CBSE |Class 10th MATHS | Chapter 1 | Real Numbers

1. Which of the following is not irrational?

(a) (3 + √7)

(b) (3 – √7)

(c) (3 + √7) (3 – √7)

(d) 3√7

2. The prime factorisation of 96 is

(a) 2⁵ × 3

(b) 2⁶

(c) 2⁴ × 3

(d) 2⁴ × 32

3.  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

4. The multiplication of two irrational numbers is:

(a) irrational number

(b) rational number

(c) Maybe rational or irrational

(d) None

5. The addition of a rational number and an irrational number is equal to:

(a) rational number

(b) Irrational number

(c) Both

(d) None of the above

6. The least number that is divisible by all the numbers from 1 to 5 is:

(a) 70

(b) 60

(c) 80

(d) 90

7. The decimal expansion of 22/7  is

(a) Terminating

(b) Non-terminating and repeating

(c) Non-terminating and Non-repeating

(d) None of the above

8. For any two positive integers a and b, HCF (a, b) × LCM (a, b) = 

(a) 1

(b) (a × b)/2

(c) a/b

(d) a × b

9. The decimal expansion of the rational number 23/(2² . 5) will terminate after

(a) one decimal place

(b) two decimal places

(c) three decimal places

(d) more than 3 decimal places

10. The values of the remainder r, when a positive integer a is divided by 3 are

(a) 0, 1, 2

(b) Only 1

(c) Only 0 or 1

(d) 1, 2

11. For some integer m, every even integer is of the form

(a) m

(b) m + 1

(c) 2m

(d) 2m + 1

12. n² – 1 is divisible by 8, if n is

(a) an integer

(b) a natural number

(c) an odd integer

(d) an even integer

13. Using Euclid’s division algorithm, the HCF of 231 and 396 is

(a) 32

(b) 21

(c) 13

(d) 33

14. The sum or difference of two irrational numbers is always

(a) rational

(b) irrational

(c) rational or irrational

(d) not determined

15. If p and q are integers and is represented in the form of p/q, then it is a:

(a) Whole number

(b) Rational number

(c) Natural number

(d) Even number

16. Euclid’s division lemma states that for two positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy

(a) 1 < r < b

(b) 0 < r ≤ b

(c) 0 ≤ r < b

(d) 0 < r < b

17. The largest number that divides 70 and 125, which leaves the remainders 5 and 8, is:

(a) 65

(b) 15

(c) 13

(d) 25

18. If set A = {1, 2, 3, 4, 5,…} is given, then it represents:

(a) Whole numbers

(b) Rational Numbers

(c) Natural numbers

(d) Complex numbers

19. For some integer n, the odd integer is represented in the form of:

(a) n

(b) n + 1

(c) 2n + 1

(d) 2n

20. HCF of 26 and 91 is:

(a) 15

(b) 13

(c) 19

(d) 11