Q1. [1]
Directions: Two statements are given, one labelled as Assertion (A) and the other labelled as Reason (R). Select the correct answer from the codes (a), (b), (c) and (d).
Assertion (A) : The probability that a leap year has 53 Mondays is $\frac{2}{7}$.
Reason (R) : The probability that a non-leap year has 53 Mondays is $\frac{5}{7}$.
- (a) Both, Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
- (b) Both, Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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
2026 30/1/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:30 · grounding rag
Model Answer
(c) Assertion (A) is true, but Reason (R) is false.
A leap year has 366 days = 52 weeks + 2 extra days. The 2 extra days can be any of 7 pairs; 2 pairs contain Monday, so P(53 Mondays) = 2/7 ✓. A non-leap year has 365 days = 52 weeks + 1 extra day; only 1 out of 7 days can be Monday, so P(53 Mondays) = 1/7, not 5/7. ✗
Source: Chapter 14, Probability
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Explanation
- Assertion is correct: leap year has 2 odd days → 2 favourable pairs out of 7 → P = 2/7.
- Reason is wrong: non-leap year has only 1 odd day → only 1 day out of 7 can be Monday → P = 1/7, not 5/7.
- So the answer is (c). Remember: always verify both A and R independently before choosing the option.
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