$m$ men and $n$ women are to be seated in a row so that no two women sit together. If $m > n$,then the number of ways in which they can be seated is

$A$ parallelogram is cut by two sets of $m$ parallel lines,each set being parallel to one of its sides. How many parallelograms are formed in total?

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?

$T_m$ denotes the number of triangles that can be formed with the vertices of a regular polygon of $m$ sides. If $T_{m+1}-T_m=15$,then $m$ is equal to

If the number of diagonals of a regular polygon is $35$,then the number of sides of the polygon is

Let $n \geq 2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points blue and the rest red. If the number of red and blue line segments are equal,then the value of $n$ is