# 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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