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Directions: In Question Numbers… (Class 10 Maths 2025, Q19)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/6/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2025: question 19

Set in the CBSE Class 10 board exam of 2025, paper 30/6/1, 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

Directions: In Question Numbers 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option from the following:

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.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is correct explanation of Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of Assertion (A).
  3. (C)Assertion (A) is true, but Reason (R) is false.
  4. (D)Assertion (A) is false, but Reason (R) is true.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/6/1.

Hints

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

Hint 1

Test with p = 2, q = 3.

Hint 2

What is the LCM of two numbers with no common factor?

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.

  1. For distinct primes p, q: HCF = 1 and LCM = pq, not p + q (e.g. 2, 3: LCM 6 ≠ 5). So A is false.

    ½ mark

  2. HCF × LCM = product holds for any two natural numbers, so R is true. Option (D).

    ½ mark

Answer: Option (D)

Where the marks are

  • Shows A false (LCM = pq) (½ mark)
  • States R true (½ mark)

Revise the chapter

Practise this chapterBoard-style questions from Real Numbers, one at a time, marked against the answer key and marking points.Back to the full paper2025 board paper, set 30/6/1 (Standard): 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.