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


CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
CBSE Class 10 Sample Paper for 2024 Boards - Maths Standard
Last updated at Dec. 13, 2024 by Teachoo
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)