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

If $S$ is a set of polynomials $P(x)$ of degree $\le 2$ such that $P(0) = 0$,$P(1) = 1$,and $P'(x) > 0$ for all $x \in (0, 1)$,then which of the following describes $S$?

Let $S = \mathbb{N} \cup \{0\}$. Define a relation $R$ from $S$ to $\mathbb{R}$ by: $R = \{(x, y) : \log_e y = x \log_e \left(\frac{2}{5}\right), x \in S, y \in \mathbb{R}\}$. Then,the sum of all the elements in the range of $R$ is equal to

The graph of the function $y = f(x)$ is symmetrical about the line $x = 2$,then

Let $A = \{1, 2, 3, 4\}$ and $B = \{1, 4, 9, 16\}$. Then the number of many-one functions $f: A \rightarrow B$ such that $1 \in f(A)$ is equal to:

If $R \subset A \times B$ and $S \subset B \times C$,then the relation $(SoR)^{-1} = $