# AP 9th Class Maths Bits Chapter 1 Real Numbers with Answers

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## AP State Syllabus 9th Class Maths Bits 1st Lesson Real Numbers with Answers

Question 1.
A rational number equivalent to $$\frac{-3}{4}$$ is
A) $$\frac { -4 }{ 3 }$$
B) $$\frac { -4}{ 5 }$$
C) $$\frac { 3 }{ 4 }$$
D) $$\frac { -6 }{ 8 }$$
D) $$\frac { -6 }{ 8 }$$

Question 2.
$$\frac { -2 }{ 3 }$$ lies on …………. on the number line.
A) right side of the zero
B) left side of the zero
C) zero
D) can’t be determined
B) left side of the zero

Question 3.
Which of the following is false?
A) Every rational number is a natural number
B) Every rational number is a whole number
C) Every rational number is an integer
D) Every integer is a rational number
D) Every integer is a rational number

Question 4.
A rational number between 5 and 6 is
A) $$\frac { 9 }{ 2 }$$
B) $$\frac { 10}{ 2 }$$
C) $$\frac { 11 }{ 2 }$$
D) $$\frac { 12 }{ 2 }$$
C) $$\frac { 11 }{ 2 }$$

Question 5.
$$\mathbf{0 . \overline { 3 }}$$ …………….
A) $$\frac { 3 }{ 8 }$$
B) $$\frac { 2}{ 9 }$$
C) $$\frac { 3 }{ 7 }$$
D) $$\frac { 1 }{ 3 }$$
D) $$\frac { 1 }{ 3 }$$

Question 6.
The decimal form of $$\frac { 1 }{ 18 }$$ ix
A) $$0.0 \overline{5}$$
B) $$0 . \overline{05}$$
C) $$0 . \overline{5}$$
D) 0.06
A) $$0.0 \overline{5}$$

Question 7.
1.25 in $$\frac{\mathbf{p}}{\mathbf{q}}$$ form
A) $$\frac { 4 }{ 5 }$$
B) $$\frac { 5}{ 4 }$$
C) $$\frac { 5 }{ 6 }$$
D) $$\frac { 6 }{ 5 }$$
B) $$\frac { 5}{ 4 }$$

Question 8.
If a and b are any two rational num¬bers then a rational number between
a and b is
A) a + 1
B) b -1
C) $$\frac{a+b}{2}$$
D) a . b
C) $$\frac{a+b}{2}$$

Question 9.
If n is a natural number other than a perfect square then $$\sqrt{n}$$ is number.
A) rational
B) irrational
C) natural
D) none
B) irrational

Question 10.
If ‘x’ is an irrational number then x + 2 is ………………….. number.
A) natural
B) rational
C) irrational
D) can’t be determined
C) irrational

Question 11.
If ‘x’ is an irrational number then x – 3 is …………. number.
A) rational
B) natural
C) irrational
D) complex
C) irrational

Question 12.
Number which can’t be expressed in p/q form are………… numbers.
A) irrational
B) rational
C) whole
D) natural
A) irrational

Question 13.
The combination of Q and S given the set of ……………. numbers.
A) natural
B) integers
C) whole
D) real
D) real

Question 14.
(2 + $$\sqrt{2}$$ )(2 – $$\sqrt{2}$$) is a……………. number.
A) irrational
B) rational
C) can’t be determined
D) none
C) can’t be determined

Question 15.
$$\sqrt{\frac{a}{b}}$$

(C)

Question 16.
$$(\sqrt{\mathbf{a}}+\mathbf{b})(\sqrt{\mathbf{a}}-\mathbf{b})=$$
A) a2 – b2
B) a – b
C) a2 – b
D) a – b2
D) a – b2

Question 17.
$$(\sqrt{\mathbf{a}}+\mathbf{b})(\sqrt{\mathbf{a}}-\mathbf{b})$$ =
A) 10
B) $$7+2 \sqrt{10}$$
C)$$7-2 \sqrt{10}$$
D) $$2 \sqrt{10}$$
B) $$7+2 \sqrt{10}$$

Question 18.
$$(\mathbf{7}+\sqrt{2})(\mathbf{7}-\sqrt{\mathbf{2}})=$$
A) 45
B) 5
C) 3
D) 47
D) 47

Question 19.
The rationalising factor of $$\frac{1}{5 \sqrt{2}}$$ is

(C)

Question 20.
The rationalising factor of $$\frac{1}{\sqrt{27}}$$ is
A) $$\frac{1}{\sqrt{27}}$$
B) $$\sqrt{27}$$
C) $$\sqrt{3}$$
D) 3
C) $$\sqrt{3}$$

Question 21.
$$\left(\frac{3}{4}\right)^{-3} \times\left(\frac{3}{4}\right)^{3} \times\left(\frac{3}{4}\right)^{6}=\ldots \ldots$$

(B)

Question 22.
$$\sqrt[5]{32}$$ =
A) 325
B) 2
C) 4$$\sqrt{2}$$
D) 2$$\sqrt{2}$$
B) 2

Question 23.
(128)1/7 =
A) 2
B) 4
C) 8
D) $$8 \sqrt{2}$$
A) 2

Question 24.
A) $$\sqrt{27}$$
B) $$3 \sqrt{27}$$
C) $$4\sqrt{27}$$
D) $$5\sqrt{27}$$
D) $$5\sqrt{27}$$

Question 25.
a1/n =
A) $$\sqrt[n]{a}$$
B) $$\frac{\mathrm{a}}{\mathrm{n}}$$
C) na
D) n + a
A) $$\sqrt[n]{a}$$

Question 26.
The Rationalising factor of $$\frac{1}{5-\sqrt{3}}$$ is
A) $$5+\sqrt{3}$$
B) $$\sqrt{3}-5$$
C) $$\frac{1}{5+\sqrt{3}}$$
D) $$\frac{1}{\sqrt{3}-5}$$
C) $$\frac{1}{5+\sqrt{3}}$$

Question 27.
$$\sqrt[n]{a^{m}}$$ =
A) am/n
B) an/m
C) amn
D)am-n
A) am/n

Question 28.
If x3 = 10, then x is
A) a rational number
B) an irrational number
C) a perfect number
D) an even number
B) an irrational number

Question 29.
If p3 = 216, then p is
A) an odd nuipber
B) an irrational number
C) a perfect number
D) a rational number
D) a rational number

Question 30.
The radical form of 152/3 is
A) $$\sqrt[3]{30}$$
B) $$\sqrt[3]{15}$$
C) $$\sqrt[3]{225}$$
D) $$\sqrt[3]{45}$$
C) $$\sqrt[3]{225}$$

Question 31.
The radical form of 62/3 is
A) $$\sqrt[3]{36}$$
B) $$\sqrt{36}$$
C) $$\sqrt{48}$$
D) $$\sqrt{216}$$
A) $$\sqrt[3]{36}$$

Question 32.
The exponential form of $$\sqrt[4]{81}$$ is
A) 91/4
B) 92/4
C) 31/4
D) 31/8
B) 92/4

Question 33.
The exponential form of $$\sqrt[35]{105}$$ is
A) 31/35
B) 51/35
C) 71/35
D) 1051/35
D) 1051/35

Question 34.
$$(\sqrt{\mathbf{a}}+\mathbf{b})(\sqrt{\mathbf{a}}-\mathbf{b})=$$
A) a2 – b2
B) a – b2
C) a – b
D) a + b2
B) a – b2

Question 35.
$$(\sqrt{x}+y)^{2}=$$
A) x + y + 2$$\sqrt{xy}$$
B) $$\sqrt{x}$$ + y2 + 2xy
C) x + y2 + 2 $$\sqrt{x}$$ .y
D) x2 + y2 + 2 $$\sqrt{x}$$ .y
C) x + y2 + 2 $$\sqrt{x}$$ .y

Question 36.
$$(\sqrt{3}+\sqrt{2})(\sqrt{3}-\sqrt{2})=$$
A) 1
B) 0
C) 5
D) 13
A) 1

Question 37.
(- 8)7/5 x (- 8)-4/5 x (- 8)-3/5 =
A) 0
B) – 8
C) 1
D) – 512
C) 1

Question 38.
The decimal form of $$\mathbf{0 . \overline { 3 2 }}$$ is
A) $$\frac{32}{100}$$
B) $$\frac{32}{99}$$
C) $$\frac{32}{90}$$
D) $$\frac{32}{50}$$
B) $$\frac{32}{99}$$

Question 39.
$$\sqrt{9} \times \sqrt{16}=$$
A) $$\sqrt{25}$$
B) $$\frac{3}{4}$$
C) 12
D) 144
C) 12

Question 40.
$$\sqrt{a} \div \sqrt{b}=$$
A) $$\sqrt{a b}$$
B) $$a \sqrt{b}$$
C) $$\sqrt{a b}$$
D) $$\sqrt{\frac{a}{b}}$$
D) $$\sqrt{\frac{a}{b}}$$

Question 41.
$$\left(\frac{-2}{3}\right)^{2 / 7} \times\left(\frac{-2}{3}\right)^{5 / 7}=$$
A)1
B) $$\frac{-2}{3}$$
C) 0
D) $$\left(\frac{-2}{3}\right)^{2 / 5}$$
B) $$\frac{-2}{3}$$

Question 42.
If $$\sqrt{3}$$ = 1732, then $$\sqrt{27}$$ =
A) 3 x 1.732
B) 9 x 1.732
C) 27 x 1.732
D) 6 x 1.732
A) 3 x 1.732

Question 43.
Whose value is 11.18 if $$\sqrt{5}$$ = 2.236 ?
A) $$\sqrt{25}$$
B) $$\sqrt{75}$$
C) $$\sqrt{125}$$
D) $$\sqrt{250}$$
C) $$\sqrt{125}$$

Question 44.
The decimal value of $$\frac{\mathbf{2 2}}{\mathbf{7}}$$ is
A) 3.421
B) 3.142
C) 3.412
D) 3.124
B) 3.142

Question 45.
If $$\sqrt{10}$$ = 3.162, then $$\sqrt{40}$$ = mi i
A) 6.324
B) 9.486
C) 12.648
D) 31.62
A) 6.324

Question 46.
$$\sqrt[5]{32^{-2}}=$$
A) 2
B) 4
C) 6
D) 1/2
B) 4

Question 47.
Rationalising factor of $$\sqrt{5}+\sqrt{6}$$ is
A) $$\sqrt{5}$$ – 6
B) 5 – $$\sqrt{6}$$
C) $$\sqrt{5}-\sqrt{6}$$
D) 5 + $$\sqrt{6}$$
C) $$\sqrt{5}-\sqrt{6}$$

Question 48.
Express 3.25 in the form of p/q
A) $$\frac { 13 }{ 4 }$$
B) $$\frac { 65 }{ 2 }$$
C) $$\frac { 13 }{ 40 }$$
D) $$\frac { 13 }{ 20 }$$
A) $$\frac { 13 }{ 4 }$$

Question 49.
If an = b, then $$\sqrt[n]{b}$$ =
A) n
B) a
C) b1/n
D) a1/n
B) a

Question 50.
$$\frac{3^{1 / 5}}{3^{1 / 3}}=$$
A) 31/15
B) 32/15
C) 3-2/15
D) 38/15
C) 3-2/15

Question 51.
The collection of negative numbers and whole numbers is denoted by
A) Q
B) W
C) Z or l
D) N
C) Z or l

Question 52.
The rational number which lies be¬tween two rational numbers a and b is
A) a—b
B) b—a
C) $$\sqrt{a b}$$
D) $$\frac{a+b}{2}$$
D) $$\frac{a+b}{2}$$

Question 53
2/3 =
A) $$0 . \overline{6}$$
B) 0.66
C) 0.666
D) 0.6
A) $$0 . \overline{6}$$

Question 54.
The decimal value of $$\frac{1}{2^{3}}$$ is
A) 0.5
B) 0.25
C) 0.125
D) 1.125
C) 0.125

Question 55.
π is
A) a naturaF number
B) an irrational number
C) a rational number
D) none of these
B) an irrational number

Question 56.
$$\sqrt{7}$$ = 2.65 (approximately), then the approximate value of $$\sqrt{28}$$ is
A) 2.65
B) 5.3
C) 7.95
D) 10.6
B) 5.3

Question 57.
Cube root of $$\sqrt{4}+\sqrt{36}$$ is
A) $$\sqrt[3]{144}$$
B) 8
C) 2
D) $$\sqrt[3]{40}$$
C) 2

Question 58.
Value of $$\sqrt[4]{81}+\sqrt[5]{32}$$ is
A) 5
B) 9
C) – 1
D) A or C
A) 5

Instructions: Observe the number line and give answer from Q. No. 6-10.
In the number line at ‘O’ draw a unit square OABC with each side 1 unit in length and OB = OP, OD = OQ, OE = OR.

Observe above number line and answer the following:

Question 59.
The length of $$\overline{\mathrm{OP}}$$ is
A) $$\frac{3}{2}$$Units
B) $$\sqrt{2}$$ Units
C) $$\sqrt{3}$$ Units
D) 1 Unit
B) $$\sqrt{2}$$ Units

Question 60.
The length of $$\overline{\mathrm{AQ}}$$ is
A) $$\sqrt{3}$$ – 1 Units
B) $$\sqrt{3}$$ + $$\sqrt{2}$$ Units
C) $$\sqrt{3}$$ – $$\sqrt{3}$$ Units
D) $$\sqrt{3}$$ + 1 Units
A) $$\sqrt{3}$$ – 1 Units

Question 61.
Perimeter of the rectangle OCSQ
A) 2($$\sqrt{3}$$ + 1) Units
B) 6 Units
C) 2($$\sqrt{2}$$ + $$\sqrt{3}$$) Units
D) 2($$\sqrt{2}$$ + 1) Units
B) 6 Units

Question 62.
Area of rectangle PQRS in sq. units
A) $$\sqrt{3}$$ – 1
B) $$\sqrt{3}$$ + $$\sqrt{2}$$
C) $$\sqrt{3}$$ – $$\sqrt{2}$$
D) $$\sqrt{2}$$ – 1
C) $$\sqrt{3}$$ – $$\sqrt{2}$$

Question 63.
$$\sqrt{5}$$ lie between
A) 1 and 2
B) 2 and 3
C) 3 and 4
D) 0 and 1
B) 2 and 3

Question 64.
A Rectangular park dimensions are (3 + $$\sqrt{2}$$) and (2 + $$\sqrt{2}$$) units, then the area of that park in square unit.
A) 8 + 5$$\sqrt{2}$$
B) 5 + 2$$\sqrt{2}$$
C) 13$$\sqrt{2}$$
D) 5 + $$\sqrt{2}$$
A) 8 + 5$$\sqrt{2}$$

Question 65.
The value of 1.999 ……………… in the form of $$\frac{\mathbf{p}}{\mathbf{q}}$$ (p,q are integers, q ≠ 0 )
A) $$\frac{1999}{1000}$$
B) 2
C) $$\frac{1}{9}$$
D) $$\frac{19}{10}$$

Question 66.
Observe the successive magnification of 2.8746 on the number line.

Arrange these steps orderly.
A) 1,3, 4, 2
B) 3, 4, 2,1
C) 3, 4, 1, 2
D) 1, 2, 4, 3
A) 1,3, 4, 2

Question 67.
If ‘x’ is a positive real number and x2 = 2, then the value of x3 is
A) 2$$\sqrt{2}$$
B)3$$\sqrt{2}$$
C) 4
D) $$\sqrt{2}$$
A) 2$$\sqrt{2}$$

Question 68.
If $$\sqrt{10}$$ = 3.162, then the value of $$\frac{1}{\sqrt{10}}$$ is
A) 31.62
B) 3.162
C) 0.3162
D) 316.2
C) 0.3162

Question 69.
If x = $$\frac{\sqrt{3}+\sqrt{2}}{\sqrt{3}-\sqrt{2}}$$ and y = $$\frac{\sqrt{3}-\sqrt{2}}{\sqrt{3}+\sqrt{2}}$$ then the value of x + y is
A) 5
B) 5 + 2$$\sqrt{6}$$
C) 10
D) 5 – 2$$\sqrt{6}$$
C) 10

Question 70.
If x = 2 + 7$$\sqrt{3}$$ , then the value of x – $$\frac{1}{x}$$ is
A) 4
B) $$\sqrt{3}$$.
C) 2 $$\sqrt{3}$$.
D) 2 + $$\sqrt{3}$$.
B) $$\sqrt{3}$$.

Question 71.
A rational number equivalent to $$\frac{5}{7}$$ is
A) $$\frac { 15 }{ 17 }$$
B) $$\frac { 25 }{ 27 }$$
C) $$\frac { 10 }{ 14 }$$
D) $$\frac { 10 }{ 27 }$$
C) $$\frac { 10 }{ 14 }$$

Question 72.
If x = $$\sqrt{5}$$ + 2, then the value of x – $$\frac{1}{x}$$ is
A) 2$$\sqrt{5}$$
B) 4
C) -4
D) -2$$\sqrt{5}$$

Question 73.
The value of $$\left(\frac{1}{2}\right)^{3}+\left(\frac{1}{3}\right)^{3}-\left(\frac{5}{6}\right)^{3}$$ is
A) $$\frac { 5 }{ 6 }$$
B) $$\frac { 5 }{ 12 }$$
C) $$\frac { -5 }{ 36 }$$
D) $$\frac { -5 }{ 12 }$$
D) $$\frac { -5 }{ 12 }$$

Question 74.
If the length and breadth of a rectangular sheet are $$\sqrt{5}$$ + $$\sqrt{2}$$ and $$\sqrt{5}$$ – $$\sqrt{2}$$ units, then it’s area in sq. units
A) $$\sqrt{3}$$
B) 2$$\sqrt{5}$$
C) 3
D) 7
C) 3

Question 75.
Ail irrational number between 4 and 5
A) $$\sqrt{20}$$
B) $$\sqrt{9}$$
C) $$\sqrt{4.5}$$
D) 4.5
A) $$\sqrt{20}$$

Question 76.
Rationalizing Factor of 3$$\sqrt{9}$$
A) $$\sqrt[3]{3}$$
B) $$\sqrt[3]{6}$$
C) $$\sqrt[3]{9}$$
D) $$\sqrt[3]{27}$$
A) $$\sqrt[3]{3}$$

Question 77.
There are three odd numbers and one even number. What type of number is their sum ?
A) Even number
B) Neither even nor odd number
C) Cannot be determined as actual numbers are not given
D) Odd number.
D) Odd number.

Question 78.
$$\sqrt[5]{32^{2}}$$ = …………..
A) 1
B) 2
C) 4
D) 5
C) 4

Question 79.
The product of first 2019 whole numbers……
A) 0
B) 2019
C) 1.2.3.4 …………..2018.2019
D) 1 + 2 + 3 + ………………+ 2019
A) 0

Question 80.
Express 3.25 in the form of $$\frac{\mathbf{p}}{\mathbf{q}}$$.
A) $$\frac{13}{4}$$
B) $$\frac{65}{2}$$
C) $$\frac{13}{40}$$
D) $$\frac{13}{20}$$
A) $$\frac{13}{4}$$

Question 81.
Radical form of $$3^{\frac{1}{5}}$$ is
A) $$\sqrt[5]{3^{1}}$$
B) $$\sqrt[3]{5^{1}}$$
C) $$\sqrt[5]{1^{3}}$$
D) $$\sqrt[3]{1^{5}}$$
A) $$\sqrt[5]{3^{1}}$$

Question 82.
Which of the following is the $$\frac{\mathbf{p}}{\mathbf{q}}$$ form of 3.72 ? (q ≠ 0 and p and q are coprimes)
A) $$\frac{372}{100}$$
B) $$\frac{31}{5}$$
C) $$\frac{93}{25}$$
D) $$\frac{93}{5}$$
A) $$\sqrt[5]{3^{1}}$$

Question 83.
Which of the following rational numbers lies between 2 and 3 ?
A) $$\frac{2}{3}$$
B) $$\frac{3}{2}$$
C) $$\frac{5}{2}$$
D) $$\frac{5}{3}$$
C) $$\frac{5}{2}$$

Question 84.
1.121231234………….. is not a rational number because it is
A) Recurring Decimal
B) Non terminating Decimal
C) Non recurring Decimal
D) Both B and C
D) Both B and C

Question 85.
The exponential form of $$\sqrt[5]{3^{2}}$$ is
A) $$3^{5 / 2}$$
B) $$3^{2 / 5}$$
C) $$3^{5 /times 2}$$
D) $$3^{5 – 2}$$
B) $$3^{2 / 5}$$

Question 86.
The square root of which number is a rational number ?
A) 14
B) 80
C) 1.96
D) 0.004
A) $$\frac{-7}{5}$$
B) $$-\frac{5}{7}$$
C) $$\frac{7}{5}$$
D) $$\frac{5}{7}$$
A) $$\frac{-7}{5}$$