There are $5$ roads leading to a town from a village. The number of different ways in which a villager can go to the town and return back is:

Let $T_n$ be the number of all possible triangles formed by joining vertices of an $n$-sided regular polygon. If $T_{n+1} - T_n = 10$,then the value of $n$ is:

There are $15$ persons in a party and each person shakes hands with every other person exactly once. What is the total number of handshakes?

The number of ways in which an examiner can assign $30$ marks to $8$ questions,giving not less than $2$ marks to any question,is

$n$ balls each of weight $w$ are weighed in pairs. The sum of the weights of all possible pairs is $120$. When they are weighed in triplets,the sum of the weights of all possible triplets is $480$. Then $n$ is:

How many words can be formed from the letters of the word $COURTESY$,whose first letter is $C$ and the last letter is $Y$?