Assertion (A) : The prime numbers which divide 36 also divide 6. Reason (R) : Any number which divides p² also divides p. (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.

MathsCBSE Class 10 · Basic · Board exam 2026, set 430/2/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Basic 2026: question 19

Set in the CBSE Class 10 board exam of 2026, paper 430/2/1, section A, question 19, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q19 · 1 mark · Assertion-reasonCompetency-basedReal Numbers

Assertion (A) : The prime numbers which divide 36 also divide 6. Reason (R) : Any number which divides $p^{2}$ also divides p.

(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.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2026 board paper, set 430/2/1.

Hints

Open one hint at a time and try again before the next.

Hint 1

Factorise 36 into primes.

Hint 2

Test R with $p = 2$ and the divisor 4.

Step-by-step solution

Each step shows the marks it earns, as an examiner would award them. Checked by an independent re-solve from the question paper.

Since $36 = 2^{2} \times 3^{2}$ , the primes dividing 36 are 2 and 3. Both divide 6, so (A) is true.
½ mark
(R) is false: 4 divides $2^{2} = 4$ but 4 does not divide 2. The statement holds only for prime divisors. Option (C).
½ mark

Answer: Option (C)

Where the marks are

Shows A is true and gives a counterexample proving R false (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2026 board paper, set 430/2/1 (Basic): every question, by section.

The question is transcribed from the official paper; figures are described in words. The solution, hints and chapter tag are ours. Spotted an error? Write tosupport@questionbuddy.in.

CBSE Class 10 Mathematics Basic 2026: question 19

Hints

Step-by-step solution

Revise the chapter

More questions from Real Numbers