The sum of the coefficients in the expansion of $\left(1+\frac{x}{2}\right)^{12}$ is

If $b$ is very small as compared to the value of $a$,so that the cube and other higher powers of $\frac{b}{a}$ can be neglected in the identity $\frac{1}{a-b}+\frac{1}{a-2b}+\frac{1}{a-3b}+\ldots+\frac{1}{a-nb}=\alpha n+\beta n^2+\gamma n^3$,then the value of $\gamma$ is:

The last two digits of the number $3^{400}$ are:

The roots of the equation $x^4 - 4x^3 + 6x^2 - 4x + 1 = 0$ are

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

If $(2+\sqrt{3})^{49}+(\sqrt{3}-2)^{49}=a+b \sqrt{3}$,where $a, b \in \mathbb{Q}$,then