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Direction: In the… (Class 10 Maths SQP 2024-25, Q19)

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MathsCBSE Class 10 · Standard · Sample paper, session 2024-25 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2024-25: question 19

From the official CBSE sample question paper for 2024-25, 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

Direction: In the question number 19 and 20, a statement of Assertion (A) is followed by a statement of Reason (R). Choose the correct option.

Assertion (A): HCF of any two consecutive even natural numbers is always 2.

Reason (R): Even natural numbers are divisible by 2.

  1. (A)Both assertion (A) and reason (R) are true and reason (R) is the correct explanation of assertion (A)
  2. (B)Both assertion (A) and reason (R) are true and 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 sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2024-25.

Hints

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

Hint 1

Write two consecutive even numbers as and .

Hint 2

Does 'divisible by 2' alone prove that the HCF is exactly 2?

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. Consecutive even numbers are and . Their HCF is , so (A) is true.

  2. (R) is true. However, divisibility by 2 only shows that 2 is a common factor; it does not show that there is no larger common factor. So (R) does not explain (A). The answer is option (B).

    1 mark

Answer: Option (B)

Where the marks are

  • Judges both A and R true, with R not the correct explanation of A (1 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 paperSample paper 2024-25 (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.