MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 2 marks · Very short answer

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 21(A)

From the official CBSE sample question paper for 2026-27, section B, question 21(A), for 2 marks. Try it first; the hints and our step-by-step solution are below.

Q21(A) · 2 marks · Very short answerCompetency-basedReal Numbers

A hall has a length of 9.75 m, breadth of 6.75 m and height of 5.25 m. What is the length of the longest unmarked ruler that can exactly measure the dimensions of the hall?

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2026-27.

Hints

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

Hint 1

The ruler's length must divide each dimension exactly.

Hint 2

Change to cm and find the HCF using prime factors.

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.

Convert to cm: length $= 975$ cm, breadth $= 675$ cm, height $= 525$ cm. The longest ruler that measures all three exactly has length $HCF (975, 675, 525)$ .
½ mark
Prime factorisation: $975 = 3 \times 5^{2} \times 13$ , $675 = 3^{3} \times 5^{2}$ , $525 = 3 \times 5^{2} \times 7$ .
1 mark
$HCF = 3 \times 5^{2} = 75$ . The longest ruler is 75 cm, that is 0.75 m.
½ mark

Answer: 75 cm (0.75 m)

Where the marks are

Recognises that the HCF of the three dimensions (in cm) is required (½ mark)
Correct prime factorisation of 975, 675 and 525 (1 mark)
HCF = 75 cm (½ mark)

Revise the chapter

Chapter: Real Numbers (notes, formulas, where marks are lost and every past question)
Topic: HCF and LCM by Prime Factorisation

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 2026-27 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2026-27: question 21(A)

Hints

Step-by-step solution

Revise the chapter

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