ASSERTION & REASON QUESTIONS CLASS 10 
CHAPTER 1  REAL NUMBERS

1) Assertion: for some integer n the odd integer
is represented in the form of 2n + 1



Reason: 2n represent the even number and 2n + 1 will
represent odd

Ans: a)

2)
Assertion: HCF of 26 and 91 is 13



Reason: the prime factorization of 26 = 2✕13 and 91 = 7 ✕ 13

Ans: a)

3) Assertion: the addition of rational number and
irrational number is equal to irrational number



Reason: the sum of irrational number and rational
number is always rational number

Ans: c)

4) Assertion: the multiplication of two irrational
no. is may be rational or irrational



Reason: the product of two irrational no.is always
rational

Ans: a)

5) Assertion: a ✕ 543 = 543 ✕ 289 then the value of a is 289



Reason: a ✕ b = b ✕ a is commutative property of real number

Ans: a)

6) Assertion: m(n + r) = mn + nr



Reason: 5 ✕ (2 + 3) = 5 ✕ 2 + 5 ✕ 3 here both side will get 25

Ans: a)

7) Assertion: if P and q are integers and is
represented in the form of P/q then it is a rational number



Reason: 17/3 is a rational number

Ans: a)

8)
Assertion: the largest number that divide 70 and125 which leaves remainder 5
and 8 is 13



Reason: HCF (65,117) =13

Ans: a)

9) Assertion :the least number that is divisible
by all number from 1 to 5 is 60



Reason: LCM( 1, 2, 3, 4, 5) =60

Ans: a)

10) Assertion: the prime factorization of  96 is 2⁵  ✕ 3



Reason: 96 = 2 ✕ 2 ✕ 2 ✕ 2 ✕ 2 ✕ 3

Ans: a)

11) Assertion: if HCF (26,169) =13 then LCM
(26,169)= 338



Reason: HCF(a, b) ✕ LCM(a, b) = a ✕ b

Ans: a)

12) Assertion: if the LCM of a and 18 is 36 and
HCF of a and 18 is 2 then a=4



Reason: 2 ✕ 36 = a ✕ 18 

⇒ 2 ✕ (36/18) = a ⇒ a = 4

Ans: a)

13) Assertion: Square of real no. is always non
negative

Reason: Square of 25 is 625

Ans: a)

14) Assertion: every real number is either
rational or irrational



Reason: rational and irrational number taken
together form the set of real number

Ans: a)

15) Assertion: if two positive integer m and n are
expressible in the form m= pq³ and n= p³q²
where P, q are prime number then HCF ( m, n )= pq²



Reason: HCF is the product of smallest power of
each common prime factor in the numbers

Ans: a)

16) Assertion: if q = 2ⁿ 5^m
where n, m are non negative integers then P/q is a terminating decimal fraction.



Reason: 13/3125 is a terminating decimal fraction.

Ans: a)

17) Assertion: The given pair of no. 231, 396 are
coprime to each other



Reason: 231, 396 have only 1 common factor

Ans: a)

18)
Assertion: HCF of two coprime no. is 1



Reason: Two no. having only 1 as the common factor
is known as coprime no.

Ans: a)

19) Assertion: HCF of two consecutive even no. is 2



Reason: HCF of 22 & 24 is 2

Ans: a)

20) Assertion: √5 is an irrational no.



Reason: The square root of every positive integer
is always irrational

Ans: c)

21) Assertion: Every composite no. Can be
expressed as product of primes



Reason: 11 × 4 × 3 × 2 + 4 is a composite number.

Ans: a)

22) Assertion: (7 × 13 × 11) + 11 &
(7 × 6 × 5 × 4 × 3 × 2 × 1 ) + 3 are composite no.



Reason: (3 × 12 × 101) + 4 is not a composite no.

Ans: c)

23)
Assertion: (18, 25) is a pair of coprime



Reason: pair of coprime has common factor 2

Ans: c)

24) Assertion: 3 + 2√7 is an irrational no.



Reason:  3 + 2√7 can not be written in p/q form

Ans: a)

25) Assertion: whole no. are known as non negative
integers and it does not include any fractional or decimal part



Reason: set of whole numbers are {-1, -2, -3 _____)

Ans: c)

26)
Assertion: the LCM of two no. is 1200 . 500 is not be their HCF


Reason: LCM of two or more no. is always divisible
by their HCF

Ans: a)

27) Assertion: the largest no. that will divisible
398, 436,and 542 leaving remainder 7, 11, 15 is 17



Reason: HCF of 391, 425, 527 is 17

Ans: a)

28) Assertion: if P is prime then √p is irrational
so √7 is irrational number



Reason: √7 is not expressed in the form of p/q so
it is irrational no.

Ans: a)

Question 29

Assertion: The H.C.F. of two numbers is 16 and their
product is 3072. Then their L.C.M. = 162.
Reason: If a and b are two positive integers, then H.C.F. × L.C.M. = a × b.
Answer: (d)

Question 30
Assertion: For any two positive integers p and q, HCF (p, q) × LCM (p, q) = p ×
q
Reason: If the HCF of two numbers is 5 and their product is 150, then their LCM
is 40.
Answer: (c)