An organization awarded $48$ medals in event $A$,$25$ in event $B$,and $18$ in event $C$. If these medals were awarded to a total of $60$ men and only $5$ men received medals in all three events,how many men received medals in exactly two of the three events?

In a group of $400$ people,$250$ can speak Hindi and $200$ can speak English. How many people can speak both Hindi and English?

In a survey of $600$ students in a school,$150$ students were found to be taking tea and $225$ taking coffee,$100$ were taking both tea and coffee. Find how many students were taking neither tea nor coffee?

In a committee of $25$ members,each member is proficient either in Mathematics or in Statistics or in both. If $19$ of them are proficient in Mathematics and $16$ of them are proficient in Statistics,then the probability that a person selected at random from the committee is proficient in both is

In a school,there are $20$ teachers who teach mathematics or physics. Of these,$12$ teach mathematics and $4$ teach both physics and mathematics. How many teach physics?

If $A = \{5^{n} - 4n - 1 : n \in N\}$ and $B = \{16(n - 1) : n \in N\}$, then: