Everybody in a room shakes hands with everybody else. The total number of handshakes is $66$. The total number of persons in the room is:

There are $n$ straight lines in a plane,no two of which are parallel and no three pass through the same point. Their points of intersection are joined. Then the number of fresh lines thus obtained is

If $^{2017}C_0 + ^{2017}C_1 + ^{2017}C_2 + ...... + ^{2017}C_{1008} = \lambda^2$ where $\lambda > 0$,then the remainder when $\lambda$ is divided by $33$ is:

If $110$ triangles can be formed by joining $10$ points as vertices,in which $n$ points are collinear,then the value of $n$ is:

$^{14}C_4 + \sum_{j=1}^4 {^{18-j}C_3}$ is equal to

The number of ways of selecting $15$ teams from $15$ men and $15$ women,such that each team consists of a man and a woman,is