If $C_0, C_2, \ldots, C_n$ are the binomial coefficients in the expansion of $(1+x)^n$, then

$$ \left(C_0+C_1\right)-\left(C_2+C_3\right)+\left(C_4+C_5\right)-\left(C_6+C_7\right)+\ldots= $$

The mean and variance of a binomial distribution are $x$ and 5 respectively. If $x$ is an integer, then the possible values for $x$ are

If the coefficients of $x^{10}$ and $x^{11}$ in the expansion of $\left(1+\alpha x+\beta x^2\right)(1+x)^{11}$ are 396 and 144 respectively, then $\alpha^2+\beta^2=$

If $-\frac{2}{3} < x < \frac{2}{3}$, then the value of the 5 th term in the expansion of $\frac{1}{\sqrt[3]{2-3 x}}$ when $x=\frac{1}{2}$ is