MathsCBSE Class 10 · Basic · Board exam 2025, set 430/3/1 · 3 marks · Short answer

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

Set in the CBSE Class 10 board exam of 2025, paper 430/3/1, 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

Find which among the following numbers a, b and c is/are composite numbers.

$a = 7 \times 11 \times 13 + 13$

$b = 6 \times 5 \times 4 + 4$

$c = 7 \times 13 + 6$

Source: official question paper from cbse.gov.in (PDF). See it in the full 2025 board paper, set 430/3/1.

Hints

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

Hint 1

Look for a common factor in each sum that can be taken out.

Hint 2

For c, work out the number and test it for divisibility by small primes.

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.

$a = 7 \times 11 \times 13 + 13 = 13 (7 \times 11 + 1) = 13 \times 78 = 1014$ . It has factors other than 1 and itself, so $a$ is composite.
1 mark
$b = 6 \times 5 \times 4 + 4 = 4 (30 + 1) = 4 \times 31 = 124$ . It has factors other than 1 and itself, so $b$ is composite.
1 mark
$c = 7 \times 13 + 6 = 91 + 6 = 97$ . 97 is not divisible by 2, 3, 5 or 7 (and $1 1^{2} > 97$ ), so $c$ is prime, not composite.
Hence only $a$ and $b$ are composite.
1 mark

Answer: a and b are composite; c = 97 is prime

Where the marks are

Shows a = 13 × 78 is composite (1 mark)
Shows b = 4 × 31 is composite (1 mark)
Shows c = 97 is prime and concludes only a and b are composite (1 mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: Fundamental Theorem of Arithmetic

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 430/3/1 (Basic): 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.

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

Hints

Step-by-step solution

Revise the chapter

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