The largest $n \in N$ for which $7^n$ divides $101!$ is:

The last two digits of $2015! + 3^{2015}$ are:

Total number of $3$ letter words that can be formed from the letters of the word $'SAHARANPUR'$ is equal to

In an examination,there are $5$ multiple choice questions with $3$ choices each,out of which exactly one is correct. There are $3$ marks for each correct answer,$-2$ marks for each wrong answer,and $0$ marks if the question is not attempted. The number of ways a student appearing in the examination can get exactly $5$ marks is:

The digit in the unit place of the number $(183!) + (3^{183})$ is

Let $S = \{1, 2, 3, 4, 5, 6, 7, 8, 9\}$. Let $x$ be the number of $9$-digit numbers formed using the digits of the set $S$ such that only one digit is repeated and it is repeated exactly twice. Let $y$ be the number of $9$-digit numbers formed using the digits of the set $S$ such that only two digits are repeated and each of these is repeated exactly twice. Then,