$A$ natural number $n$ such that $n!$ ends in exactly $1000$ zeros is

The number of natural number solutions to the equation $xyz = 2^5 \times 3^2 \times 5^2$ is equal to

The total number of $3$-digit numbers whose greatest common divisor (g.c.d.) with $36$ is $2$ 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 largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:

The number of $6$-digit numbers of the form $ababab$ (in base $10$) each of which is a product of exactly $6$ distinct primes is