Sets JEE Questions PDF with Solution, Practice Now

Sets JEE Questions: Sets are a crucial concept of mathematics and a significant part of the algebra section of JEE Main as well as Advanced. The topic of “Sets and Relations” in JEE questions checks your understanding of logic, grouping and relations between elements. Understanding how to approach and solve set problems is also essential as it will let you solve problems quicker during exams.

Sets questions are commonly asked in JEE Mains as well as JEE Advanced. Sets holds a weightage that is subject to change, but typically, you may expect around 1–3 questions in JEE Mains and 2–4 in JEE Advanced. Practicing sets questions will aid you in solving problems both swiftly and correctly, specifically those tricky logic-based questions. Solving sets and relations questions JEE Mains and Advanced, will help you recognise the JEE Main pattern from important PYQs JEE, build confidence and score higher.

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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

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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.