The total number of possible ways in which a person can go from $A(0,0)$ to $B(3,3)$ if he can travel only to the right or upward along the grid lines is:

Let $l_1$ and $l_2$ be two lines intersecting at $P$. If $A_1, B_1, C_1$ are points on $l_1$,and $A_2, B_2, C_2, D_2, E_2$ are points on $l_2$,and if none of these points coincides with $P$,then the number of triangles formed by these eight points is:

There are $16$ points in a plane,no three of which are in a straight line except $8$ which are all in a straight line. The number of triangles that can be formed by joining them is equal to:

If the number of diagonals of a regular polygon of $n$ sides is $104$,then $n=$

The number of arrangements of the letters of the word $PALANHAR$ in which no two vowels are together and exactly two vowels are at odd places,is

The number of triangles $(T_n)$ that can be formed using the vertices of a polygon with $n$ sides is given by $T_n = \binom{n}{3}$. If $T_{n+1} - T_n = 21$,then what is the value of $n$?