Three coins are tossed once. Find the probability of getting at most $2$ heads.

Let $N$ denote the sum of the numbers obtained when two dice are rolled. If the probability that $2^{N} < N!$ is $\frac{m}{n}$,where $m$ and $n$ are coprime,then $4m - 3n$ is equal to $......$.

Let $S_n = \sum_{k=1}^n k$ denote the sum of the first $n$ positive integers. The numbers $S_1, S_2, S_3, \ldots, S_{99}$ are written on $99$ cards. The probability of drawing a card with an even number written on it is

Two dice are rolled one after the other. The probability that the number on the first die is smaller than the number on the second die is:

Two dice are thrown simultaneously. What is the probability of obtaining a sum of the numbers less than $11$?

$P, Q$ and $R$ try to hit the same target one after the other. If their probabilities of hitting the target are $\frac{2}{3}, \frac{3}{5}, \frac{5}{7}$ respectively,then the probability that the target is hit by $P$ or $Q$ but not by $R$ is