Two JEE problems together level 5.O

Calculus Level 5

If 21C1+5.21C5+9.21C9+.........17.21C17+21.21C21=k^{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 kk is/are AA.

andand

The value of limx2x2+1[tan1y].dy1x[1+1y].dy\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 BB

Find A+B\color{#D61F06}{A+B}

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