$^{n - 1}{C_r} = ({k^2} - 3)\,.{\,^n}{C_{r + 1}}$ if $k \in $
$[ - \sqrt 3 ,\,\sqrt 3 ]$
$( - \infty ,\, - 2)$
$(2,\,\infty )$
$(\sqrt 3 ,\,2)$
Out of $6$ boys and $4$ girls, a group of $7$ is to be formed. In how many ways can this be done if the group is to have a majority of boys
A group of students comprises of $5$ boys and $n$ girls. If the number of ways, in which a team of $3$ students can randomly be selected from this group such that there is at least one boy and at least one girl in each team, is $1750$, then $n$ is equal to
The least value of natural number $n$ satisfying $C(n,\,5) + C(n,\,6)\,\, > C(n + 1,\,5)$ is
A country has ten smart cities. The government decides to connect all these cities by road. How many roads the government need to construct so that every city is connected to every other city ?
The number of ways in which $10$ persons can go in two boats so that there may be $5 $ on each boat, supposing that two particular persons will not go in the same boat is