If $15^k$ divides $47!$ but $15^{k+1}$ does not divide it,then $k=$

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

If $33!$ is divisible by $2^n$,where $n \in N$,then the sum of all possible values of $n$ is:

Among the positive divisors of the number $12600$,if $n_1$ is the number of divisors which are multiples of $3$ and $n_2$ is the number of divisors which are multiples of $14$,then $n_1 + n_2 =$

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 . . . . . . .

If the integer represented by $100!$ has $K$ consecutive zeroes at the end,then $K=$