If $n(U) = 600$,$n(A) = 100$,$n(B) = 200$,and $n(A \cap B) = 50$,then $n(\bar{A} \cap \bar{B})$ is (where $U$ is the universal set and $A$ and $B$ are subsets of $U$).

In a class of $140$ students numbered $1$ to $140$,all even-numbered students opted for the Mathematics course,those whose number is divisible by $3$ opted for the Physics course,and those whose number is divisible by $5$ opted for the Chemistry course. The number of students who did not opt for any of the three courses is:

If $f: R \to R$,then the range of the function $f(x) = \frac{x^2}{x^2 + 1}$ is

Given $n(U) = 20$,$n(A) = 12$,$n(B) = 9$,$n(A \cap B) = 4$,where $U$ is the universal set,$A$ and $B$ are subsets of $U$,then $n((A \cup B)^C) = $

In a city $20$ percent of the population travels by car,$50$ percent travels by bus and $10$ percent travels by both car and bus. Then the percentage of persons travelling by car or bus is......$\%$.

If $A = \{a, d\}, B = \{b, c, e\}$ and $C = \{b, c, f\},$ then $A \times (B \cup C) =$