If $f(y) = 1 - (y - 1) + {(y - 1)^2} - {(y - 1)^{^3}} + ... - {(y - 1)^{17}},$ then the coefficient of $y^2$ in it is

If $\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L$, then $L$ is equal to $.....$

If $S_n =$$\sum\limits_{r = 0}^n {\frac{1}{{^n{C_r}}}} $ and $T_n =$$\sum\limits_{r = 0}^n {\frac{r}{{^n{C_r}}}} $ then $\frac{{{T_n}}}{{{S_n}}}$ is equal to

$\frac{1}{{1!(n - 1)\,!}} + \frac{1}{{3!(n - 3)!}} + \frac{1}{{5!(n - 5)!}} + .... = $

$\sum_{\mathrm{k}=0}^{20}\left({ }^{20} \mathrm{C}_{\mathrm{k}}\right)^{2}$ is equal to :

$^n{C_0} - \frac{1}{2}{\,^n}{C_1} + \frac{1}{3}{\,^n}{C_2} - ...... + {( - 1)^n}\frac{{^n{C_n}}}{{n + 1}} = $