Q1. [1]
Directions: A statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.
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 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.
Previously asked in CBSE board exam
2025 30/6/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
Option D: Assertion (A) is false, but Reason (R) is true.
The LCM of two primes p and q is p × q, not p + q. So Assertion is false. Reason (R) is a standard correct result: HCF × LCM = product of two numbers.
Explanation
- Assertion is FALSE: For two distinct primes p and q, HCF = 1 (correct), but LCM = p × q (not p + q). E.g., primes 2 and 3: LCM = 6, not 5.
- Reason is TRUE: HCF(a, b) × LCM(a, b) = a × b holds for any two positive integers — this is explicitly stated in the textbook (Chapter 1, Section 1.2).
- Since A is false and R is true, the answer is D.
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