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A relation $f: N \rightarrow N$ be defined by $f(x) = x^2$, $x \in N$ (Set of Natural numbers). Then $f(x)$ is

Let $R = \{(L_1, L_2): L_1 \perp L_2\$ where $L_1, L_2 \in L$ (set of straight line in a plane)}, then

If R be a relation on the set of integers Z, given by R = {(a, b) : (a - b) is a multiple of 3}, then R is:

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

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:

The relation R in $\mathbb{R}$ (set of real numbers) is defined by $R = \{(a,b): a \leq b^3\}$, then R is

Match List-I with List-II

Where ℝ is set of real numbers

Choose the correct answer from the options given below:

If R and S are two equivalence relations on a set A, then

Which of the following are correct?

(A) If a ≡ b(mod n), then -a ≡ -b (mod n)

(B) If a + b = c, then a(mod n) + b(mod n) ≡ (a + b + c)(mod n).

(C) If a ≡ b (mod n), then ka ≡ kb(mod n), ∀ k ∈ I.

(D) If a ≡ b (mod n), then (a + k) ≡ (b + k)(mod n), ∀ k ∈ I.

Choose the correct answer from the options given below:

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

If $A = \{1, 2, 3, 4, ..., n\}$ and $B = \{x, y\}$, then the number of surjections from A to B is

A relation R in the set A = {1, 2,3, 4} is given by R = {(1,1), (2,2), (1,2), (2,3), (3,4), (4,4), (1,3), (2,4), (1,4)} is

Which of the following functions from $\mathbb{Z}$ to $\mathbb{Z}$ is a bijective function? (where $\mathbb{Z}$ is set of integers)

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:

Let a relation R = {(a, b) : a is a factor of b, a, b $\in$ N}. Then, R is ______.

The function $f: [0, \infty) \rightarrow \mathbb{R}$ defined by, $f(x) = 2x^2 + 3$, is

Let f: $\mathbb{R} \rightarrow \mathbb{R}$ be defined as $f(x) = 10x$. Then (Where $\mathbb{R}$ is the set of real numbers)

Let $A = \{1, 2, 3\}$. Then, the number of relations containing $(1, 2)$ and $(1, 3)$ which are reflexive and symmetric but not transitive, is

Match List-I with List-II

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

Choose the correct answer from the options given below:

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:

Let $f: \mathbb{R}$ -> $\mathbb{R}$ be a function defined as $f(x) = x^4$. Which one of the following is true?

Let $A = \{a, b, c\}$. Then number of relations containing $(a,b)$ and $(b, c)$ which are reflexive and transitive but not symmetric is

If the function $f: \mathbb{N} \rightarrow \mathbb{N}$ is defined as $f(n)=\left\{\begin{array}{ll}n-1, & \text { if } n \text { is even } \\ n+1, & \text { if } n \text { is odd }\end{array}\right.$, then

(A) f is injective

(B) f is into

(C) f is surjective

(D) f is invertible

Let R be the relation over the set A of all straight lines in a plane such that $l_{1} \mathrm{R} l_{2} \Leftrightarrow l_{1}$ is parallel to $l_{2}$. Then R is :

The number of all onto functions from the set {1, 2, .......n} to itself is

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

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

Match List - I with List - II.

Choose the correct answer from the options given below :

Let R be a relation on the set of natural numbers N defined by nRm if n divides m. Then R is :

(A) Reflexive Relation

(B) Symmetric Relation

(C) Transitive Relation

(D) Identity Relation

Choose the correct answer from the options given below :

If $f(x) = \sqrt{x}$, $g(x) = 2x - 3$, then domain of $fog(x)$ is :