Sets, Relations & Functions for Competitive Exam Prep

My Learning Cart

Sets, Relations & Functions

Download Q&A

Sets, Relations & Functions MCQ & Objective Questions

Understanding "Sets, Relations & Functions" is crucial for students aiming to excel in their exams. This topic forms the foundation of many mathematical concepts and is frequently tested in various assessments. Practicing MCQs and objective questions not only enhances your grasp of the subject but also boosts your confidence in tackling important questions during exams.

What You Will Practise Here

Basic definitions and properties of sets
Types of relations and their characteristics
Functions: definitions, types, and notations
Operations on sets: union, intersection, and difference
Venn diagrams and their applications
Domain, range, and co-domain of functions
Important theorems related to sets and functions

Exam Relevance

The topic of "Sets, Relations & Functions" is integral to the curriculum of CBSE, State Boards, and competitive exams like NEET and JEE. You can expect questions that require you to apply concepts in problem-solving scenarios. Common question patterns include identifying properties of sets, solving problems involving relations, and interpreting functions graphically. Mastery of this topic can significantly enhance your performance in both objective and subjective formats.

Common Mistakes Students Make

Confusing the definitions of sets and subsets
Misunderstanding the types of relations (reflexive, symmetric, transitive)
Overlooking the importance of domain and range in functions
Errors in Venn diagram representations
Neglecting to apply the correct operations on sets

FAQs

Question: What are the different types of sets?
Answer: The different types of sets include finite sets, infinite sets, equal sets, null sets, and singleton sets.

Question: How do I determine the domain and range of a function?
Answer: The domain is the set of all possible input values, while the range is the set of all possible output values based on the function's definition.

Start solving practice MCQs today to solidify your understanding of "Sets, Relations & Functions". Testing your knowledge with objective questions will prepare you for success in your exams!

Functions & types Inverse trigonometric functions Sets, subsets, power set Types of relations

Q. Consider the relation R on the set of real numbers defined by R = {(x, y) | x^2 + y^2 = 1}. What type of relation is R?

A. Reflexive
B. Symmetric
C. Transitive
D. None of the above

Solution

R is symmetric because if (x,y) is in R, then (y,x) is also in R. It is not reflexive or transitive.

Correct Answer: B — Symmetric

Q. Evaluate cos^(-1)(0).

A. 0
B. π/2
C. π
D. 3π/2

Solution

cos^(-1)(0) = π, since cos(π) = 0.

Correct Answer: C — π

Q. Evaluate sin^(-1)(sin(π/4)).

A. π/4
B. 3π/4
C. π/2
D. 0

Solution

sin^(-1)(sin(π/4)) = π/4

Correct Answer: A — π/4

Q. Evaluate tan(sin^(-1)(1/√2)).

A. 1
B. √2
C. 0
D. 2

Solution

If sin(x) = 1/√2, then x = π/4, thus tan(sin^(-1)(1/√2)) = tan(π/4) = 1.

Correct Answer: A — 1

Q. Evaluate tan^(-1)(√3).

A. π/3
B. π/4
C. π/6
D. π/2

Solution

tan^(-1)(√3) = π/3, since tan(π/3) = √3.

Correct Answer: A — π/3

Q. Evaluate the expression sin^(-1)(x) + cos^(-1)(x).

A. 0
B. π/2
C. π
D. undefined

Solution

sin^(-1)(x) + cos^(-1)(x) = π/2 for all x in the domain [-1, 1].

Correct Answer: B — π/2

Q. Evaluate the expression sin^(-1)(x) + sin^(-1)(√(1-x^2)).

A. π/2
B. π/4
C. π/3
D. 0

Solution

Using the identity sin^(-1)(x) + sin^(-1)(√(1-x^2)) = π/2 for x in [0, 1], the value is π/2.

Correct Answer: A — π/2

Q. Evaluate the expression: 2sin^(-1)(1/2) + 2cos^(-1)(1/2).

A. π
B. 2π
C. π/2
D. 0

Solution

2sin^(-1)(1/2) = 2(π/6) = π/3 and 2cos^(-1)(1/2) = 2(π/3) = 2π/3. Therefore, the total is π/3 + 2π/3 = π.

Correct Answer: A — π

Q. Evaluate \( \cos(\cos^{-1}(\frac{3}{5})) \).

A. 0
B. \( \frac{3}{5} \)
C. 1
D. undefined

Solution

By definition, \( \cos(\cos^{-1}(x)) = x \). Therefore, \( \cos(\cos^{-1}(\frac{3}{5})) = \frac{3}{5} \).

Correct Answer: B — \( \frac{3}{5} \)

Q. Find the value of cos(tan^(-1)(3/4)).

A. 4/5
B. 3/5
C. 5/4
D. 3/4

Solution

Using the identity, cos(tan^(-1)(3/4)) = 4/5

Correct Answer: A — 4/5

Q. Find the value of cos^(-1)(0).

A. 0
B. π/2
C. π
D. 3π/2

Solution

cos^(-1)(0) = π/2, since cos(π/2) = 0.

Correct Answer: B — π/2

Q. Find the value of sin^(-1)(√3/2) + cos^(-1)(1/2).

A. π/3
B. π/2
C. π/4
D. π/6

Solution

sin^(-1)(√3/2) = π/3 and cos^(-1)(1/2) = π/3. Therefore, the sum is π/3 + π/3 = 2π/3.

Correct Answer: A — π/3

Q. Find the value of \( \sin(\sin^{-1}(\frac{1}{2})) \).

A. 0
B. \( \frac{1}{2} \)
C. 1
D. undefined

Solution

By definition, \( \sin(\sin^{-1}(x)) = x \). Therefore, \( \sin(\sin^{-1}(\frac{1}{2})) = \frac{1}{2} \).

Correct Answer: B — \( \frac{1}{2} \)

Q. For the set E = {1, 2, 3, 4}, how many subsets contain the element 1?

A. 4
B. 8
C. 12
D. 16

Solution

If 1 is included, we can choose from the remaining elements {2, 3, 4}, which has 2^3 = 8 subsets.

Correct Answer: C — 12

Q. For the set E = {1, 2, 3, 4}, how many subsets have exactly 2 elements?

A. 4
B. 6
C. 8
D. 10

Solution

The number of ways to choose 2 elements from 4 is given by the combination formula C(4,2) = 6.

Correct Answer: B — 6

Q. For the set F = {a, b, c}, how many subsets have exactly 2 elements?

A. 1
B. 2
C. 3
D. 4

Solution

The subsets with exactly 2 elements are {a, b}, {a, c}, and {b, c}. Total = 3.

Correct Answer: C — 3

Q. How many elements are in the power set of the empty set?

A. 0
B. 1
C. 2
D. Infinite

Solution

The power set of the empty set contains only one subset, which is the empty set itself. Thus, it has 1 element.

Correct Answer: B — 1

Q. How many relations can be formed from a set with 3 elements?

A. 3
B. 6
C. 8
D. 16

Solution

The number of relations on a set with n elements is 2^(n^2). For n = 3, it is 2^(3^2) = 2^9 = 512.

Correct Answer: C — 8

Q. How many subsets can be formed from the set C = {x, y, z, w}?

A. 4
B. 8
C. 16
D. 2

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 4, so 2^4 = 16.

Correct Answer: B — 8

Q. How many subsets can be formed from the set G = {1, 2, 3, 4, 5, 6}?

A. 32
B. 64
C. 128
D. 256

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 6, so the number of subsets is 2^6 = 64.

Correct Answer: C — 128

Q. How many subsets can be formed from the set H = {a, b, c, d, e, f}?

A. 32
B. 64
C. 128
D. 256

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 6, so 2^6 = 64.

Correct Answer: B — 64

Q. How many subsets can be formed from the set {1, 2, 3, 4, 5, 6}?

A. 32
B. 64
C. 128
D. 256

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 6, so the number of subsets is 2^6 = 64.

Correct Answer: D — 256

Q. How many subsets can be formed from the set {x, y, z, w, v}?

A. 16
B. 32
C. 64
D. 8

Solution

The number of subsets of a set with n elements is 2^n. Here, n = 5, so 2^5 = 32.

Correct Answer: A — 16

Q. How many subsets does the set A = {a, b, c, d} have?

A. 4
B. 8
C. 16
D. 2

Solution

The number of subsets of a set with n elements is given by 2^n. Here, n = 4, so the number of subsets is 2^4 = 16.

Correct Answer: B — 8

Q. How many subsets does the set B = {a, b, c, d} have?

A. 4
B. 8
C. 16
D. 2

Solution

The number of subsets of a set with n elements is 2^n. Here, n=4, so the number of subsets is 2^4 = 16.

Correct Answer: B — 8

Q. How many subsets of the set H = {x, y} are there that do not contain the element y?

A. 1
B. 2
C. 3
D. 4

Solution

The only subset that does not contain y is {∅} and {x}. Total = 2.

Correct Answer: A — 1

Q. If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is A ⊆ B?

A. True
B. False
C. Depends on A
D. Not enough information

Solution

A is a subset of B if all elements of A are in B. Here, all elements of A are in B, so A ⊆ B is true.

Correct Answer: A — True

Q. If A = {1, 2, 3} and B = {1, 2, 3, 4}, what is the number of subsets of A ∪ B?

A. 8
B. 16
C. 4
D. 12

Solution

A ∪ B = {1, 2, 3, 4}, which has 4 elements. The number of subsets is 2^4 = 16.

Correct Answer: B — 16

Q. If A = {1, 2, 3} and B = {1, 2}, what is the number of elements in A × B?

A. 2
B. 3
C. 6
D. 4

Solution

The number of elements in the Cartesian product A × B is the product of the number of elements in A and B. Here, |A| = 3 and |B| = 2, so |A × B| = 3 * 2 = 6.

Correct Answer: D — 4

Q. If A = {1, 2, 3} and B = {3, 4}, what is the Cartesian product A × B?

A. {(1, 3), (2, 4)}
B. {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}
C. {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4), (1, 1), (2, 2), (3, 3)}
D. {}

Solution

The Cartesian product A × B is the set of all ordered pairs (a, b) where a ∈ A and b ∈ B, which is {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}.

Correct Answer: B — {(1, 3), (1, 4), (2, 3), (2, 4), (3, 3), (3, 4)}

1
2
3
4
5
6
7
8
>
>|

Showing 1 to 30 of 219 (8 Pages)

School

College

Degree

Competitve

Skills

Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely