Question 9 - T-shirts marked with numbers 4 to 99 are placed in a box.

Question 9 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: (A) (1)/(12) (B) (1)/(32) (C) (11)/(96) (D) (5)/(48) Total number of t-shirts = 99 − 4 + 1 = 96 Perfect square numbers are… 1^(2), 2^(2), 3^(2), 4^(2), 5^(2), 6^(2), 7^(2), 8^(2), 9^(2), 10^(2),… 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, … Perfect cube numbers are… 1^(3), 2^(3), 3^(3), 4^(3), 5^(3),… 1, 8, 27, 64, 125, … Since 64 is common in both, we count it once So, our perfect square or perfect cube numbers between 4 to 99 are 4, 9, 16, 25, 36, 49, 64, 81, 100, 8, 27 Number of perfect square or perfect cube numbers b/w 4 to 99 = 10 Thus, P(getting a perfect squares or perfect cube) = (𝑁𝑢𝑚𝑏𝑒𝑟 𝑜𝑓 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑠𝑞𝑢𝑎𝑟𝑒𝑠 𝑜𝑟 𝑝𝑒𝑟𝑓𝑒𝑐𝑡 𝑐𝑢𝑏𝑒)/(𝑇𝑜𝑡𝑎𝑙 𝑛𝑢𝑚𝑏𝑒𝑟𝑠) = (10)/(96) = (𝟓)/(𝟒𝟖) So, the correct answer is (D)

Question 9 - CBSE Class 10 Sample Paper for 2027 Boards - Maths Standard - Solutions of Sample Papers for Class 10 Boards

CA Maninder Singh

Class 6

Class 7

Class 8

Class 9

Class 10

Class 11

Class 12

Courses

Interesting

Popular