The number of divisors of $9600$ including $1$ and $9600$ are

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

The number of sequences of ten terms,whose terms are either $0$,$1$,or $2$,that contain exactly five $1$s,exactly three $2$s,and two $0$s,is equal to:

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 $(f(3) - f(2))$.

The largest $n \in \mathbb{N}$ such that $3^n$ divides $50!$ is:

The coefficient of $x^3 y^4 z^5$ in the expansion of $(x y+y z+x z)^6$ is