Permutations an...

How many ways $5$ persons can sit around the round table :

The number of distinct rational numbers x such that $\displaystyle 0 < x < 1$ and $\displaystyle x = \frac{p}{q}r$, where $\displaystyle p,q \epsilon \left \{ 1,2,3,4,5,6 \right \}$,is

The number of rectangles that can be obtained by joining four of the twelve vertices of a $12$ sided regular polygon is

Three vertices are chosen randomly from the seven vertices of a regular $7$ -sided polygon. The probability that they form the vertices of an isosceles triangle is

The number of ways in which three numbers in A.P. can be seleced from the set of first n natural number if n is odd is

The sides of a quadrilateral are all positive integers and three of them are $5, 10, 20.$ How many possible value are there for the fourth side?

A cabinet of ministers consists of 11 ministers, one minister being the chief minister. A meeting is to be held in a room having a round table and 11 chairsround it, one of them being meant for the chairman. The number of ways in which the ministers can take their chairs, the chief minister occupying the chairman's place, is

In a test there were n questions. In the test $\displaystyle 2^{n-i}$ students gave wrong answers to i questions where $\displaystyle i=1,2,3...,n$. If the total number of wrong answers given is 2047 then n is

If the difference of the number of arrangements of three things from a certain number of dissimilar things and the number of selections of the same number of things from them exceeds $100$, then the least number of dissimilar things is

If four points are $A(6,3),B(-3,5),C(4,-2)$ and $P(x,y),$ then the ratio of the areas of $\triangle PBC$ and $\triangle ABC$ is: