Practice the AP 10th Class Maths Bits with Answers Chapter 1 Real Numbers on a regular basis so that you can attempt exams with utmost confidence.

## AP State Syllabus 10th Class Maths Bits 1st Lesson Real Numbers with Answers

Question 1.

Find the rational number in between \(\frac { 1 }{ 2 }\) and √1

Answer:

\(\frac { 3 }{ 4 }\)

Question 2.

Write the name set of rational and ir-rational numbers.

Answer:

Real numbers.

Question 3.

Write the logarithmic form of 3^{5} = 243.

Answer:

log_{3}243 = 5

Question 4.

Write the symbol of “implies”.

Answer:

⇒

Question 5.

Write the prime factorisation of 729.

Answer:

3^{6}

Question 6.

If ‘x’ and ‘y’ are two prime numbers, then find their HCF.

Answer:

1

Explanation:

HCF of any two prime numbers is always 1.

Question 7.

Find the value of log_{10} 0.01.

Answer:

-2

Explanation:

log_{10}0.01 = log_{10} \(\frac{1}{10^{2}}\)

= log_{10}10^{-2} = – 2

Question 8.

Find the number of odd numbers in between ‘0’ and 100.

Answer:

50

Question 9.

Write the exponential form of log_{4}8 = x.

Answer:

4^{x} = 8.

Explanation:

Exponential form of log_{4}8 = x is 4^{x} = 8

Question 10.

How much the value of \(\frac{36}{2^{3} \times 5^{3}}\) in decimal form ?

Answer:

0.036.

Question 11.

LCM of two numbers is 108 and their HCF is 9 and one of them is 54, then find the second one.

Answer:

18

Explanation:

LCM x HCF = one number x second number

108 x 9 = 54 x second one , 108 x 9

⇒ Second one = \(\frac{108 \times 9}{54}\) = 18.

Question 12.

\(\frac { 3 }{ 8 }\) is example for decimal.

Answer:

Terminating decimal.

Question 13.

If \(\mathbf{a} \sqrt{\mathbf{c}}=\sqrt{\mathbf{a c}}\) , then find the value of ‘a’, (a, c are positive integers),

Answer:

a = 1

Question 14.

Find the value of 9 – \(0 . \overline{9}\).

Answer:

8

Explanation:

9 – \(\frac{9}{9}\) = 9 – 1 = 8.

Question 15.

Write rational number that equals to \(2 . \overline{6}\)

Answer:

\(\frac { 8 }{ 3 }\)

Question 16.

Write the value of log_{25} 5.

Answer:

\(\frac { 1 }{ 2 }\)

Explanation:

log_{25}5 = log_{5}5^{1} = \(\frac{1}{2}\)log_{5}5 = \(\frac{1}{2}\)

Question 17.

The fundamental theorem of arithmetic is applicable to, which least number ?

Answer:

2

Question 18.

Find the last digit of 6^{50}.

Answer:

6

Question 19.

Which of the following is a terminat¬ing decimal ?

A) \(\frac { 10 }{ 81 }\)

B) \(\frac { 41 }{ 75 }\)

C) \(\frac { 8 }{ 125 }\)

D) \(\frac { 3 }{ 14 }\)

Answer:

C)

Question 20.

Find the value of log2 32.

Answer:

5

Question 21.

Which of the following is not irrational ?

A) √2

B) √3

C) √4

D) √5

Answer:

(C)

Question 22.

Find the value of log_{10} 0.001.

Answer:

-3

Question 23.

Find the number of prime factors of 36.

Answer:

2 and 3

Explanation:

36 = 2^{2} x 3^{2}

∴ Two prime numbers i.e., 2 and 3.

Question 24.

Write the exponential form of

Iog_{10} = -3.

Answer:

10^{-3} = 0.001

Question 25.

Define an irrational number.

Answer:

Which cannot be written in the form

of p/q where p, q ∈ Z, q ≠ 0.

Question 26.

Find the LCM of 24 and 36.

Answer:

72

Question 27.

Find the logarithmic form of a^{b} = c.

Answer:

log_{a}c = b.

Question 28.

If 3 log (x + 3) = log 27, then find the value of x.

Answer:

0

Explanation:

3 log (x + 3) = log 27

⇒ log (x + 3)3 = log 33

⇒ x + 3 = 3 ⇒ x = 0

log_{3}729 = x ⇒ 3^{x} = 729 = 3^{6} ⇒ x = 6

Question 29.

If P_{1} and P_{2} are two odd prime num-bers, such that P_{1} > P_{2}, then the value of \(\mathbf{P}_{1}^{2}-\mathbf{P}_{\mathbf{2}}^{2}\) results number

Answer:

An even number.

Question 30.

Find the value of \(\log _{10} 2+\log _{10} 5\)

Answer:

1

Question 31.

If log_{3} 729 = x, then find the value of x.

Answer:

6

Explanation:

log_{3} 729 = x ⇒ 3^{x} = 729 = 3^{6} ⇒ x = 6

Question 32.

Write the number of digits in the fractional part of the decimal form of \(\frac{7}{40}\).

Answer:

3

Explanation:

\(\frac{7}{40}=\frac{7}{2^{3} \times 5^{1}}\)

In Denominator 2^{n} x 5^{m} is equal to 3.

Question 33.

Write the prime factorization of 144.

Answer:

2^{4} x 3^{2}

Question 34.

Find the number of prime factors of 72.

Answer:

2

Question 35.

log_{3} x^{2} = 2, then find the value of x.

Answer:

3

Explanation:

log_{3}x^{2} = 2 ⇒ 3^{2} = x^{2} ⇒ x = 3

Question 36.

Find the value of \(9 \sqrt{2} \times \sqrt{2}\)

Answer:

18

Question 37.

Find the value of log_{0.1} 0.01.

Answer:

2

Explanation:

log _{0.1} 0.01 = log_{10-1} 10^{-2}

= \(\frac{-2}{-1}\) log_{10} 10 = 2

Question 38.

0.3030030003 ………………. is an ………………. number.

Answer:

Irrational.

Question 39.

\(\frac{27}{82}\) is a …………. decimal.

Answer:

Non-terminating

Question 40.

If log 2 = 0.30103, then find log 32.

Answer:

1.50515

Explanation:

log 32 = log 2^{5} = 5 log 2

= 5 x 0.30103 .

= 1.50515

Question 41.

Expand log 15.

Answer:

log5 + log3

Question 42.

Find the value of log_{10} 10.

Answer:

1

Question 43.

Calculate the value of log8 128.

Answer:

\(\frac{7}{3}\)

Question 44.

Find the value of \(5 \sqrt{5}+6 \sqrt{5}-2 \sqrt{5}[/latex[

Answer:

9√5

Question 45.

743.2111111 … is a number.

Answer:

Rational

Question 46.

Find the value of log_{5} 125.

Answer:

3

Question 47.

Expand log_{10} [latex]\frac{125}{16}\)

Answer:

3 log 5 – 4 log 2

Explanation:

log_{10} \(\frac{125}{16}\) = log_{10} 125 – log_{10}16

= log_{10}5^{3} – log_{10}2^{4}

= 3 log 5 – 4 log 2

Question 48.

Find the L.C.M of the numbers 2^{7} x 3^{4} x 7 and 2^{3} x 3^{4} x 11.

Answer:

2^{7} x 3^{4} x 7 x 11

Question 49.

If log_{a} a^{x}2 – 5x + 8 = 2, then find x.

Answer:

2 or 3.

Explanation:

\(\log _{a} a^{x^{2}-5 x+8}=\log _{a} a^{2}\)

{2 was write down as 2-log_{a} a}

x^{2} – 5x + 8 = 2

x^{2} – 5x + 6 = 0

by solving equation x = 2 or 3

Question 50.

Find the value of log_{a} \(\frac{1}{a}\).

Answer:

– 1

Question 51.

Find the value of log_{1} 1.

Answer:

Not defined.

Question 52.

If log_{10} 0.00001 = x, then find x.

Answer:

-5

Question 53.

Find the value of log_{b} a • log_{a} b.

Answer:

1.

Question 54.

16 x 64 = 4^{k}, then find the value of k.

Answer:

5

Explanation:

16 x 64 = 4^{k}

⇒ 4^{2} x 4^{3} = 4^{k}

⇒ 4^{5} = 4^{k}

⇒ k = 5

I’m

Question 55.

Write exponential form of log_{4}64 = 3.

Answer:

4^{3} = 64

Question 56.

Calculate the value of \(\log _{9} \sqrt{3 \sqrt{3 \sqrt{3}}}\)

Answer:

\(\frac{7}{16}\)

Question 57.

If ‘m’ and ‘n’ are co-primes, then find H.C.F of m^{2} and n^{2}.

Answer:

1

Question 58.

\(\sqrt{5}+\sqrt{7}\) is number.

Answer:

An irrational.

Question 59.

Find the H.C.F. of the numbers

3^{7} x 5^{3} x 2^{4} and 3^{2} x 7^{4} x 2^{8}.

Answer:

2^{4} x 3^{2}

Question 60.

\(\frac{13}{125}\) is a ……………… decimaL

Answer:

Terminating

Question 61.

Write the decimal expansion of 0.225 in its rational form.

Answer:

\(\frac{9}{40}\)

Question 62.

How many prime factors are there in the prime factorization of 240.

Answer:

3

Question 63.

14.381 may certain the denominator when expressed in p/q form.

Answer:

2^{3} x 5^{3}

Question 64.

By which numbers 7 x 11 x 17 +34 is divisible, write them.

Answer:

17 and 79

Explanation:

Given number = 7 x 11 x 17 + 34

= 17 (7 x 11 + 2)

= 17 x 79

Given number has 17 and 79 are factors.

Question 65.

Write log\(\frac{x^{2} y^{3} z^{4}}{w^{5}}\) in the expanded form.

Answer:

2 log x + 3 log y + 4 log z – 5 log w

Explanation:

log x^{2}y^{3}z^{4} – log w^{5} = log x^{2} + log y^{3} + log z^{4} – log w^{5}

= 2log x + 3log y + 4log z – 51og w

Question 66.

Write the logarithmic form of 12^{2} = 144.

Answer:

log_{12} 144 = 2

Question 67.

Expand log 81 x 25.

Answer:

4log 3 + 2 log 5

Question 68.

What is the L.C.M. of greatest two digit number and the greatest three digit number.

Answer:

9 x 11 x 111

Question 69.

Write logarithmic form of 19^{2} = 361.

Answer:

log_{19}361 = 2

Question 70.

3 X 5 x 7 x 11 + 35 is number.

Answer:

Composite

Question 71.

Write the decimal expansion of \(\frac{101}{99}\).

Answer:

\(1 . \overline{02}\)

Question 72.

If P_{1}, p_{2}, p_{3}, …………… p_{n} are co-primes, then

their LCM is

Answer:

P_{1}p_{2} …………… p_{n}

Question 73.

In the above problem find HCF.

Answer:

1

Question 74.

n^{2} – 1 is divisible by 8, if ‘n’ is number.

Answer:

An odd number.

Question 75.

If x and y are any two co-primes, then find their L.C.M.

Answer:

x.y

Question 76.

Write \(\frac{70}{71}\) is which type of decimal ?

Answer:

Non-terminating, repeating.

Question 77.

0.12 112 1112 11112………………is…………… type of number.

Answer:

Irrational

Question 78.

Write \(\frac{123}{125}\) is which type of decimal ?

Answer:

Terminating.

Question 79.

Write the product of L.C.M. and H.C.F. of the least prime and least composite number.

Answer:

8

Question 80.

\(\sqrt{2}-2\) is…………………number.

An irrational.

Question 81.

Find the number of prime factors of 1024.

Answer:

Only one number, i.e., ‘2’. (i.e., 2^{10})

Question 82.

Write the LCM of 208 and 209.

Answer:

208 x 209 (Product of even and odd number is its product)

Question 83.

Write the expansion of \(\frac{87}{625}\) terminates after how many places ?

Answer:

4 places.

Question 84.

The decimal expansion of \(\frac{87}{625}\) terminates after how many places ?

Answer:

4 places.

Question 85.

What is the H.C.F. of ‘n’ and ‘n + 1’, where ‘n’ is a natural number ?

Answer:

1

Question 86.

What is the prime factorisation of 20677.

Answer:

23 x 29 x 31

Question 87.

Find the HCF of 1001 and 1002.

Answer:

1

Question 88.

p, q are co-primes and q = 2^{n} . 5^{m}, where m > n, then write the decimal expansion of p/q terminates after how many places ?

Answer:

‘m’ places.

Question 89.

Write the decimal fprm of \(\frac{80}{81}\) and write repeats after how many places ?

Answer:

81 = 3^{4}, so not possible.

Question 90.

If a rational number p/q has a termi¬nating decimal, then write the prime factorisation of ‘q’ is of the form.

Answer:

q = 2^{m} . 5^{n}

Question 91.

Write the decimal expansion of \(\frac{7}{16}\) without actual division.

Answer:

0.4375

Question 92.

In the expansion of \(\frac{123}{125}\) terminates after how many places ?

Answer:

3 places.

Question 93.

What is the L.C.M of least prime and the least composite number ?

Answer:

Least composite

Question 94.

Write the decimal expansion of \(\frac{27}{14}\)

Answer:

\(1.9 \overline{285714}\)

Question 95.

Which type of number was \(5.6789 \overline{1}\) ?

Answer:

Rational number

Question 96.

After how many places the decimal expansion of \(\frac{23}{125}\) terminates ?

Answer:

3 places.

Question 97.

Write the type of decimal expansion of \(\frac{9}{17}\)

Answer:

Non-terminating & repeating.

Question 98.

Write the period of the decimal expansion of \(\frac{19}{21}\)

Answer:

904761

Question 99.

After how many digits will the deci-mal expansion of \(\frac{11}{32}\) terminates ?

Write it.

Answer:

5 places.

Question 100.

If \(\sqrt{2}\) = 1.414, then find \(3 \sqrt{2}\).

Answer:

4.242

Question 101.

Find the value of \(\frac{3}{8}\)

Answer:

0.375

Question 102.

Find the value of log 64 – log 4.

Answer:

16

Question 103.

Find the value of 128 ÷ 32.

Answer:

4

Question 104.

Find the value of 104.

Answer:

10000

Question 105.

Find the value of \(\sqrt{\mathbf{5}}\) .

Answer:

2.236

Question 106.

Find the value of log_{27} 9.

Answer:

\(\frac{2}{3}\)

Question 107.

Find the value of | – 203 |.

Answer:

203

Question 108.

Complete the rule a(b + c).

Answer:

ab + ac

Question 109.

Find the value of log_{3} \(\frac{1}{9}\).

Answer:

-2

Question 110.

How much the LCM of 12, 15 and 21.

Answer:

420

Question 111.

Find the value of log_{a} 1, a > 0.

Answer:

0

Question 112.

a + (-a) = 0 = (- a) + a is called ……………… property.

Answer:

Inverse

Question 113.

Find the value of \(\sqrt{\mathbf{a}} \times \sqrt{\mathbf{b}}\)

Answer:

\(\sqrt{a b}\)

Question 114.

Find the value of 5^{5}.

Answer:

3125

Question 115.

Find the value of \(\frac{13}{4}\) .

Answer:

3.25

Question 116.

Find the value of \(\sqrt{12544}\)

Answer:

112

Question 117.

Find the value of log_{6}1.

Answer:

0

Question 118.

Find the value of log_{10}10000.

Answer:

4

Question 119.

How much the HCF of 12 and 18.

Answer:

6

Question 120.

Which number has no multiplicative inverse ?

Answer:

0

Question 121.

How much the LCM of 306 and 657.

Answer:

22338

Question 122.

Find the value of log_{x} \(\frac{\mathbf{a}}{\mathbf{b}}\).

Answer:

log_{x}a – log_{x}b

Question 123.

Find the value of log_{32} \(\frac{1}{4}\)

Question 124.

Find the value of \(\sqrt{2025}\)

Answer:

\(\frac{-2}{5}\)

Question 125.

Find the value of \(2 \sqrt{3}+7 \sqrt{3}+\sqrt{3}\)

Answer:

\(10 \sqrt{3}\)

Question 126.

Find the value of 2^{2} x 5 x 7.

Answer:

140

Question 127.

Find the value of log_{10} 100.

Answer:

2

Question 128.

6^{n} cannot end with this number. What is that number ? (When ‘n’ is a posi¬tive number).

Answer:

0

Question 129.

If 2^{x} = y and log_{2} y = 3 then find (x – y)^{2}.

Answer:

25

Question 130.

Find the value of log_{3} \(\frac{1}{27}\).

Answer:

-3

Question 131.

Expanded form of log_{10}1000.

Answer:

3 log 2 + 3 log 5

Question 132.

Find the value of log_{2}512.

Answer:

9

Question 133.

Write \(\frac{3}{2}\) (log x) – (log y) as single form.

Answer:

\(\log \sqrt{\frac{x^{3}}{y^{2}}}\)

Question 134.

Find HCF of 1 and 143.

Answer:

1

Question 135.

Which of the following is a correct one ?

A) N⊂Z⊂W

B) N⊂W⊂Z

C) R⊂N⊂W

D) All the above

Answer:

(B)

Question 136.

Find the value of log_{2}16.

Answer:

4

Question 137.

Find the value of \(\log _{7} \sqrt{49}\)

Answer:

1

Question 138.

Find the value of log_{2}1024.

Answer:

10

Question 139.

Find the value of log_{18}324.

Answer:

2

Question 140.

Express logarithmic form of a^{x} = b.

Answer:

loga^{b} = x .

Question 141.

Find the value of \((\sqrt{7}+\sqrt{5}) \cdot(\sqrt{7}-\sqrt{5})\)

Answer:

2

Choose the correct answer satisfying the following statements.

Question 142.

Statement (A) : 6n ends with the digit zero, where ‘n’ is natural number. Statement (B): Any number ends with digit zero, if its prime factor is of the form 2^{m} x 5^{n}, where m, n are natural numbers.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(iii)

Explanation:

6^{n} = (2 x 3)^{n} = 2^{n} x 3^{n}

Its prime factors do not contain 5n i.e., of the form 2^{m} x 5^{n}, where m, n are natural numbers. Here (A) is incorrect but (B) is correct.

Hence, (iii) is the correct option.

Question 143.

Statement (A) : \(\sqrt{a}\) is an irrational number, where ‘a’ is a prime number.

Statement (B) : Square root of any prime number is an irrational number.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Explanation:

As we know that square root of every prime number is an irrational number. So, both A and B are correct and B explains A. Hence (i) is the correct option.

Question 144.

Statement (A) : For any two positive integers a and b,

HCF (a, b) x LCM (a, b) – a x b.

Statement (B) : The HCF of two num-bers is 5 and their product is 150. Then their LCM is 40.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(ii)

Explanation:

We have,

LCM (a, b) x HCF (a, b) = a xb LCM x 5 – 150 150

∴ LCM = \(\frac{150}{5}\) = 30

=> LCM = 30, i.e., (B) is incorrect and (A) is correct.

Hence, (ii) is the correct option.

Question 145.

Statement (A) : When a positive inte-ger ’a’ is divided by 3, the values of re-mainder can be 0, 1 (or) 2.

Statement (B) : According to Euclid’s Division Lemma a = bq + r, where 0 ≤ r < b and ‘r’ is an integer.

i) Both A and B are true.

ii) A is true, 3 is false

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Explanation:

Given positive integers A and B, there exists unique integers q and r satisfy¬ing a = bq + r where 0 ≤ r < b.

This is known as Euclid’s Division Algorithm. So, both A and B are cor¬rect and B explains A.

Hence, (i) is the correct option.

Question 146.

Statement (A): A number N when di¬vided by 15 gives the remainder 2. Then the remainder is same when N is divided by 5.

Statement (B) : \(\sqrt{3}\) is an irrational number.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(ii)

Question 147.

Statement (A): \(\frac{41}{1250}\) is a terminating decimal.

Statement (B) : The rational number p/q is a terminating decimal if q = 2^{m} x 5^{n}, where m, n are non-nega¬tive integers.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Question 148.

Statement (A) : \(\sqrt{3}\) is an irrational number.

Statement (B) : The square root of a prime number is an irrational.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Explanation:

Clearly, both A and B are correct but B does not explain A.

Hence, (i) is correct option.

Question 149.

Statement (A) : \(\frac{27}{250}\) is a terminating decimal.

Statement (B) : The rational number p/q is a terminating decimal, if q = (2^{m} x 5^{n}) for some whole number m and n.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Question 150.

Statement (A): \(\frac{13}{3125}\) is a terminating decimal fraction.

Statement (B): If q = 2^{n} . 5^{m} where n, m are non-negative integers, then p/q is terminating decimal fraction.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Explanation:

(B) is correct.

Since the factors of the denominator 3125 is of the form 2° x 5^{5}.

∴ \(\frac{13}{3125}\) is a terminatmg decimal.

∴ Since (A) follows from (B).

∴ Hence, (i) is the correct option.

Question 151.

Statement (A) : Denominator of 34.12345 is of the form 2^{m} x 5^{n}, where m, n are non-negative integers.

Statement (B) : 34.12345 is a termi-nating decimal fraction.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Explanation:

(B) is clearly true.

Again 34.12345 = \(\frac{3412345}{100000}\)

= \(\frac{682469}{20000}=\frac{682469}{2^{5} \times 5^{4}}\)

Its denominator is of the form 2^{m} x 5^{n}

[m = 5, n = 4 are non-negative integers.]

∴ (A) is true.

Since (B) gives (A).

Hence, (i) is the correct option.

Question 152.

Statement (A): The H.C.F. of two num-bers is 16 and their product is 3072. Then their L.C.M. = 162.

Statement (B): If a, b are two positive integers, then H.C.F x L.C.M = a x b.

i) Both A and B are true.

ii) A is true, B is false.-

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(iii)

Explanation:

Here (B) is true (standard result)

(A) is false.

∴ \(\frac{3072}{16}\) = 192 ≠ 162

Hence, (iii) is the correct option.

Question 153.

Statement (A) : 2 is a rational num¬ber.

Statement (B): The square roots of all positive integers are irrationals.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(ii)

Explanation:

Here (B) is not true.

∴ \(\sqrt{4} \neq 2\) which is not an irrational

number.

Clearly, (A) is true.

∴ (ii) is the correct option.

Question 154.

Statement (A) : If L.C.M. {p, q} = 30 and H.C.F. {p, q} = 5, then pq = 150.

Statement (B): L.C.M. of a, b x H.C.F. of a, b = a • b.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Question 155.

Statement (A) : n^{2} – n is divisible by 2 for every positive integer.

Statement (B): \(\sqrt{2}\) is a rational num¬ber.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(ii)

Question 156.

Statement (A): n^{2} + n is divisible by 2 for every positive integer n.

Statement (B): If x and y are odd posi-tive integers, from x^{2} + y^{2} is divisible by 4.

i) Both A and B are true.

ii) A is true, B is false.

iii) A is false, B is true.

iv) Both A and B are false.

Answer:

(i)

Read the below passages and answer to the following questions.

If p is prime, then \(\sqrt{\mathbf{p}}\) is irrational and if a, b are two odd prime num-bers, then a^{2} – b^{2} is composite.

Question 157.

Is \(\sqrt{7}\) is a rational number ?

Answer:

No, it is an irrational number.

Question 158.

The results of 119^{2} – 111^{2} is a ………..

number.

Answer:

Composite

L.C.M. of several fractions

= \(\frac{\text { LCM of their numerators }}{\text { HCF of their denominators }}\)

H.C.F. of several fractions = \(\frac{\text { HCF of their numerators }}{\text { LCM of their denominators }}\)

Question 159.

Find the LCM of the fractions \(\frac{5}{16}, \frac{15}{24}\) and \(\frac{25}{8}\)

Answer:

\(\frac{75}{8}\).

Explanation:

L.C.M. of \(\frac{5}{16}, \frac{15}{24}\) and \(\frac{25}{8}\)

= \(\frac{\text { L.C.M. of numerators }}{\text { H.C.F. of denominators }}\)

L.C.M’. of 5, 15 and 25 is 75.

H.C.F. of 16, 24 and 8 is 8.

The H.C.F. of the given fractions = \(\frac{75}{8}\)

Question 160.

Find the HCF of \(\frac{2}{5}, \frac{6}{25}\) and \(\frac{8}{35}\).

Answer:

\(\frac{2}{175}\)

Explanation:

Question 161.

Find the HCF of the fractions \(\frac{8}{21}, \frac{12}{35}\) and \(\frac{32}{7}\)

Answer:

\(\frac{4}{105}\)

[H^{+}] ion concentration in a soap used by Sohan is 9.2 x 10^{-22}.

Explanation:

H.C.F. of given fraction is

\(\frac{\text { H.C.F. of } 8,12,32}{\text { L.C.M. of } 21,35,7}\)

= \(\frac{4}{105}\)

Question 162.

Which mathematical concept is used to find pH of a soap ?

Answer:

Logarithms.

Question 163.

How much the pH of soap used by Sohan ?

Answer:

pH = 21.04.

Question 164.

Write the correct matching options :

Answer:

A – (iii), B – (iv)

Question 165.

Write the correct matching options :

Answer:

A – (i), B – (ii)

Question 166.

Write the correct matching options :

Answer:

A – (iii), B – (i)

Question 167.

Write the correct matching options :

Answer:

A – (ii), B – (v), C – (iii)

Question 168.

Write the correct matching options:

A – (i), B – (iv)

Question 169.

Write the correct matching options :

Answer:

A – (ii), B – (iii)

Question 170.

Write the correct matching options :

Answer:

A – (ii), B – (v)

Question 171.

Write the correct matching options:

Answer:

A – (iii), B – (iv)

Question 172.

Write the correct matching options:

Answer:

A — (i), B – (ii), C — (v)

Question 173.

What is the value of \(\log _{\frac{2}{3}}\left(\frac{27}{8}\right)\)

Answer:

-3

Question 174.

Write the decimal form of the rational number \(\frac{7}{2^{2} \times 5}\)

AP Model Paper

Answer:

0.35

Question 175.

What is the value of \(\log _{\sqrt[3]{5}} \sqrt{5}\) ?

Solution:

Question 176.

Which statement do you agree with ? P: The product of two irrational num-bers is always a rational number.

Q : The product of a rational and an irrational number is always an irra-tional number,

i) Only P ii) Only Q iii) Both P and Q

Answer:

(ii)

Question 177.

Express 3 log_{2}2 = x in exponential form.

Solution:

3 log_{2}2 = x

log_{2}2^{3} = x ⇒ log_{2}8 = x ⇒ 2^{x} = 8