If $A = \{1, 2, 4\}, B = \{2, 4, 5\}, C = \{2, 5\},$ then $(A - B) \times (B - C)$ is

Let $A = \{(x, y) : y = e^x, x \in R\}$ and $B = \{(x, y) : y = e^{-x}, x \in R\}$. Then:

Let $Z$ be the set of integers. If $A = \{ x \in Z : 2^{(x + 2)(x^2 - 5x + 6)} = 1 \}$ and $B = \{ x \in Z : -3 < 2x - 1 < 9 \}$,then the number of subsets of the set $A \times B$ 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 function $f:R \to R$ is defined by $f(x) = \cos^2 x + \sin^4 x$ for $x \in R$,then $f(R) \in $

The natural domain of the real-valued function defined by $f(x) = \sqrt{x^2 - 1} + \sqrt{x^2 + 1}$ is