If $f(x) = 4x^3 + 3x^2 + 3x + 4$,then $x^3 f\left( \frac{1}{x} \right)$ is

Let $\bigcup_{i=1}^{50} X_{i} = \bigcup_{i=1}^{n} Y_{i} = T$,where each $X_{i}$ contains $10$ elements and each $Y_{i}$ contains $5$ elements. If each element of the set $T$ is an element of exactly $20$ of the sets $X_{i}$ and exactly $6$ of the sets $Y_{i}$,then $n$ is equal to:

If $A = \{a, b\}$,$B = \{2, 3, 5, 6, 7\}$ and $C = \{5, 6, 7, 8, 9\}$,find $A \times (B \cap C)$.

In a certain class,$72 \%$ of the students took Biology and $44 \%$ took Mathematics. If each student took at least one of Biology or Mathematics and $40$ students took both of these subjects,the total number of students in the class is:

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

Two finite sets have $m$ and $n$ elements. The total number of subsets of the first set is $56$ more than the total number of subsets of the second set. The values of $m$ and $n$ are