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

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