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Assertion (A): The… (Class 10 Maths SQP 2025-26, Q19)

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MathsCBSE Class 10 · Standard · Sample paper, session 2025-26 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard sample paper 2025-26: question 19

From the official CBSE sample question paper for 2025-26, 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 number cannot end with the digit 0, where n is a natural number
Reason (R): A number ends with 0, if its prime factorization contains both 2 and 5

  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 2025-26.

Hints

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

Hint 1

What must a number be divisible by to end in 0?

Hint 2

Write down the prime factorisation of .

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. Reason (R) is true: a number ends in 0 only if it is divisible by 10 = 2 × 5, so its prime factorisation must contain both 2 and 5.

  2. has only the prime 5 in its factorisation and no 2, so by uniqueness of prime factorisation it cannot end in 0. Hence (A) is true and (R) explains it, which is option (A).

    1 mark

Answer: Option (A)

Where the marks are

  • Recognises that has no factor 2, so (A) is true and explained by (R), option (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 2025-26 (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.