If $^nP_5 = 9 \times ^{n-1}P_4$,then the value of $n$ is

The straight lines $l_1, l_2, l_3$ are parallel and lie in the same plane. $A$ total number of $m$ points are taken on $l_1$,$n$ points on $l_2$,and $k$ points on $l_3$. The maximum number of triangles formed with vertices at these points is:

In how many ways can a team of $11$ members be formed from a group of $15$ persons?

In how many different ways can the letters in the word $ATTEND$ be arranged?

The total number of different combinations of one or more letters which can be made from the letters of the word '$MISSISSIPPI$' is

The number of ordered pairs $(r, k)$ for which $6 \cdot ^{35} C_{r} = (k^2 - 3) \cdot ^{36} C_{r+1}$,where $k$ is an integer,is: