NCERT Exemplar Problems Class 10 Mathematics

Chapter 1: Real Numbers

Multiple Choice Questions with Correct Answers

EXERCISE 1.1

Choose the correct answer from the given four options:

1. For some integer \( m \), every even integer is of the form

(A) \( m \)
(B) \( m + 1 \)
(C) \( 2m \)
(D) \( 2m + 1 \)

Correct Answer: (C)

2. For some integer \( q \), every odd integer is of the form

(A) \( q \)
(B) \( q + 1 \)
(C) \( 2q \)
(D) \( 2q + 1 \)

Correct Answer: (D)

3. \( n^2 - 1 \) is divisible by 8, if \( n \) is

(A) an integer
(B) a natural number
(C) an odd integer
(D) an even integer

Correct Answer: (C)

4. If the HCF of 65 and 117 is expressible in the form \( 65m - 117 \), then the value of \( m \) is

(A) 4
(B) 2
(C) 1
(D) 3

Correct Answer: (B)

5. The largest number which divides 70 and 125, leaving remainders 5 and 8, respectively, is

(A) 13
(B) 65
(C) 875
(D) 1750

Correct Answer: (A)

6. If two positive integers \( a \) and \( b \) are written as \( a = x^3 y^2 \) and \( b = x y^3 \); \( x, y \) are prime numbers, then HCF \( (a, b) \) is

(A) \( xy \)
(B) \( xy^2 \)
(C) \( x^3 y^3 \)
(D) \( x^2 y^2 \)

Correct Answer: (B)

7. If two positive integers \( p \) and \( q \) can be expressed as \( p = ab^2 \) and \( q = a^3 b \); \( a, b \) being prime numbers, then LCM \( (p, q) \) is

(A) \( ab \)
(B) \( a^2 b^2 \)
(C) \( a^3 b^2 \)
(D) \( a^3 b^3 \)

Correct Answer: (C)

8. The product of a non-zero rational and an irrational number is

(A) always irrational
(B) always rational
(C) rational or irrational
(D) one

Correct Answer: (A)

9. The least number that is divisible by all the numbers from 1 to 10 (both inclusive) is

(A) 10
(B) 100
(C) 504
(D) 2520

Correct Answer: (D)

10. The decimal expansion of the rational number \( \dfrac{14587}{1250} \) will terminate after:

(A) one decimal place
(B) two decimal places
(C) three decimal places
(D) four decimal places

Correct Answer: (D)

Source: NCERT Exemplar Problems Class 10 Mathematics