The number of ways of awarding $9$ scholarships among $3$ students so that each may have $3$ scholarships is

The number of positive integral solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{2025}$ is

If $1000! = 3^n \times m$ where $m$ is an integer not divisible by $3$,then $n = $

If $a$ is the number of all even divisors and $b$ is the number of all odd divisors of the number $10800$,then $2a+3b=$

Let $f(x) = 2x^n + \lambda$,where $\lambda \in R$ and $n \in N$. Given $f(4) = 133$ and $f(5) = 255$,find the sum of all the positive integer divisors of $(f(3) - f(2))$.

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