If $A = \{x: x \in R, -\frac{\pi}{2} \leq x \leq \frac{\pi}{2}\}$ and $B = \{y: y \in R, -1 \leq y \leq 1\}$ and function $f: A \rightarrow B$ defined by $f(x) = \sin x$, then $f$ is

Which of the following is true on the basis of above diagram?

Which of the following figures shows a bijective function from set $X_1$ to set $X_2$ :

Choose the correct answer from the options given below :

Let A= {1, 2, 3}, then the possible equivalence relations on A are:

(A) {(1, 1), (2, 2) , (3, 3)}

(B) {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}

(C) {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1), (1, 3)}

(D) {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}

Choose the correct answer from the options given below:

The function $f: R \to [0,1]$ defined by $f(x) = \dfrac{x^2}{x^2+1}$ is: (Where $R$ is set of real numbers)

A. One-one

B. one-one and onto

C. onto

D. Not one-one

Choose the correct answer from the options given below:

The domain of the function $\cos^{-1}(2x - 3)$ is

For the relation $R = \{(a, b): a \leq b\}$ in $\mathbb{R}$, which of the following is correct?