Assertion & Reason Questions For Math Class 10 | Real Numbers

 ASSERTION & REASON QUESTIONS CLASS 10 
CHAPTER 1  REAL NUMBERS

Competency based questions on REAL NUMBERS class 10 chapter 1 , Assertion and Reason based questions for class 10 REAL NUMBERS chapter 1

Assertion and Reason Questions

Directions

Each of these questions contain two statements Assertion (A) and Reason (R). Each of the questions has four alternative choices, any one of which is correct answer. 

You have to select one of the codes (a ), (b ), (c ), (d ) given below

a) Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of Assertion (A).

b) Both Assertion (A) and Reason (R) are true but Reason (R) is not the correct explanation of Assertion (A).

c) Assertion (A) is true but Reason (R) is false.

d) Assertion (A) is false but Reason (R) is true.

Chapter-1 Class 10 

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)

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