The number of elements in the set $\{ n \in \mathbb{N} : 10 \leq n \leq 100 \text{ and } 3^n - 3 \text{ is a multiple of } 7 \}$ is $........$.

Out of $60 \%$ female and $40 \%$ male candidates appearing in an exam,$60 \%$ of the total candidates qualify it. The number of females qualifying the exam is twice the number of males qualifying it. $A$ candidate is randomly chosen from the qualified candidates. The probability that the chosen candidate is a female 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 $A$.

$A$ survey shows that $63\%$ of the Americans like cheese whereas $76\%$ like apples. If $x\%$ of the Americans like both cheese and apples,then

The solution set of the system of equations $x + y = \frac{2\pi}{3}$ and $\cos x + \cos y = \frac{3}{2}$,where $x$ and $y$ are real,is:

Let $S$ be the set of the first $11$ natural numbers. Then the number of elements in $A = \{B \subseteq S : n(B) \ge 2 \text{ and the product of all elements of } B \text{ is even}\}$ is . . . . . . .