The coefficient of $x^{4}$ in the expansion of $\left(1+x+x^{2}+x^{3}\right)^{6}$ in powers of $x,$ is
$116$
$118$
$120$
$124$
Find the coefficient of $x^{49}$ in the expansion of $(2x + 1) (2x + 3) (2x + 5)----- (2x + 99)$
In the expansion of ${(1 + x)^n}$ the sum of coefficients of odd powers of $x$ is
If the sum of the coefficients of all the positive powers of $x$, in the binomial expansion of $\left(x^{n}+\frac{2}{x^{5}}\right)^{7}$ is $939 ,$ then the sum of all the possible integral values of $n$ is
$(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) ...... (1 + x + x^2 + ...... + x^{100})$ when written in the ascending power of $x$ then the highest exponent of $x$ is ______ .
If $\sum_{ k =1}^{10} K ^{2}\left(10_{ C _{ K }}\right)^{2}=22000 L$, then $L$ is equal to $.....$