Direction: In the following questions, a statement of Assertion (A) is followed by a statement of Reason (R). Mark the correct choice as:
(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.
1.) Assertion : the decimal expansion of 22/7 is non terminating and repeating
Reason: 22/7 = 3.1428
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
2.) 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) both Assertion and reason are correct and reason is correct explanation for Assertion
3.) Assertion: HCF of 26 and 91 is 13
Reason: the prime factorization of 26 = 2*13 and 91=7*13
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
4.) 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) Assertion is correct but reason is false
5.) Assertion: the multiplication of two irrational no. is may be rational or irrational
Reason: the product of two irrational no.is always rational
Ans: c) Assertion is correct but reason is false
6.) Assertion: if set A={ 1,2,3,4,5—-} is given then it represent natural number
Reason: natural number is always start from 1
Ans: a) both Assertion and reason are correct and reason is correct explanation for Assertion
7.) 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.
AnswerAnswer: (d) Assetion (A) is false but Reason (R) is true.
Explanation: Since HCF × LCM = a × b
⇒ 3072 = 16 × 162
⇒ 3072 ≠ 2592
8.) Assertion: Denominator of 34.12345. When expressed in the form p/q, q ≠ 0, is of the form
2m × 5n, where m and n are non-negative integers.
Reason: 34.12345 is a terminating decimal fraction.
9.) Assertion: 13/3125 is a terminating decimal fraction.
Reason: If q = 2n.5m where n and m are non-negative integers, then p/q is a terminating decimal fraction.
AnswerAnswer: (a)
10.) Assertion: 2 is an example of a rational number.
Reason: The square roots of all positive integers are irrational numbers.
AnswerAnswer: (c)
Explanation: Here, reason is false. As √16 = ±4, which is not an irrational number.
11.) 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.
AnswerAnswer: (c)
We have, LCM (p, q) × HCF (p, q) = p × q
LCM × 5 = 150
LCM = 150 / 5 = 30 ≠ 40
Therefore, Reason is false.
12.) Assertion: Every composite no. Can be expressed as product of primes
Reason: 11 × 4 × 3 × 2 +4 is a composite number.
Ans: a) both Assertion and reason are correct and reason is correct explanation for assertion
13.) Assertion: (7×13×11)+11 & (7×6×5×4×3×2×1)+3 have exactly composite no.
Reason: (3×12×101)+4 is not a composite no.
Ans: c) Assertion is correct but reason is false
14.)
Assertion: 1/6 has non terminating repeating decimal expansion
Reason: 1/7 is an irrational no.
Ans: c) Assertion is correct but reason is false