TS ICET 24 May 2018 Shift 1 Paper

The last three digits of $2^{40}$ is the same as the remainder when $2^{40}$ is divided by 1,000
$2^{40}={\left(2^{10}\right)}^4={\left(1024\right)}^4$
1,024 when divided by 1,000, the remainder = 24
${\left(1024\right)}^2$ when divided by 1,000, the remainder
$={24}^2=576$
${\left(1024\right)}^4$ when divided by 1,000, the remainder
$={\left(576\right)}^2=776$