Combinations

If $\dfrac{{}^{n+2}C_6}{{}^{n-2}P_2}=11$, then n satisfies the equation :

Let A and B be two sets containing four and two elements respectively. Then the number of subsets of the set A × B, each having at least three elements is :

The number of ways of selecting 15 teams from 15 men and 15 women, such that each team consists of a man and a woman, is :

Let $A=\{x_1,x_2,\dots,x_7\}$ and $B=\{y_1,y_2,y_3\}$ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f:A\to B$ that are onto, if there exist exactly three elements $x$ in A such that $f(x)=y_2$, is equal to :

If in a regular polygon the number of diagonals is 54, then the number of sides of this polygon is :

Let $n\ge2$ be an integer. Take $n$ distinct points on a circle and join each pair of points by a line segment. Colour the line segment joining every pair of adjacent points by blue and the rest by red. If the number of red and blue line segments are equal, then the value of $n$ is

Coefficient of $x^{11}$ in the expansion of $(1+x^2)^4(1+x^3)^7(1+x^4)^{12}$ is

A set S contains 7 elements. A non-empty subset A of S and an element $x$ of S are chosen at random. Then the probability that $x\in A$ is :

Two women and some men participated in a chess tournament in which every participant played two games with each of the other participants. If the number of games that the men played between them-selves exceeds the number of games that the men played with the women by 66, then the number of men who participated in the tournament lies in the interval :

The coefficient of $x^{1012}$ in the expansion of $(1+x^n+x^{253})^{10}$, (where $n\le22$ is any positive integer), is :

Consider the set of eight vectors $V=\left\{a\hat i+b\hat j+c\hat k:a,b,c\in\{-1,1\}\right\}$. Three non-coplanar vectors can be chosen from $V$ in $2^p$ ways. Then $p$ is

The number of matrices in $\mathcal A$ is