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State true or false for each… (Class 10 Maths 2025, Q26b)

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MathsCBSE Class 10 · Standard · Board exam 2025, set 30/5/1 · 3 marks · Short answer

CBSE Class 10 Mathematics Standard 2025: question 26(b)

Set in the CBSE Class 10 board exam of 2025, paper 30/5/1, section C, question 26(b), for 3 marks. Try it first; the hints and our step-by-step solution are below.

Q26(b) · 3 marks · Short answerReal Numbers

State true or false for each of the following statements and justify in each case:

(i) is a composite number.

(ii) is a composite number.

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 30/5/1.

Hints

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

Hint 1

In (i), look for a factor common to both terms.

Hint 2

In (ii), work out the number and test it for divisibility by primes up to its square root.

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. (i) True.

    1 mark

  2. . It has factors 1, 7, 31 and 217, i.e. more than two factors, so it is composite.

    ½ mark

  3. (ii) False.

    1 mark

  4. . It is not divisible by any prime up to (2, 3, 5, 7, 11, 13). So its only factors are 1 and 211, i.e. it is prime, not composite.

    ½ mark

Answer: (i) True (= 7 × 31); (ii) False (211 is prime)

Where the marks are

  • (i) States True (1 mark)
  • (i) Justifies by showing 7 is a common factor: (½ mark)
  • (ii) States False (1 mark)
  • (ii) Justifies that 211 has only two factors (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 30/5/1 (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.