Q1. [1]
Assertion (A): A ladder leaning against a wall, stands at a horizontal distance of 6 m from the wall. If the height of the wall up to which the ladder reaches is 8 m, then the length of the ladder is 10 m.
Reason (R): The ladder makes an angle of $60^\circ$ with the ground.
Select the correct answer from the codes (A), (B), (C) and (D) given below:
- 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
2025 30/3/1 Q19
Generated by claude-sonnet-4-6 · 2026-06-15 10:34 · grounding rag
Model Answer
(C) Assertion (A) is true, but Reason (R) is false.
Assertion is true: by Pythagoras theorem, ladder = $\sqrt{6^2 + 8^2} = \sqrt{100} = 10$ m. Reason is false: the angle the ladder makes with the ground is $\tan^{-1}(8/6) \approx 53°$, not $60°$.
Explanation
- Verify the Assertion using the Pythagoras theorem (no trigonometry needed).
- To check Reason, use $\tan\theta = \text{opposite}/\text{adjacent} = 8/6 = 4/3$; this gives $\approx 53°$, not $60°$. So Reason is false, making option (C) correct.
- In Assertion-Reason questions, always verify both statements independently before choosing the option.
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