The number of diagonals of a polygon is $35$. If $A$ and $B$ are two distinct vertices of this polygon,then the number of all those triangles formed by joining three vertices of the polygon having $AB$ as one of its sides is:

Three numbers are chosen at random from $1$ to $15$. The probability that no two numbers are consecutive is:

$A$ polygon has $54$ diagonals. The number of sides of this polygon is

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

How many chords can be drawn through $21$ points on a circle?

The lines $L_1, L_2, \ldots, L_{20}$ are distinct. For $n=1, 2, 3, \ldots, 10$,all the lines $L_{2n-1}$ are parallel to each other,and all the lines $L_{2n}$ pass through a given point $P$. The maximum number of points of intersection of pairs of lines from the set $\{L_1, L_2, \ldots, L_{20}\}$ is equal to: