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Question 16 - CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

Last updated at July 21, 2023 by

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

(a) π/4   (b) (4-π)/4   (c) (π - 4)/4    (d) 4/π

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Transcript

Probability of placing a dot on shaded region = (𝐴𝑟𝑒𝑎 𝑜𝑓 𝑠ℎ𝑎𝑑𝑒𝑑 𝑟𝑒𝑔𝑖𝑜𝑛 (𝑏𝑙𝑢𝑒))/(𝑇𝑜𝑡𝑎𝑙 𝑎𝑟𝑒𝑎) = (𝑨𝒓𝒆𝒂 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆 − 𝑨𝒓𝒆𝒂 𝒐𝒇 𝒄𝒊𝒓𝒄𝒍𝒆)/(𝑨𝒓𝒆𝒂 𝒐𝒇 𝒄𝒊𝒓𝒄𝒍𝒆) Area of square Side = 2a Area = 〖(2𝑎)〗^2 =〖 𝟒𝒂〗^𝟐 units Area of circle Radius of circle = 2𝑎/2 = a Area of circle = π𝑎^2 Now, Probability of placing a dot on shaded region = (𝑨𝒓𝒆𝒂 𝒐𝒇 𝒔𝒒𝒖𝒂𝒓𝒆 − 𝑨𝒓𝒆𝒂 𝒐𝒇 𝒄𝒊𝒓𝒄𝒍𝒆)/(𝑨𝒓𝒆𝒂 𝒐𝒇 𝒄𝒊𝒓𝒄𝒍𝒆) = (4𝑎^2−𝜋𝑎^2)/(4𝑎^2 ) = ((4 − 𝜋 ) 𝑎^2)/〖 4𝑎〗^2 = (4 − 𝜋)/4So, the correct answer is (b)

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Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.