One hundred identical coins, each with probability, $$p,$$ of showing up heads are tossed once. If $$0 < p < 1$$ and the probability of heads showing on $$50$$ coins is equal to that of heads showing on $$51$$ coins, then the value of $$p$$ is

For two given events $$A$$ and $$B,$$ $$P\left( {A \cap B} \right)$$

A box contains $$2$$ fifty paise coins, $$5$$ twenty five paise coins and a certain fixed number $$N\,\,\left( { \ge 2} \right)$$ of ten and five paise coins. Five coins are taken out of the box at random. Find the probability that the total value of these $$5$$ coins is less than one rupee and fifty paise.

The components of a vector $$\overrightarrow a $$ along and perpendicular to a non-zero vector $$\overrightarrow b $$ are ......and .....respectively.