Sets JEE Questions PDF with Solution, Practice Now

Sets JEE Questions: As JEE Main 2026 Session 2 is currently ongoing, sets remain an important concept in Mathematics and a key part of the algebra section in both JEE Main and JEE Advanced. The topic of “Sets and Relations” tests your understanding of logic, grouping of elements, and relationships between them. A clear grasp of this topic helps you solve questions faster and more accurately during the exam.

Questions from sets are regularly asked in JEE Main as well as Advanced. While the exact weightage may vary each year, students can typically expect around 1–3 questions in JEE Main and 2–4 in JEE Advanced. Practicing sets and relations questions, especially previous year questions (PYQs), can help you quickly recognize patterns, improve accuracy, and boost your score in the remaining shifts.

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Sets JEE Questions Overview

Sets and Relations involve the definition of collection of elements and the relationship among them. For instance, the collection of all even numbers, all students in a class or all the elements with a given property can be defined as a set and relations define the relationship of the elements of one set with another set.

It's not just a topic for rote learning of formulas. The problems under this topic generally test your logical, reasoning and analytical skills. This is an important topic for JEE Main and Advanced exams. The problems are generally in the same pattern as asked in JEE exams i.e. in the form of multiple choice questions, integer type questions or reasoning-based questions.

Practice Sets JEE Questions

Consistent practice of sets questions in JEE is essential to master the topic. Students who solve past year's questions can learn the patterns and shortcuts necessary for rapid problem solving. Here are some practice Sets JEE Questions:

Q1. Let f(x) = x² - 2x - 3; x ≥ 1 and g(x) = 1 + √(x² + 4); x ≥ -4, then the number of real solutions of equation f(x) = g(x) is/are

A. 0
B. 1
C. 2
D. 4

2. The complete set of values of x in the domain of function f(x) = √[log₈(x+2){x} (|x|² - 5|x| + 7)] is:

A. (-1/3, 0) ∪ (1/3, 1) ∪ (2, ∞)
B. (0, 1) ∪ (1, ∞)
C. (-2/3, 0) ∪ (1/3, 1) ∪ (1, ∞)
D. (-1/3, 0) ∪ (1/3, 1) ∪ (1, ∞)

3. Let f: R → R is defined by f(x) = {(x+1)³ ; x ≤ 1, ln(x+b² - 3b + 10) ; x > 1} is invertible, then the set of all values of ‘b’ is:

A. {1, 2}
B. ϕ
C. {2, 5}
D. None of these

4. Consider all function f: {1, 2, 3, 4} → {1, 2, 3, 4} which are one-one, onto and satisfy the following property: if f(k) is odd then f(k+1) is even, k = 1, 2, 3. The number of such function is:

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

5. Number of elements in the range set of f(x) = [x/15] - [15/x], ∀ x ∈ (0, 90) ; (where [.] denotes greatest integer function):

A. 5
B. 6
C. 7
D. Infinite

6. If 3 ≤ a < 4 then the value of sin⁻¹(sin[a]) + tan⁻¹(tan[a]) + sec⁻¹(sec[a]), where [x] denotes greatest integer function less than or equal to x, is equal to:

A. 3
B. 2π - 9
C. 2π - 3
D. 9 - 2π

7. Range of the function f(x) = cot⁻¹{-x} + sin⁻¹{x} + cos⁻¹{x}, where {.} denotes fractional part function:

A. (3π/4, π)
B. [3π/4, π)
C. [3π/4, π]
D. (3π/4, π]

8. The solution set of the inequality (cosec⁻¹ x)² - 2cosec⁻¹ x ≥ π/6 (cosec⁻¹ x - 2) is (−∞, a] ∪ [b, ∞), then (a² + b²) equals:

A. 0
B. 5
C. 2
D. 10

9. The complete solution set of the inequality (cos⁻¹ x)² - (sin⁻¹ x)² > 0 is:

A. (0, 1/√2)
B. [-1, 1/√2)
C. (-1, 1)
D. [-1, 1/2)

10. sin⁻¹(x²/4 + y²/9) + cos⁻¹(x/2√2 + y/3√2 - 2) equals to:

A. π/2
B. π
C. π/√2
D. 3π/2

Watch Sets Question Practice Video on YT

Sets JEE Questions PDF with Solution

To help students prepare well, Physics Wallah provides a Sets JEE Questions PDF that includes carefully selected problems with step-by-step answers and solutions. The PDF also covers important tricks and theory points so that students can revise quickly. It is designed to follow the JEE exam pattern, giving real exam-like practice for both Mains and Advanced.