Assertion :Let $A = x ∣ x is a prime number < 25$ , then the number of distinct rationals except one whose numerator & denominator are elements of A is 36 . Reason: $\frac{p}{q}$ is a rational $\forall q \neq 0,$ HCF of (p,q)is equal to 1.

Both (A) & (R) are individually true & (R) is correct explanation of (A),

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Both (A) & (R) are individually true but (R) is not the correct (proper) explanation of (A).

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(A)is true but (R) is false,

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(A)is false but (R) is true.

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Solution

The correct option is D (A)is false but (R) is true.
As A is a prime $< 25 ∴ A = {2, 3, 5, 7, 11, 13, 17, 19, 23} ∴ n (A) = 9$
We needed two distinct numbers out of 9
$∴$ Required number of ways $= 2 \times^{9} C_{2} = 72$
$∴$ Assertion (A) is false and Reason (R) is correct

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Similar questions

DIRECTIONS (Qs. 52 AND 53): The following item consist of two statements: one labelled as the Assertion a) and the other as Reason (R). You are to examine these two statements carefully and select the answers to these items using the codes given below:

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

53. Assertion a): Saluva Narasimha put an end to the old dynasty and assumed the royal title.

Reason

(R): He wanted to save the kingdom from further degeneration and disintegration. [2003]

a) Both A and R are individually true but R is the correct explanation of A

b) Both A and R are individually true but R is not the correct explanation of A

c) A is true but R is false

d) Both A and R are false

52. Assertion a): Shah Alam II spent the initial years as an emperor far away from his capital.

Reason

(R): There was always a lurking danger of foreign invasion from the north-west frontier. [2003]

Q. Assertion (A)

\frac{1242}{49}

is a non-terminating, repeating decimal.
Reason (R)
The rational number

\frac{p}{q}

is a terminating decimal if q = (2m × 5n) for some whole numbers m and n.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both Assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

Q. Assertion(A): Some algae are unicellular.
Reason(R): They belong to the kingdom Monera.

Q. Assertion (A)
The polynomial p(x) = x³ + x has one real zero.

Reason (R)
A polynomial of nth degree has at most n zeros.

(a) Both Assertion (A) and Reason (R) are true and Reason (R) is a correct explanation of Assertion (A).
(b) Both assertion (A) and Reason (R) are true but Reason (R) is not a correct explanation of Assertion (A).
(c) Assertion (A) is true and Reason (R) is false.
(d) Assertion (A) is false and Reason (R) is true.

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Assertion :Let A=x∣x is a prime number<25 , then the number of distinct rationals except one whose numerator & denominator are elements of A is 36 . Reason: pq is a rational ∀q≠0, HCF of (p,q)is equal to 1.

The correct option is D (A)is false but (R) is true.As A is a prime <25∴A={2,3,5,7,11,13,17,19,23}∴n(A)=9 We needed two distinct numbers out of 9∴ Required number of ways =2×9C2=72 ∴ Assertion (A) is false and Reason (R) is correct

Assertion :Let $A = x ∣ x is a prime number < 25$ , then the number of distinct rationals except one whose numerator & denominator are elements of A is 36 . Reason: $\frac{p}{q}$ is a rational $\forall q \neq 0,$ HCF of (p,q)is equal to 1.

The correct option is D (A)is false but (R) is true.
As A is a prime $< 25 ∴ A = {2, 3, 5, 7, 11, 13, 17, 19, 23} ∴ n (A) = 9$
We needed two distinct numbers out of 9
$∴$ Required number of ways $= 2 \times^{9} C_{2} = 72$
$∴$ Assertion (A) is false and Reason (R) is correct