If $a, b, c, d, e$ are prime integers,then the number of divisors of $a b^2 c^2 d e$ excluding $1$ as a factor is:

If $(1-x^3)^{10} = \sum_{r=0}^{10} a_r x^r (1-x)^{30-2r}$,then $\frac{9a_9}{a_{10}}$ is equal to . . . . . . .

What is the total number of divisors of $9600$,including $1$ and $9600$?

The largest natural number $n$ such that $3^{n}$ divides $66!$ is $............$.

If the number of terms in the expansion of ${\left( {1 - \frac{2}{x} + \frac{4}{{{x^2}}}} \right)^n}, x \ne 0$ is $28$,then the sum of the coefficients of all the terms in this expansion is:

The constant term in the expansion of $\left(2x + \frac{1}{x^7} + 3x^2\right)^5$ is $........$.