Q1. [1] § 1.4 Summary
Directions: Two statements are given, one labelled Assertion (A) and the other labelled Reason (R). Select the correct answer from the codes (A), (B), (C) and (D) as given below.
Assertion (A) : H.C.F. $(36m^2, 18m) = 18m$, where $m$ is a prime number.
Reason (R) : H.C.F. of two numbers is always less than or equal to the smaller number.
- (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 30/5/1 Q20
Generated by claude-sonnet-4-6 · 2026-06-15 10:31 · grounding rag
Model Answer
(B) Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
$36m^2 = 2^2 \times 3^2 \times m^2$ and $18m = 2 \times 3^2 \times m$. HCF $= 2 \times 3^2 \times m = 18m$ ✓. Reason (R) is also true (HCF ≤ smaller number), but it does not explain why HCF equals 18m specifically.
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Explanation
- Check A: Use prime factorisation. $36m^2 = 2^2·3^2·m^2$; $18m = 2·3^2·m$. HCF = lowest powers of common factors = $2^1·3^2·m^1 = 18m$. ✓
- Check R: HCF of any two numbers is always ≤ the smaller number — this is a standard true property. Here HCF $= 18m =$ the smaller number, consistent.
- Why (B) not (A): R explains a general inequality property, not the specific calculation that gives HCF $= 18m$. So R is true but not the correct explanation of A. Choose (B).
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