$A$ simple graph contains $24$ edges. The degree of each vertex is $3$. The number of vertices is:

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

If three distinct vertices are chosen at random from the vertices of a cube,then the probability that they form the vertices of an equilateral triangle is:

Let $t_n$ denote the number of integral-sided triangles with distinct sides chosen from $\{1, 2, 3, \ldots, n\}$. Then,$t_{20} - t_{19}$ equals

Let $S = \{(a, b) : a, b \in \mathbb{Z}, 0 \leq a, b \leq 18\}$. The number of lines in $\mathbb{R}^2$ passing through $(0,0)$ and exactly one other point in $S$ is:

The number of straight lines that can be formed by joining $20$ points,no three of which are in the same straight line,except $4$ of them which are in the same line,is: