The number of symmetric relations on set $A = \{1,2,3\}$ is

If n(A) = 3 and n(B) = 2, then number of non-empty relations from A to B is

Let $f : R \to R$ defined by $f(x) = 2x^3 - 7$ for $x \in R$. Then :

(A) $f$ is one-one function

(B) $f$ is many to one function

(C) $f$ is bijective function

(D) $f$ is into function

Choose the correct answer from the options given below :

Let N be set of natural numbers, then the function $f: \mathbb{N} \rightarrow \mathbb{N}$, defined by

$f(x) = \begin{cases} \frac{n+1}{2} & \text{, if } n \text{ is odd} \\ \frac{n}{2} & \text{, if } n \text{ is even} \end{cases}$, is

If $f: R \to R$ is defined by $f(x) = \sin x + x$, then $f(f(x))$ is:

Consider a function $f: \left[0, \dfrac{\pi}{2}\right] \to R$ given by $f(x) = \sin x$ and $g: \left[0, \dfrac{\pi}{2}\right] \to R$ given by $g(x) = \cos x$, where $R$ is set of real numbers then which of the following are correct?

A. $f$ is one-one

B. $g$ is one-one

C. $f + g$ is one-one

D. $f + g$ is not one-one

Choose the correct answer from the options given below:

Consider a function $f:\left[0,\frac{\pi}{2}\right] \to R$, given by $f(x)=\sin x$ and $g:\left[0,\frac{\pi}{2}\right] \to R$, given by $g(x)=\cos x$, Where R is a set of real numbers, Which of the following statements are correct?

(A) f and g are one-one

(B) f and g are not one-one

(C) f+g is not one-one

(D) f+g is one-one

Choose the correct answer from the options given below: