If $^{10}C_r = ^{10}C_{r+2}$,then $^5C_r$ equals:

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

In how many ways can the letters of the word '$EXCELLENT$' be arranged?

The number of points,having both coordinates as integers,that lie in the interior of the triangle with vertices $(0,0)$,$(0,41)$,and $(41,0)$ is:

$4$ alphabets $E, K, S$ and $V$,one in each,were purchased from a plastic warehouse. How many ordered pairs of alphabets,to be used as initials,can be formed from them?

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