MathsCBSE Class 10 · Standard · Sample paper, session 2023-24 · 1 mark · MCQ

CBSE Class 10 Mathematics Standard sample paper 2023-24: question 16

From the official CBSE sample question paper for 2023-24, section A, question 16, for 1 mark. Try it first; the hints and our step-by-step solution are below.

Q16 · 1 mark · MCQCompetency-basedProbability

There is a square board of side '2a' units circumscribing a red circle. Jayadev is asked to keep a dot on the above said board. The probability that he keeps the dot on the shaded region is.

(A) $\frac{π}{4}$
(B) $\frac{4 - π}{4}$
(C) $\frac{π - 4}{4}$
(D) $\frac{4}{π}$

Figure in the paper: A square board with a circle inscribed in it (touching all four sides). The region outside the circle but inside the square is shaded. See it in the official paper.

Source: official sample paper from cbseacademic.nic.in (PDF). See it in the full Sample paper 2023-24.

Hints

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

Hint 1

The circle's diameter equals the side 2a.

Hint 2

Probability = shaded area ÷ total area.

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.

The inscribed circle has radius $a$ . Area of square $= 4 a^{2}$ and area of circle $= π a^{2}$ .
Shaded area $= 4 a^{2} - π a^{2}$ .
$P = \frac{( 4 - π ) a ^{2}}{4 a ^{2}} = \frac{4 - π}{4}$ . Option (B).
1 mark

Answer: $\frac{4 - π}{4}$ , option (B)

Where the marks are

Finds shaded area ÷ square area $= \frac{4 - π}{4}$ , option (B) (1 mark)

Revise the chapter

Chapter: Probability (notes, formulas, where marks are lost and every past question)

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 2023-24 (Standard): every question, by section.

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CBSE Class 10 Mathematics Standard sample paper 2023-24: question 16

Hints

Step-by-step solution

Revise the chapter

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