The relation $R$ defined on the set of natural numbers as $\{(a, b) : a\}$ differs from $b$ by $\{3\}$,is given by

If two sets $A$ and $B$ have $99$ elements in common,then the number of elements common to each of the sets $A \times B$ and $B \times A$ is:

The set $A = \{ x: x \in R, x^2 = 16 \text{ and } 2x = 6 \}$ equals

Given the sets $A = \{1, 2, 3\}$,$B = \{3, 4\}$,and $C = \{4, 5, 6\}$,then $A \cup (B \cap C)$ is:

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