = \(\frac{B C}{15.4}\)
⇒ BC = \(\frac{8 \times 15.4}{11}\) = 11.2 cm

Section – II (6 × 3 = 18 Marks)

Note :

1. Answer ALL the following questions.
2. Each question carries 2 marks.

Question 7.
Check whether the given pair of linear equations represent intersecting, parallel or coincident lines. Find the
solution if the equations are consistent.
i) 3x + 2y = 5 ; 2x – 3y = 7
ii) 2x – 3y = 5 ; 4x -6y = 15
Solution:
Given pair of linear equations
i) 3x + 2y = 5 …………….. (1)
2x – 3y = 7 …………….. (2)
3x + 2y – 5 = 0
2x – 3y – 7 = 0
a₁ = 3, b₁ = 2, c₁ = -5
a₂ = 2, b₂ = -3, c₂ -7
\(\frac{a_1}{a_2}\) = \(\frac{3}{2}\), \(\frac{b_1}{b_2}\) = \(\frac{2}{-3}\)
\(\frac{a_1}{a_2}\) ≠ \(\frac{b_1}{b_2}\)
∴ Given pair of linear equations rep-resent intersecting lines.
∴ Given equations are consistent.

ii) 2x – 3y = 5 ………….. (3)
4x – 6y = 15 …………… (4)
2x – 3y – 5 = 0
4x – 6y – 15 = 0
a₁ = 2, b₁ = -3, c₁ = -5
a₂ = 4, ₂ = -6, c₂ = -15
\(\frac{a_1}{a_2}\) = \(\frac{2}{4}\) = \(\frac{2}{4}\),
\(\frac{b_1}{b_2}\) = \(\frac{-3}{-6}\) = \(\frac{1}{2}\)
\(\frac{c_1}{c_2}\) = \(\frac{-5}{-15}\) = \(\frac{1}{3}\)
\(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\)
∴ Given pair of linear equations represent parallel lines.
∴ Given equations are inconsistent.

Question 8.
The 10^th term of an AP is 52 and 16^th term is 82, then find the 32^nd term.
Solution:
Given : An AP where
10^th term = 52
16^th term = 82

⇒ -6d = -30
⇒ d = \(\frac{-30}{-6}\) = 5
Substituting d = 5 in the equation (1) we get
a + 9d = 52
a + 9 × 5 = 52
⇒ a + 45 = 52 ⇒ a = 52 – 45 = 7
Now 32^nd term = a + 31 d
= 7 + 31 × 5.
= 7 + 155 = 162

Question 9.
Find the zeroes of the quadratic polynomial x² + 5x + 6 and verify the relationship between the zeroes and coefficients.
Solution:
p(x) = x² + 5x + 6
If p(x) = 0, then x² + 5x + 6 = 0
x² + 2x + 3x + 6 = 0
x(x + 2) + 3(x + 2) = 0
(x + 2) (x + 3) = 0
x + 2 = 0 (or) x + 3 = 0
x = -2 (or) x = -3
∴ Zeroes of p(x) = -2, -3
Let α = -2 and β = -3
Sum of the zeroes α + β = (- 2) + (- 3)
= -5

Question 10.
A toy is in the form of a cone mounted on a hemisphere. The diameter of the base and the height of the cone are 6 cm and 4 cm respectively. Find the surface area of the toy. (Take π = 3.14)
Solution:
Diameter of the base of the cone d = 6 cm.
∴ Radius of the base of the cone.
r = \(\frac{d}{2}\) = \(\frac{1}{2}\) = 3 cm.

Height of the cone = h = 4 cm
Slant height of the cone
l = \(\sqrt{r^2+h^2}\)
= \(\sqrt{(3)^2+(4)^2}\) = \(\sqrt{9+16}\) = \(\sqrt{25}\) = 5 cm
∴ C.S.A. of cone = πrl
= \(\frac{22}{7}\) × 3 × 5 = \(\frac{330}{7}\) cm²
Radius of the hemisphere
\(\frac{d}{2}\) = \(\frac{6}{2}\) = 3 cm.
C.S.A. of the hemisphere = 2πr²
= 2 × \(\frac{22}{7}\) × 3 × 3 = \(\frac{396}{7}\)
Hence the surface area of the toy = C.S.A. of cone + C.S.A. of hemisphere
= \(\frac{330}{7}\) +\(\frac{396}{7}\)
= \(\frac{726}{7}\) = 103.71 cm²

Question 11.
If sec β + tan β = p, then express the value of sin β in terms of ‘p’.
Solution:
Given sec β + tan β = p ………….. (1)
sec² β – tan² β = 1
(sec β + tan β) (sec β – tan β) = 1
p(sec β – tan β) = 1
∴ sec β – tan β = \(\frac{1}{\mathrm{p}}\) ………….. (2)


Hence proved.

Question 12.
One card is drawn from a well-shuffled deck of 52 cards. Find the probability of getting
i) a king of red colour
ii) a face card
iii) a red face card
iv) the jack of hearts.
Solution:
Out of 52 cards one card can be drawn in 52 ways.
∴ The total number of outcomes n(S) = 52

i) Let E be the event ‘The card is a king of red colour”. ,
The no.of favourable outcomes n(E) = 2
∴ P(E) = \(\frac{\mathrm{n}(\mathrm{E})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{2}{52}\) = \(\frac{1}{26}\)

ii) Let F be a event “The card is a face card”.
n(F) = 12
∴ P(E) = \(\frac{\mathrm{n}(\mathrm{F})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{12}{52}\) = \(\frac{3}{13}\)

iii) Let G be a event The card is.a red face card”.
n(G) = 6
P(G) = \(\frac{\mathrm{n}(\mathrm{G})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{6}{52}\) = \(\frac{3}{26}\)

iv) Let H be a event “The card is the jack of hearts”.
n(H) = 1
P(H) = \(\frac{\mathrm{n}(\mathrm{H})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{1}{52}\)

Section – III (6 × 5 = 30 Marks)

Note :

1. Answer all the following questions.
2. In this section, every question has internal choice. Answer any one alternative.
3. Each question carries 5 marks.

Question 13.
A) Two men on either side of a temple of 30 meter height observe its top at the angles of elevation 30° and 60° respectively. Find the distance between the two men.
Solution:
Height of the temple BD = 30 meters
Angle of elevation of one person ∠DAB = 30°
Angle of elevation of another person ∠BCD = 60°
Let the distance between the first person and the temple, AD = x and distance between the second person and the temple, CD = d

From ΔBAD
tan 30° = \(\frac{\mathrm{BD}}{\mathrm{AB}}\)
\(\frac{1}{\sqrt{3}}=\frac{30}{x}\) ⇒ x = 30√3 …………. (1)
From ΔBCD
tan 60° = \(\frac{B D}{d}\)
√3 = \(\frac{30}{\mathrm{~d}}\)
d = \(\frac{30}{\sqrt{3}}\) ………….. (2)
From (1) and (2) distance between the persons
= BC + BA = x + d
= 30√3 + \(\frac{30}{\sqrt{3}}=\frac{30 \times 4}{\sqrt{3}}=\frac{120}{\sqrt{3}}\) = 40√3m
The required distance is 40√3 m.

(OR)

B) If cosec A = √2, then find the value of \(\frac{2 \sin ^2 A+3 \cot ^2 A}{4\left(\tan ^2 A-\cos ^2 A\right)}\).
Solution:
Given cosec A = √2

Question 14.
A) Prove that √3 + √5 is an irrational number.
Solution:
Let us suppose that -√3 + √5 is rational.

Since a, b are integers, \(\frac{a^2+2 b^2}{2 a b}\) is rational and so √5 is rational.
This contradicts the fact √5 is irrational.
Hence √3 + √5 is irrational.

(OR)

B) A right circular cylinder has base radius 14 cm and Height 21 on. Find its
i) Area of the base (area of each end)
ii) Curved surface area
iii) Total surface area iv) Volume
Solution:
Given that base radius of
cylinder r = 14 cm
Height h = 21 cm
i) Area of base = πr²
= π(14)²

Question 15.
A) The sum of the third and seventh terms of an AP is 6 and their product is 8. Find the sum of first sixteen terms of the AP.
Solution:
In an AP
3^rd term = a₃ = a + 2d
7^th term = a₇ = a + 6d
From given a₃ + a₇ = 6 and a₃ + a₇ = 8
Now take a₃ + a₇ = 6
a + 2d + a + 6d = 6
2a + 8d = 6
a + 4d = 3
a = 3 – 4d …………… (1)
Now take a₃ × a₇ = 8
(a + 2d) (a + 6d) = 8 …………… (2)
Substitute a = 3 – 4d in eqn. (2)
(3 – 4d + 2d) (3 – 4d + 6d) = 8
(3 – 2d) (3 + 2d) = 8
(3)² – (2d)² = 8
9 – 4d² = 8
9 – 8 = 4d²
4d² = 1 => d² = \(\frac{1}{4}\)
d = \(\frac{1}{2}\)
From (I) a = 3 – 4d
= 3 – 4 × \(\frac{1}{2}\) = 3 – 2 = 1
a = 1
Sum of 16 terms
= S_n = \(\frac{n}{2}\)[2a + (n – 1)d]
S₁₆ = \(\frac{16}{2}\)[2 × 1 + (16 – 1) \(\frac{1}{2}\)]
= 8[\(\frac{2}{1}\) +\(\frac{15}{2}\)] = 8[latex]\frac{4+15}{2}[/latex]
= 4 × 19 = 76

(OR)

B) If the median of 60 observations, given below is 28.5 find the values of x and y.

Solution:

Class Interval	Frequency	c.f
0 – 10	5	5
10 – 20	x	5 + x
20 – 30	20	25 + x
30 – 40	15	40 + x
40 – 50	y	40 + x + y
50 – 60	5	45 + x + y

Median = l + (\(\frac{\left(\frac{n}{2}-c . f\right)}{f}\)) × h
It is given that Σf = n = 60
So, 45 + x + y = 60
x + y = 60 – 45 = 15
x + y= 15 ………….. (1)
The median is 28.5 which lies between 20 and 30.
∴ Median class = 20 – 30
Lower boundary of the median class ‘l’ = 20
\(\frac{N}{2}\) = \(\frac{60}{2}\) = 30
cf – cumulative frequency = 5 + x
h = 10
Median =l + (\(\frac{\left(\frac{n}{2}-c . f\right)}{f}\)) × h
⇒ 28.5 = 20 + \(\frac{30-5-x}{20}\) × 10
28.5 = 20 + \(\frac{25-x}{2}\)
\(\frac{25-x}{2}\) = 28.5 – 20 = 8.5
25 – x = 2 × 8.5
x = 25 – 17 = 8
also from (1); x + y = 15 8 + y = 15 ⇒ y = 7
∴ x = 8; y = 7.

Question 16.
A) From a pack of 52 playing cards, Jacks, Queens, Kings and Aces of red colour are removed. From the remaining, a card is drawn at random. Find the probability that the card drawn is (i) a black queen, (ii) a red card.
Solution:
Probability of black queen = \(\frac{1}{26}\)
Probability of red card = \(\frac{1}{2}\)
n(S) = 52
Probability of black queen n(a) = 2
p(a) = \(\frac{\mathrm{n}(\mathrm{a})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{2}{52}\) = \(\frac{1}{26}\)
Probability of a red card n(b) = 26
p(b) = \(\frac{\mathrm{n}(\mathrm{b})}{\mathrm{n}(\mathrm{S})}\) = \(\frac{26}{52}\) = \(\frac{1}{2}\)

(OR)

B) If A = (x : x is a prime less than 20} and B = {x : x is a whole number less than 10},
then verify n(A∪B) = n(A) + n(B) – n(A∩B).
Solution:
Given
A = {x : x is a prime less than 20}
A = {2,3, .5, 7, 11,13, 17,19} n(A) = 8
B = {x: x is a whole number less than 10} = {0,1,2, 3,4, 5, 6, 7, 8, 9} n(B) = 10
n(A∪B) = n(A) + n(B) – n(A∩B) ………. (1)
A∩B = {2, 3, 5, 7, 11, 13, 17, 19} ∩ {0, 1,2, 3,4, 5, 6, 7, 8, 9}
= {2, 3, 5, 7}
n(A∩B) = 4
From (1) n (A∪B) = 8 + 10 – 4 = 14.

Question 17.
A) Draw the graph of p(x) = x² – 6x + 9 and find zeroes. Verify the zeroes of the polynomial.
Solution:
Given p(x) = x² – 6x + 9
Let y = x² – 6x + 9

We observe that the graph touches the X – axis at (3, 0).
So, the zeroes of the given polynomial are equal.
∴ The zeroes of p(x) are 3, 3.
Justification:
Given p(x) = x² – 6x + 9 = 0
⇒ x² – 3x – 3x + 9 = 0
⇒ x(x – 3) – 3(x – 3) = 0
⇒ (x- 3) (x – 3) = 0
x – 3 = 0 (or) x – 3 – 0
x = 3 (or) x = 3
∴ Zeroes of p(x) = 3,3

(OR)

B) Solve the following pair of linear equations by graph method.
2x + y = 6 and 2x – y + 2 = 0.
Solution:
2x + y = 6

x	0	1	2	3
y	6	4	2	0
(x, Y)	(0, 6)	(1, 4)	(2, 2)	(3, 0)

2x – y + 2 =0

x	0	1	2
y	2	4	6
(x, y)	0, 2)	(1, 4)	(2, 6)

point of intersection is (1, 4)
∴ x = 1; y = 4

Question 18.
A) Draw a pair of tangents to a circle of radius 5 cm which are inclined to each other at an angle 60°.
Solution:
Given that, ∠APB = 60°
Join OP.

OP bisects ∠APB
∴ ∠OPA = ∠OPB = 30°

In ΔOAP sin 30° = \(\frac{\mathrm{OA}}{\mathrm{OP}}\) ⇒ \(\frac{1}{2}\) = \(\frac{5}{\mathrm{OP}}\)
∴ OP = 10 cm.
Now,

1. Draw a circle of radius 5 cm with centre ’O’.
2. Mark a point P at a distance of 10 cm from the centre of the circle.
3. Join OP and draw the perpendicular bisector of OP. Let it meet OP at M.
4. Taking M as centre and MO = MP as radius draw a circle. Which cuts the previous circle at A, B. Join PA and PB. Which are the required tangents.

(OR)

Construct a triangle PQR, in which PQ = 4 cm, QR = 6 cm and ∠PQR = 70°. Construct triangle such that each side of the new triangle is \(\frac{3}{4}\) of the triangle of PQR.
Solution:
Steps of construction :

• Draw a triangle PQR with given measurements.

• Draw \(\overrightarrow{\mathrm{PY}}\) such that ∠QPY is an acute angle.
• Locate points A₁, A₂, A₃, A₄ on \(\overrightarrow{\mathrm{PY}}\) such that PA₁ = A₁ A₂ = A₂ A₃ = A₃ A₄.
• Join A₄ and Q.
• Draw a parallel line to A₄ Q through A₃ to meet PQ at Q¹.
• Draw a parallel line to QR through Q¹ to meet PR at R¹.
• ΔPQ¹ R¹ is required similar triangle.

Part – B (20 Marks)

Note :

1. Answer all the questions.
2. Each question carries 1 mark.
3. Answers are to ]be written in the Question paper only.
4. Marks will not be awarded in any case of over writing, rewriting or erased answers.

Note : Write the capital letters (A, B, C, D) showing the correct answer for the following questions in the brackets provided against them. (Marks : 20 × 1 = 20)

Question 1.
Which of the following is an irrational number ?
A) \(\frac{2}{3}\)
B) \(\sqrt{\left(\frac{16}{25}\right)}\)
C) √8
D) \(\sqrt{0.04}\)
Answer:
C) √8

Question 2.
The product of zeroes of the cubic polynomial 2x³ – 5x² – 14x + 8 is
A) -4
B) 4
C) -7
D) 25
Answer:
A) -4

Question 3.
A pair of linear equations which satisfies dependent system
A) 2x + y- 5 = 0; 3x – 2y – 4 = 0
B) 3x + 4y = 2 ; 6x + 8y = 4
C) x + 2y = 3 ; 2x + 4y = 5
D) x + 2y – 30 =t 0 ; 3x + 6y + 60 = 0
Answer:
B) 3x + 4y = 2 ; 6x + 8y = 4

Question 4.
The n^th term of AP is t_n = a + (n – 1)d, where ‘d’ represents
A) First term
B) Common difference
C) Common ratio
D) Radius
Answer:
B) Common difference

Question 5.
The number of two digit numbers which are divisible by 3
A) 30
B) 20
C) 29
D) 31
Answer:
A) 30

Question 6.
If A = {x: x is a letter in the word MATHEMATICS} and
B = {x: x is a letter in the word MISTEACH} then
A) A⊆ B
B) B ⊆ A
C) A = B
D) B = A
Answer:
B) B ⊆ A

Question 7.
The coordinates of the centre of the circle if the ends of the diameter are (2, -5) and (-2,9)
A) (0, 0)
B) (2, -2)
C) (-5, 9)
D) (0, 2)
Answer:
D) (0, 2)

Question 8.
The Discriminant of the Quadratic equation x² + x + 1 = 0 is
A) 2
B) -3
C) 3
D) -2
Answer:
B) -3

Question 9.
The lines l and m represents.

A) Inconsistent equation
B) Consistent equations
C) Dependent lines
D) Parallel lines
Answer:
B) Consistent equations

Question 10.
The slope of a ladder making an angle 30° with the floor is
A) 1
B) \(\frac{1}{\sqrt{3}}\)
C) √3
D) \(\frac{1}{2}\)
Answer:
B) \(\frac{1}{\sqrt{3}}\)

Question 11.
The distance between the points (cos α, 0), (0, sin α) is
A) 1
B) -1
C) 0
D) -2
Answer:
A) 1

Question 12.
The Arithmetic mean of 30 students is 42. Among them two got zero marks, then Arithmetic mean of remaining students.
A) 40
B) 42
C) 45
D) 28
Answer:
C) 45

Question 13.
The probability of getting king or queen card from the deck of cards
A) \(\frac{1}{52}\)
B) \(\frac{2}{13}\)
C) \(\frac{3}{26}\)
D) \(\frac{5}{52}\)
Answer:
B) \(\frac{2}{13}\)

Question 14.
Which of the following statement Is incorrect ?
A) The ratio of surface areas of cylinder and cone is 1 : 1
B) The ratio Surface Areas of sphere and hemisphere is 2 : 1
C) The ratio Total Surface Area of sphere and hemisphere is 2 : 1
D) The ratio of volumes of cylinder and cone is 3 : 1
Answer:
A) The ratio of surface areas of cylinder and cone is 1 : 1 & C) The ratio Total Surface Area of sphere and hemisphere is 2 : 1

Question 15.
The value of sin 30°+ cos60°is
A) 1
B) 0
C) -1
D) 2
Answer:
A) 1

Question 16.
At a particular time, if the angle of elevation of the sun is 45°, then the length of the shadow of a 5 m high tree is ……………… .
A) 5√3 m
B) 10 m
C) 5 m
D) \(\frac{5}{\sqrt{3}}\)m
Answer:
C) 5 m

Question 17.
When a dice is rolled, the probability of getting a composite number is [ ]
A) \(\frac{1}{4}\)
B) \(\frac{1}{2}\)
C) \(\frac{1}{3}\)
D) \(\frac{1}{6}\)
Answer:
C) \(\frac{1}{3}\)

Question 18.
The sum of first 100 natural numbers
A) 55
B) 505
C) 5050
D) 5500
Answer:
C) 5050

Question 19.
The sides PQ and PR of right angle triangle PQR are such that PQ = 5 cm, PR = 13 cm. If ∠Q = 90° then QR = ?
A) 11.2 cm
B) 9.6 cm
C) 12 cm
D) 10.2 cm
Answer:
C) 12 cm

Question 20.
If a quadrilateral ABCD is drawii to circumscribe a circle, then AB + CD is equal to !
A) AC + BD
B) AD + BC
C) AB + AD
D) AC + BD + BC
Answer:
B) AD + BC