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Assertion (A): The number 5^n… (Class 10 Maths 2023, Q20)

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MathsCBSE Class 10 · Standard · Board exam 2023, set 30/5/1 · 1 mark · Assertion-reason

CBSE Class 10 Mathematics Standard 2023: question 20

Set in the CBSE Class 10 board exam of 2023, paper 30/5/1, section A, question 20, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q20 · 1 mark · Assertion-reasonCompetency-basedReal Numbers

Assertion (A): The number cannot end with the digit 0, where n is a natural number.

Reason (R): Prime factorisation of 5 has only two factors, 1 and 5.

  1. (A)Both Assertion (A) and Reason (R) are true and Reason (R) is the correct explanation of the Assertion (A).
  2. (B)Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the 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 2023 board paper, set 30/5/1.

Hints

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

Hint 1

Which primes must divide a number ending in 0?

Hint 2

Is 1 a prime 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. To end in 0, a number needs prime factors 2 and 5; has no factor 2, so A is true.

  2. 1 is not a prime factor; the prime factorisation of 5 is just 5, so R is false. Option (C).

    1 mark

Answer: Option (C)

Where the marks are

  • Justifies A by absence of factor 2 and identifies R as false (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 paper2023 board paper, set 30/5/1 (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.