In how many ways can $21$ English books and $19$ Hindi books be placed in a row so that no two Hindi books are together?

Ten points are marked on a circle. The number of distinct convex polygons of three or more sides that can be drawn using some or all of the ten points as vertices is:

If the number of diagonals in a polygon with $n$ sides is $275$,then $n = .....$

In a tournament with five teams,each team plays against every other team exactly once. Each game is won by one of the playing teams and the winning team scores one point,while the losing team scores zero. Which of the following is $NOT$ necessarily true?

$A$ regular polygon of $n$ sides has $170$ diagonals,then $n$ is equal to

The number of diagonals in a regular polygon of $100$ sides is