If $n$ is even and the value of $^nC_r$ is maximum,then $r = $

Out of $10$ points in a plane,$6$ are in a straight line. The number of triangles formed by joining these points is:

$^nC_r \div ^nC_{r-1} = $

In how many ways can $6$ persons be selected from $4$ officers and $8$ constables,if at least one officer is to be included?

$6$ boys and $5$ girls sit in a line such that $(I)$ no two girls sit together $(II)$ all the girls sit together. If $p$ is the number of arrangements in case $(I)$ and $q$ is the number of arrangements in case $(II)$,then $p/q =$

If ${}^n{P_4} : {}^n{P_5} = 1 : 2$,then $n = $