Question

Fractional part of $\frac{2^{78}}{31}$ is

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$2^{78}$ + $2^3$​.$2^{75}$= 8 ${25}^{15}$​ = 8${(1+31)}^{15}$= 8${}^{15}{C}_0+{}^{15}{C}_{1}31+........................+{}^{15}{C}_{15}(31{)}^{15}$

$2^{78}$​ = 8 + an integer multiple of 31

$\frac{2^{78}}{31}$ =$\frac{8}{31}$ + an integer