In a class of $60$ students,$30$ opted for $NCC$,$32$ opted for $NSS$,and $24$ opted for both $NCC$ and $NSS$. If one of these students is selected at random,find the probability that the student opted for $NCC$ or $NSS$.

The sum of all the elements of the set $\{\alpha \in \{1, 2, \ldots, 100\} : \operatorname{HCF}(\alpha, 24) = 1\}$ is

In a class of $100$ students,$55$ students have passed in Mathematics and $67$ students have passed in Physics. Then the number of students who have passed in Physics only is

In a city of $10,000$ families,$40\%$ families buy newspaper $A$,$20\%$ buy newspaper $B$,$10\%$ buy newspaper $C$,$5\%$ buy newspapers $A$ and $B$,$3\%$ buy $B$ and $C$,and $4\%$ buy $A$ and $C$. If $2\%$ families buy all three newspapers,find the number of families that buy only newspaper $A$.

Out of all the patients in a hospital $89\%$ are found to be suffering from heart ailment and $98\%$ are suffering from lungs infection. If $K\%$ of them are suffering from both ailments,then $K$ cannot belong to the set :

In a group of $70$ people,$37$ like coffee,$52$ like tea and each person likes at least one of the two drinks. How many people like both coffee and tea?