If $^{15}C_{3r} = ^{15}C_{r+3}$,then the value of $r$ is

The sides $AB, BC, CA$ of a triangle $ABC$ have respectively $3, 4$ and $5$ points lying on them. The number of triangles that can be constructed using these points as vertices is

There are $5$ gentlemen and $4$ ladies to dine at a round table. In how many ways can they seat themselves so that no $2$ ladies are together?

How many $3$-digit numbers,each less than $600$,can be formed from the digits $1, 2, 3, 4, 5,$ and $9$,if repetition of digits is allowed?

The number of diagonals in an octagon is:

The number of different words that can be formed out of the letters of the word $MORADABAD$ taken four at a time is