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T-shirts marked with… (Class 10 Maths SQP 2026-27, Q9)

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MathsCBSE Class 10 · Standard · Sample paper, session 2026-27 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2026-27: question 9

From the official CBSE sample question paper for 2026-27, section A, question 9, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q9 · 1 mark · MCQProbability

T-shirts marked with numbers 4 to 99 are placed in a box. Gunika is fond of numbers. She randomly takes out a T-shirt from this box. The probability that she gets a T-shirt marked with a number that is either a perfect square or a perfect cube is:

  1. (A)
  2. (B)
  3. (C)
  4. (D)

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

Count the numbers from 4 to 99 carefully.

Hint 2

List the squares and cubes, and don't count 64 twice.

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. Numbers 4 to 99 give outcomes.

  2. Perfect squares are 4, 9, 16, 25, 36, 49, 64, 81 (8 numbers). Perfect cubes are 8, 27, 64 (3 numbers). The number 64 is in both lists, so the favourable outcomes are .

  3. , which is option (D).

    1 mark

Answer: , option (D)

Where the marks are

  • Counts 96 outcomes and 10 favourable outcomes, getting 5/48 (1 mark)

Revise the chapter

Practise this chapterBoard-style questions from Probability, 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.

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.