SECTION – 1

20. The smallest perfect square that is divisible by 7!

A. 44100 B. 176400 C. 705600 D. 19600

Solution:

7! = 7 ´ 6 ´ 5 ´ 4 ´ 3 ´ 2 ´ 1 i.e. 2⁴ ´ 3² ´ 5¹ ´ 7¹

Hence the least perfect square which is divisible by 7! should be

(2⁴ ´ 3² ´ 5¹ ´ 7¹) ´ (5¹ ´ 7¹) i.e. 5040 ´ 35 = 176400 Choice (B)