The number of rectangles that can be obtained by joining four of $12$ vertices of a $12$-sided regular polygon is:

There are $10$ points in a plane,out of which $6$ are collinear. If $N$ is the total number of triangles formed by joining these points,then $N=$

$l_1, l_2, l_3$ are three parallel lines in the same plane. If there are $m$ points on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$,what is the maximum number of triangles that can be formed with vertices at these points?

There are $n$ distinct points on a circle. If the number of pentagons that can be formed using these points as vertices is equal to the number of triangles that can be formed,then the value of $n$ is:

$T_m$ 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

The number of shortest paths from point $A$ to $D$ (as shown in the figure) is: