If $x$ and $y$ are digits such that $17! = 355687428096000$,then $x+y$ equals

Number of $4-$digit numbers (the repetition of digits is allowed) which are made using the digits $1, 2, 3$ and $5$,and are divisible by $15$,is equal to $............$.

In the product $(1 + x) (1 + x + x^2) (1 + x + x^2 + x^3) \dots (1 + x + x^2 + \dots + x^{100})$,when written in ascending powers of $x$,the highest exponent of $x$ is . . . . . . .

The remainder obtained when $1! + 2! + 95!$ is divided by $15$ is

The digit in the unit place of the number $2009! + 3^{7886}$ is

If $^nC_r = ^nC_{r-1}$ and $^nP_r = ^nP_{r+1}$,then the value of $n$ is