Limits JEE Questions PDF with Solution, Practice Now

With JEE Main 2026 Session 2 ongoing, students should now focus on quick revision and high-impact topics like Limits. This chapter is a fundamental part of Calculus and builds the base for derivatives, continuity, and other advanced concepts. It helps in understanding how a function behaves as the input approaches a specific value. Regular practice of Limits JEE questions improves speed, increases accuracy, and prepares students to solve tricky and application-based problems asked in both JEE Main and Advanced.

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Limits JEE Questions Overview

The concept of limit is used in evaluating standard limits, application of L’Hospital’s Rule for calculus, Continuity and in various real life problems. JEE limits and continuity questions are asked to test the students’ understanding of the application of limits in problems involving polynomials, trigonometric functions, exponential functions, and logarithms. Limits JEE Mains questions are usually direct questions based on a formula. JEE calculus limits problems for Advanced are multi-stepped reasoning questions and sometimes they involve a combination of more than one concepts. Practicing important limits and continuity previous year's questions JEE will help you get an idea about the JEE exam patterns that may be followed in the exam.

Practice Limits JEE Questions

Practice is a crucial step in understanding the chapter Practicing Limits JEE Questions. Students should practice questions related to the evaluation of limits at a point, limits at infinity, and piecewise functions.

1. If the function f(x) = -4e^((1-x)/2) + 1 + x + x^2/2 + x^3/3 and g(x) = f^(-1)(x), then the value of g(-7/6) equals

A. 1/5
B. -1/5
C. 6/7
D. -6/7

2. If f(x) =
 for x < 3: [(e^((x+3)ln27))^(x/27) - 9] / (3^x - 27)
 for x > 3: λ (1 - cos(x-3)) / [(x-3) tan(x-3)]
and if lim x→3 f(x) exists, then λ =

A. 9/2
B. 2/9
C. 2/3
D. None of these

3. lim x→π/2 cos^(-1) [ (sin x /4)(3sin x - sin 3x) ] (where [.] denotes greatest integer function) is

A. 2/π
B. 1
C. 4/π
D. does not exist

4. The value of lim x→0 [ (1 - 2x)^n Σ (r=0 to n) nCr [(x + x^2)/(1 - 2x)]^r ]^(1/x) is

A. e^n
B. e^(-n)
C. e^(3n)
D. e^(-3n)

5. If lim x→c^- {ln x} and lim x→c^+ {ln x} exist finitely but they are not equal (where {.} denotes fractional part function), then:

A. 'c' can take only rational values
B. 'c' can take only irrational values
C. 'c' can take infinite values in which only one is irrational
D. 'c' can take infinite values in which only one is rational

6. If m and n are positive integers, then lim x→0 [ (cos x)^m - (cos x)^(1/n) ] / x^2 equals

A. m - n
B. 1/n - 1/m
C. (m - n) / (2 m n)
D. None of these

7. What is the value of a + b, if lim x→0 [ sin(ax) - ln(e^(x cos x)) ] / [ x sin(bx) ] = 1/2?

A. 1
B. 2
C. 3
D. -1/2

8. If f(x) = e^(x-1), for 0 ≤ x ≤ 1 x + 1 - {x}, for 1 < x < 3 and g(x) = x^2 - a x + b such that f(x) g(x) is continuous in , then the ordered pair (a,b) is (where {.} denotes fractional part)

A. (2, 3)
B. (1, 2)
C. (3, 2)
D. (2, 2)

9. The value of lim x→0 [ (sin x - tan x)^2 - (1 - cos 2x)^4 + x^5 ] / [ (7 tan^(-1) x)^7 + (sin^(-1) x)^6 + 3 sin^5 x ] equals

A. 0
B. 1/7
C. 2
D. 1/3

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Limits JEE Questions PDF with Solution

To help you prepare better, PW has created a practice question PDF with answer and solution for Limits JEE Questions. The PDF consists of a blend of problems, such as direct limits JEE Mains questions, conceptual JEE calculus limits questions, and important limits and continuity PYQs JEE. Step by step solutions are provided so that students can learn methods and formulas in a better way. Practice this PDF regularly and you will be able to revise important concepts, solve examplike questions, and enhance your speed and accuracy.