In the expansion of $(1 + x)^5$,the sum of the coefficients of the terms is

If $x$ is so small that all terms containing $x^2$ and higher powers of $x$ can be neglected, then the approximate value of $\frac{(1+\frac{2x}{3})^{-4}(4+5x)^{1/2}}{(9+x)^{3/2}}$ when $x=\frac{6}{371}$, is

The coefficient of $x^{50}$ in the binomial expansion of $(1 + x)^{1000} + x(1 + x)^{999} + x^{2}(1 + x)^{998} + \dots + x^{1000}$ is

The number of terms in the expansion of $(a + b + c)^n$ will be

If the coefficients of $x$ and $x^2$ in the expansion of $(1+x)^p(1-x)^q$ are $4$ and $-5$ respectively,then $2p+3q$ is equal to

$2{C_0} + \frac{2^2}{2}{C_1} + \frac{2^3}{3}{C_2} + \dots + \frac{2^{11}}{11}{C_{10}} = \dots$