$(102)^4 = ?$

For $|x| < 1$,the constant term in the expansion of $\frac{1}{(x-1)^2(x-2)}$ is

Find $(a+b)^{4}-(a-b)^{4}$. Hence,evaluate $(\sqrt{3}+\sqrt{2})^{4}-(\sqrt{3}-\sqrt{2})^{4}$. (in $\sqrt{6}$)

If the number of terms in the binomial expansion of $(2x + 3)^{3n}$ is $22$,then the value of $n$ is:

The last three digits of the number $N = 7^{100} - 3^{100}$ are

Evaluate the expression: $\frac{1}{81^{n}} - {}^{2n}C_1 \frac{10}{81^{n}} + {}^{2n}C_2 \frac{10^2}{81^{n}} - \dots + \frac{10^{2n}}{81^{n}} = $