If $^n{P_r} = 840,{\,^n}{C_r} = 35,$ then $n$ is equal to
$1$
$3$
$5$
$7$
In an election the number of candidates is $1$ greater than the persons to be elected. If a voter can vote in $254$ ways, then the number of candidates is
There are $12$ volleyball players in all in a college, out of which a team of $9$ players is to be formed. If the captain always remains the same, then in how many ways can the team be formed
The number of onto functions $f$ from $\{1, 2, 3, …, 20\}$ only $\{1, 2, 3, …, 20\}$ such that $f(k)$ is a multiple of $3$, whenever $k$ is a multiple of $4$, is
The total number of different combinations of one or more letters which can be made from the letters of the word ‘$MISSISSIPPI$’ is