CUET Mathematics: AlgebraRelations & Functions. Free, no login required.

Relation R on Real Numbers is defined as $R = \{(a, b) : a \leq b\}$. The relation is :

Which of the following graphs represent a function ?

If a set P contains 5 elements and the set Q contains 8 elements, then the number of one-one functions from A to B is :

Given relation $R = \{(x, y) : y = x + 5, x < 4, x, y \in N\}$. Where N is a set of natural numbers then :

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 :

The inverse of the function $f : R \to R$ given by $f(x) = 2x + 7$ is :

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

Let L be the set of all lines in a plane and R be the relation in L defined as $R = \{(l_1, l_2) : l_1 \text{ is perpendicular to } l_2, \text{ where } l_1, l_2 \in L\}$. Choose the correct answer :

The Relation $R = \{(x, y) : x \leq y^2\}$ defined on the set $\mathbf{R}$ of Real numbers is :

(A) reflexive but not symmetric

(B) neither reflexive nor symmetric

(C) neither reflexive nor transitive

(D) reflexive but not transitive

(E) not reflexive but symmetric

Choose the correct answer from the options given below :

Let $f : [2, \infty) \to \mathbf{R}$ be a function defined by $f(x) = x^2 - 4x + 5$. The range of $f$ is :

Which of the following relations on the set $A = \{1, 2, 3\}$ are equivalence ?

(A) $R = \{(1,1), (2,2), (1,2), (2,1)\}$

(B) $R = \{(1,1), (2,2), (3,3)\}$

(C) $R = \{(1,1), (1,2), (2,1)\}$

(D) $R = \{(1,1), (2,2), (3,3), (1,2), (2,1), (2,3), (3,2), (1,3), (3,1)\}$

(E) $R = \{(1,1), (2,2), (3,3), (1,2)\}$

Choose the correct answer from the options given below :

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 :

If a relation R is defined on the set $X = \{1, 2, 3, 4\}$ as $R = \{(1,1), (2,2), (3,4), (4,3)\}$, then R is

Match List I with List II

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A function f: R $\to$ R is given by $f(x) = x^3 + 3$. If $f(x) = -24$, then the value of x is:

If R is a relation on $A = \{a, b, c\}$ such that $R = \{(a,a), (b,b)\}$, which element/elements should be included to make R an equivalence relation.

A. (c, c)

B. (c, c), (a, c), (c, a)

C. (a, b), (b, c), (a, c)

D. (b, c), (c, c), (c, a), (b, a)

Choose the correct answer from the options given below:

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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If $R$ is a relation on $Z$ (set of all integers) defined by $xRy$, iff $|x - y| \leq 1$, then

(a) $R$ is reflexive

(b) $R$ is symmetric

(c) $R$ is transitive

(d) $R$ is not symmetric

(e) $R$ is not transitive

Choose the most appropriate answer from the options given below

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

If $f:\mathbb{R} \to [-5, \infty)$ is defined as $f(x) = x^2 - 5$, then the function f is

A. one-one

B. many-one

C. onto

D. into

Which of the above statements are true?

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A relation R = {(1,1),(2,2),(3,3),(1,2),(2,1),(1,3),(2,3)} on A = {1,2,3} will be an equivalence relation, if we delete:

Choose the correct answer from the options given below:

Which of the following statements are true?

(A) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = 3x$ is one-one onto.

(B) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = x^4$ is one-one and onto.

(C) $f:\mathbb{Z} \to \mathbb{Z}$ given by $f(x) = x^2$ is neither one-one nor onto.

(D) $f:\mathbb{R} \to \mathbb{R}$ given by $f(x) = |x|$ is neither one-one nor onto.

(Where $\mathbb{R}$ is the set of all real numbers and $\mathbb{Z}$ is the set of all integers)

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Let $R : \mathbb{R} \to \mathbb{R}$, where $\mathbb{R}$ is the set of real numbers and R be a relation. An element $(x, y) \in R$ if $x + y - \sqrt{2}$ belongs to the set of irrational numbers. Then the relation R is :

If $n(A) = 3$, $n(B) = 2$, then number of all possible surjective function from set A to set B are :

Let A = {1,2,3}. Consider the relation R = {(1,1),(2,2),(3,3),(1,2),(2,3),(1,3)}. Then R is

A manufacturer can sell $x$ items at a price of Rs $3x+5$ each. The cost price of $x$ items is Rs $x^2 + 5x$. If x is the number of items she should sell to get no profit and no loss, then:

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

The range of the function $f(x) = \frac{1}{3 - \sin 4x}$ is: