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 \(\color{red}{A+B}\)
by
Tanishq Varshney