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## Real Numbers Class 10 MCQs Questions with Answers

Question 1.

For any positive integer a and b, there exist unique integers q and r such that a = 3q + r, where r must satisfy.

(a) 0 ≤ r < 3

(b) 1 < r < 3

(c) 0 < r < 3

(d) 0 < r ≤ 3

## Answer

Answer: (a) 0 ≤ r < 3

Question 2.

The values of x and y is the given figure are

(a) x + 10, y = 14

(b) x = 21, y = 84

(c) x = 21, y = 25

(d) x = 10, y = 40

## Answer

Answer: (b) x = 21, y = 84

Question 3.

If HCF (a, b) = 12 and a × b = 1800 then LCM (a, b) is

(a) 3600

(b) 900

(c) 150

(d) 90

## Answer

Answer: (c) 150

Question 4.

If m^{n} = 32, where m and n are positive integers, then the value of (n)^{mn} is

(a) 9765625

(b) 9775625

(c) 9785625

(d) 9865625

## Answer

Answer: (a) 9765625

Question 5.

If (\(\frac{9}{7}\))^{3} × (\(\frac{49}{81}\))^{2x-6} = (\(\frac{7}{9}\))^{9} then value of x is

(a) 12

(b) 9

(c) 8

(d) 6

## Answer

Answer: (d) 6

Question 6.

The decimal expansion of \(\frac{17}{8}\) will terminate after how many places of decimals?

(a) 1

(b) 2

(c) 3

(d) will not terminate

## Answer

Answer: (c) 3

Question 7.

The decimal expansion of n is

(a) terminating

(b) non-terminating and non-recurring

(c) non-terminating and recurring

(d) does not exist.

## Answer

Answer: (b) non-terminating and non-recurring

Question 8.

If HCF of 55 and 99 is expressible in the form 55 m – 99, then the value of m:

(a) 4

(b) 2

(c) 1

(d) 3

## Answer

Answer: (b) 2

Question 9.

Given that LCM of (91, 26) = 182 then HCF (91, 26) is

(a) 13

(b) 26

(c) 7

(d) 9

## Answer

Answer: (a) 13

Question 10.

The decimal expansion of number \(\frac{441}{2^2×5^3×7}\) is

(a) A terminating decimal

(b) Non-terminating but repeating

(c) Non-terminate non repeating

(d) terminating after two places of decimal

## Answer

Answer: (a) A terminating decimal

Question 11.

If A = 2n + 13, B = n + 7 where n is a natural number then HCF of A and B

(a) 2

(b) 1

(c) 3

(d) 4

## Answer

Answer: (b) 1

Question 12.

(-1)^{n} + (-1)^{8n} = 0 when n is

(a) any positive integer

(b) any odd natural number

(c) any even numeral number

(d) any negative integer

## Answer

Answer: (b) any odd natural number

Question 13.

If the LCM of 12 and 42 is 10 m + 4 then the value of m is

(a) 50

(b) 8

(c) \(\frac{1}{5}\)

(d) l

## Answer

Answer: (b) 8

Question 14.

The decimal expansion of the rational number \(\frac{6243}{2^2×5^4}\) will terminate after

(a) 4 places of decimal

(b) 3 places of decimal

(c) 2 places of decimal

(d) 1 place of decimal

## Answer

Answer: (a) 4 places of decimal

Question 15.

n² – 1 is divisible by 8, if n is

(a) an integer

(b) a natural number

(c) an odd natural number

(d) an even natural number

## Answer

Answer: (c) an odd natural number

Question 16.

If n is a natural number, then exactly one of numbers n, n + 2 and n + 1 must be a multiple of

(a) 2

(b) 3

(c) 5

(d) 7

## Answer

Answer: (b) 3

Question 17.

The rational number between 72 and 73 is

(a) \(\frac{6}{5}\)

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

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

(d) \(\frac{4}{5}\)

## Answer

Answer: (c) \(\frac{3}{2}\)

Question 18.

If a and 6 are two positive numbers and H and L are their HCF and LCM respectively. Then

(a) a × b = H × L

(b) a = b × H

(c) a = \(\frac{b×L}{H}\)

(d) H = \(\frac{L}{a×b}\)

## Answer

Answer: (a) a × b = H × L

Question 19.

LCM of 2³ × 3² and 2² × 3³ is

(a) 2³

(b) 3³

(c) 2³ × 3³

(d) 2² × 3²

## Answer

Answer: (c) 2³ × 3³

Question 20.

The LCM of 2.5, 0.5 and 0.175 is

(a) 2.5

(b) 5

(c) 7.5

(d) 0.875

## Answer

Answer: (d) 0.875

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