The greatest integer less than or equal to $(\sqrt{3}+2)^5$ is

For $2 \le r \le n$,the expression $\binom{n}{r} + 2\binom{n}{r-1} + \binom{n}{r-2}$ is equal to:

If $A$ denotes the sum of all the coefficients in the expansion of $(1-3x+10x^2)^n$ and $B$ denotes the sum of all the coefficients in the expansion of $(1+x^2)^n$,then:

If $(1+x+x^2+x^3)^5 = \sum_{k=0}^{15} a_k x^k$,then $\sum_{k=0}^7 a_{2k}$ is equal to

The approximate value of $(1.0002)^{3000}$ is

The coefficient of $x^{50}$ in $(1+x)^{101} (1-x+x^2)^{100}$ is......