# Two JEE problems together level 5.O

**Calculus**Level 5

If \(^{21}C_{1}+5.^{21}C_{5}+9.^{21}C_{9}+.........17.^{21}C_{17}+21.^{21}C_{21}=k\),then the **number of prime factors** of \(k\) is/are \(A\).

\(and\)

The value of \(\displaystyle \lim_{x \to - \infty}\frac{\int^{\sqrt{x^{2}+1}}_{2}[tan^{-1}y].dy}{\int^{x}_{-1}[1+\frac{1}{|y|}].dy}\),**(where [.] denotes greatest integer function)** is \(B\)

Find \(\color{red}{A+B}\)