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

The relation R on the set of real numbers defined by $R = \{(a, b): a \leq b^2\}$ is

(A) Reflexive

(B) Not symmetric

(C) Neither reflexive nor transitive

(D) Transitive

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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)}

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The function $f: \mathbb{R} \rightarrow [-1, 1]$ defined by $f(x) = \cos x$ is:

Match List-I with List-II

Let $f: A \rightarrow B$ be a function given by $f(x) = x^2$

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Let a function $f:\mathbb{R}\to\mathbb{R}$ defined as $f(x)=x-[x]$, (where $\mathbb{R}$ is set of real numbers & $[.]$ denotes greatest integer function) .Then the function:

A. A relation $R$ on a set $A$ is called an equivalence relation, if it is reflexive, symmetric and transitive.

B. The function $f : R \to R$ defined by $f(x) = e^x$ is not one-one.

C. The one-one function is also known as injective function.

D. The onto function is also known as subjective function.

E. A function $f : X \to Y$ is said to be many-one, if two or more than two elements in set $X$ have the different image in set $Y$.

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