Question

Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R).
Choose the correct option from the following:
(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.

Assertion (A): For any two prime numbers $p$ and $q$, their HCF is 1 and LCM is $p + q$.
Reason (R): For any two natural numbers, HCF × LCM = product of numbers.

• 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.

Hint:

Remember: LCM of primes $p$ and $q$ is $p \cdot q$, not $p + q$.

Answer 1

The Correct Option is D

Solution: Evaluate the Assertion (A) and Reason (R) by examining each statement and determining if the Reason explains the Assertion.

Assertion (A): The HCF of any two prime numbers $p$ and $q$ is 1 and the LCM is $p + q$.

The HCF of prime numbers is 1 because they share no factors other than 1. However, the LCM is not their sum, but their product. Therefore, Assertion (A) is incorrect.

Reason (R): For any two natural numbers, HCF × LCM = product of the numbers.

This is a fundamental arithmetic property and is always true. Therefore, Reason (R) is correct.

Conclusion: Since Assertion (A) is false and Reason (R) is true, the answer is:

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