The domain of definition of the function $f(x) = \frac{3}{4 - x^2} + \log_{10}(x^3 - x)$ is

Suppose $A_1, A_2, A_3, \dots, A_{30}$ are $30$ sets each having $5$ elements and $B_1, B_2, \dots, B_n$ are $n$ sets each with $3$ elements. Let $\bigcup_{i=1}^{30} A_i = \bigcup_{j=1}^n B_j = S$ and each element of $S$ belongs to exactly $10$ of the $A_i$'s and exactly $9$ of the $B_j$'s. Then $n$ is equal to:

The range of $f(x) = \frac{x^2 + 34x - 71}{x^2 + 2x - 7}$ is

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. Then the percentage of the population who look into advertisements is:

If $A = \{x : x \text{ is a multiple of } 4\}$ and $B = \{x : x \text{ is a multiple of } 6\}$,then $A \cap B$ consists of all multiples of

Domain of the function $f(x) = \frac{x - 3}{(x - 1)\sqrt{x^2 - 4}}$ is