Skip to content

Sign in Sign up free

JEE Advanced Limits questions with solutions

Evaluation of limits and standard limit forms. 20 questions from our 2016–2025 JEE Advanced pattern papers, from the Class 11 Mathematics syllabus. Each has the answer and a full solution.

Also practise: Limits for JEE Main · Limits for NDA

JEE Advanced 2025

Define f(x)=lim n→∞(x^2n x^2+x)/(x^2n+1) for real x.JEE Advanced 2025 Paper 1 · medium
Match each limit in List-I with its value in List-II. List-I (P) lim x→0(tan x-x)/(x^3 (Q) lim x→0(x-sin x)/(x^3 (R) lim x→0(1-cos xcos 2xcos…JEE Advanced 2025 Paper 1 · medium

JEE Advanced 2024

Let L=lim n→∞Σk=1^n(k^2/(n^3+k^3. The value of e^3L is ______.JEE Advanced 2024 Paper 1 · easy
Match the entries of List-I with those of List-II. List-I P. lim x→0(1-cos xcos 2x)/(x^2 Q. ∫0^π(xsin x)/(1+cos ^2x) dx R. Area of the region bounded…JEE Advanced 2024 Paper 1 · medium
If L=lim x→0(e^x^2-cos x-frac32x^2/(x^4, then 24L equalsJEE Advanced 2024 Paper 2 · easy

JEE Advanced 2023

Let L=lim x→0(tan (sin x)-sin (tan x))/(x^7. Find 1/L.JEE Advanced 2023 Paper 1 · hard
Let L=lim x→0(1)/(x^4∫0^x(tan t-sin t) dt. The value of 1/L isJEE Advanced 2023 Paper 2 · medium

JEE Advanced 2022

Evaluate lim n→∞prodk=1^n(1+(k^2/(n^2)^1/n.JEE Advanced 2022 Paper 1 · medium
Match the limits in List-I with their values in List-II. List-I (P) lim x→0(e^x^2-cos x)/(x^2 (Q) lim x→0(x-sin x)/(x^2tan x) (R) lim…JEE Advanced 2022 Paper 1 · medium

JEE Advanced 2021

Limits has (have) the stated value?JEE Advanced 2021 Paper 1 · medium
Define f(x)=lim n→∞((x+1) x^2n+x^2/(x^2n+1) for every real x for which the limit exists.JEE Advanced 2021 Paper 2 · medium

JEE Advanced 2020

Lim x→0^+(1)/(x^5(∫0^x^2sin √ t dt-2/3x^3 equalsJEE Advanced 2020 Paper 1 · hard
Constants a and b are chosen so that L=lim x→0(x+a xcos x-bsin x)/(x^5 exists and is finite. Find 240 L.JEE Advanced 2020 Paper 2 · medium

JEE Advanced 2019

The value of lim x→0((sin x+tan x)/(2x))^1/x^2 is ______.JEE Advanced 2019 Paper 2 · medium

JEE Advanced 2018

Evaluate L=lim x→0((tan x)/(x)·(sin x)/(x))^1/x^2.JEE Advanced 2018 Paper 1 · hard
For real numbers p and q, define f(x)=lim n→∞(x^2n+2+(px+q))/(x^2n+1) for every real x, and suppose f is continuous on mathbb R.JEE Advanced 2018 Paper 2 · hard

JEE Advanced 2016

Let f(x)=lim n→∞(x^2n(x+2)+x^2/(x^2n+1).JEE Advanced 2016 Paper 1 · hard
Let L=lim n→∞1/n[(n+1)(n+2)…(2n)]^1/n. The value of e L isJEE Advanced 2016 Paper 1 · medium
Paragraph 2: For each positive integer n define an=Σk=1^n(n)/(n^2+k^2 and cn=Σk=1^n(k)/(n^2+k^2. Both are Riemann sums, with right end points, for…JEE Advanced 2016 Paper 2 · 2-question set

Other Mathematics topics

Area Under Curves 13 Binomial Theorem 10 Complex Numbers 24 Conic Sections 34 Differential Equations 18 Differentiation and Application of Derivatives 20 Indefinite and Definite Integrals 18 Matrices and Determinants 28 Permutations and Combinations 18 Probability 38 Quadratic Equations 12 Sequences and Series 11 Sets, Relations and Functions 8 Straight Lines and Circles 10 Three Dimensional Geometry 22 Trigonometry and Inverse Trigonometric Functions 18 Vector Algebra 9