Question

(i) Find the remainder, when $5^{99}$ is divided by 13.

(ii) If the middle term of ${(\frac{1}{x}+xsinx)}^{10}$ is equal to $7\frac{7}{8}$, then find the value of x.

Answer 1

(i) Remainder = 8 (ii) $x=n\pi +(-1{)}^n\frac{\pi }{6}$