Question

The fractional part of `2^(4n)//15 is (n in N)`
A. `1/15`
B. `2/15`
C. `4/15`
D. none of these

Answer 1

Correct Answer - A
`(2^(4n))/(15)=((15+1)^(n))/(15)`
`=(.^(n)(C_(0)15^(n)+.^(n)C_(1)15^(n-1)+"......"+.^(n)C_(n-1)15+.^(n)C_(n)))/(15)`
`= "Integer" + 1/15`
Hence, the fractional part of `(2^(4n))/(15)` is `(1)/(15)`.