If n is a whole number greater then 1, then n² (n² - 1) is always divisible by -

A. 16

B. 12

C. 10

D. 8

Answer: Option B

Solution(By Examveda Team)

n²(n² - 1)
put n = 2
= 2²(2² - 1)
= 4(4 - 1)
= 4 × 3
= 12
Check the option it is divisible by 12.
$$\eqalign{ & {\text{Take n = 3}} \cr & \Rightarrow {{\text{3}}^3}\left( {{3^3} - 1} \right) \cr & \Rightarrow 9\left( {9 - 1} \right) \cr & \Rightarrow 9 \times 8 = 72 \cr & {\text{It is divisible by 12}} \cr & {\text{So 12 is answer}} \cr} $$