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:

The set $\{x \in R : [x - |x|] = 5\}$ is equal to

Each set $X_r$ contains $5$ elements and each set $Y_r$ contains $4$ elements. If $\bigcup_{r=1}^{24} X_r = S = \bigcup_{r=1}^{n} Y_r$,and each element of set $S$ belongs to exactly $10$ of the $X_r$'s and to exactly $6$ of the $Y_r$'s,then find the value of $n$.

Two newspapers $A$ and $B$ are published in a city. It is known that $25\%$ of the city population reads $A$ and $20\%$ reads $B$,while $8\%$ reads both $A$ and $B$. Further,$30\%$ of those who read $A$ but not $B$ look into advertisements,$40\%$ of those who read $B$ but not $A$ look into advertisements,and $50\%$ of those who read both $A$ and $B$ look into advertisements. The percentage of the population who look into advertisements is:

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

In a city,$20\%$ of persons read an English newspaper,$40\%$ read a Hindi newspaper,and $5\%$ read both newspapers. The percentage of people who do not read either paper is: (in $\%$)