Let L be the set of all lines in a plane and R be the relation on set L defined by $R = \{(L_1, L_2): L_1 \perp L_2\}$ Then R is (A) an equivalence Relation (B) a symmetric Relation (C) not a transitive Relation (D) a reflexive Relation Choose the correct answer from the options given below:

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:

Let $f(x) = x^3$ be a function with domain {0, 1, 2, 3} then domain of $f^{-1}$ is :

The modulus function $f : R \to R$, given by $f(x) = |x|$, is :

Match the LIST-I with LIST-II (Consider N and R as set of natural numbers and set of real numbers respectively)

Choose the correct answer from the options given below:

If $A$ be the set of all real numbers and R be the relation on A defined by $R = \{(a,b): a^2+b^2=1, \forall a,b \in A\}$, then R is

A function $f: \mathbb{R} \rightarrow \{x \in \mathbb{R}: -1 < x < 1\}$ is defined as $f(x) = \frac{x}{1+|x|}$, then $f$ is: