If the sum of the coefficients in the expansion of $({\alpha ^2}{x^2} - 2\alpha x + 1)^{51}$ vanishes,then the value of $\alpha$ is

If the coefficients of $x^2$ and $x^3$ are both zero in the expansion of the expression $(1 + ax + bx^2)(1 - 3x)^{15}$ in powers of $x$,then the ordered pair $(a, b)$ is equal to

If $\{ p \}$ denotes the fractional part of the number $p$,then $\left\{\frac{3^{200}}{8}\right\}$ is equal to

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

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

For $|x| < \frac{1}{5}$,the coefficient of $x^3$ in the expansion of $\frac{1}{(1-5 x)(1-4 x)}$ is