The coefficient of ${x^{100}}$ in the expansion of $\sum\limits_{j = 0}^{200} {{{(1 + x)}^j}} $ is
$\left( \begin{array}{l}200\\100\end{array} \right)$
$\left( \begin{array}{l}201\\102\end{array} \right)$
$\left( \begin{array}{l}200\\101\end{array} \right)$
$\left( \begin{array}{l}201\\100\end{array} \right)$
If the coefficients of second, third and fourth term in the expansion of ${(1 + x)^{2n}}$ are in $A.P.$, then $2{n^2} - 9n + 7$ is equal to
If $^n{C_{r - 2}} = 36$ , $^n{C_{r - 1}} = 84$ and $^n{C_r} = 126$ , then value of $^n{C_{2r}}$ is
The Coefficient of $x ^{-6}$, in the expansion of $\left(\frac{4 x}{5}+\frac{5}{2 x^2}\right)^9$, is $........$.
Coefficient of $x^3$ in the expansion of $(x^2 - x + 1)^{10} (x^2 + 1 )^{15}$ is equal to
The coefficient of ${x^{ - 7}}$ in the expansion of ${\left( {ax - \frac{1}{{b{x^2}}}} \right)^{11}}$ will be