1

JEE Main 2023 (Online) 8th April Morning Shift

MCQ (Single Correct Answer)

+4

-1

$$\lim_\limits{x \rightarrow 0}\left(\left(\frac{\left(1-\cos ^{2}(3 x)\right.}{\cos ^{3}(4 x)}\right)\left(\frac{\sin ^{3}(4 x)}{\left(\log _{e}(2 x+1)\right)^{5}}\right)\right)$$ is equal to _____________.

2

JEE Main 2023 (Online) 6th April Morning Shift

MCQ (Single Correct Answer)

+4

-1

Let $$a_{1}, a_{2}, a_{3}, \ldots, a_{\mathrm{n}}$$ be $$\mathrm{n}$$ positive consecutive terms of an arithmetic progression. If $$\mathrm{d} > 0$$ is its common difference, then

$$\lim_\limits{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_{1}}+\sqrt{a_{2}}}+\frac{1}{\sqrt{a_{2}}+\sqrt{a_{3}}}+\ldots \ldots \ldots+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_{n}}}\right)$$ is

3

JEE Main 2023 (Online) 31st January Evening Shift

MCQ (Single Correct Answer)

+4

-1

$$
\lim\limits_{x \rightarrow \infty} \frac{(\sqrt{3 x+1}+\sqrt{3 x-1})^6+(\sqrt{3 x+1}-\sqrt{3 x-1})^6}{\left(x+\sqrt{x^2-1}\right)^6+\left(x-\sqrt{x^2-1}\right)^6} x^3
$$

4

JEE Main 2023 (Online) 30th January Evening Shift

MCQ (Single Correct Answer)

+4

-1

Let $f, g$ and $h$ be the real valued functions defined on $\mathbb{R}$ as

$f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right.$

$g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-1\end{array}\right.$

and $h(x)=2[x]-f(x)$, where $[x]$ is the greatest integer $\leq x$. Then the

value of $\lim\limits_{x \rightarrow 1} g(h(x-1))$ is :

$f(x)=\left\{\begin{array}{cc}\frac{x}{|x|}, & x \neq 0 \\ 1, & x=0\end{array}\right.$

$g(x)=\left\{\begin{array}{cc}\frac{\sin (x+1)}{(x+1)}, & x \neq-1 \\ 1, & x=-1\end{array}\right.$

and $h(x)=2[x]-f(x)$, where $[x]$ is the greatest integer $\leq x$. Then the

value of $\lim\limits_{x \rightarrow 1} g(h(x-1))$ is :

Questions Asked from Limits, Continuity and Differentiability (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2024 (Online) 9th April Evening Shift (1)
JEE Main 2024 (Online) 8th April Evening Shift (1)
JEE Main 2024 (Online) 6th April Evening Shift (1)
JEE Main 2024 (Online) 5th April Evening Shift (1)
JEE Main 2024 (Online) 5th April Morning Shift (1)
JEE Main 2024 (Online) 4th April Evening Shift (1)
JEE Main 2024 (Online) 4th April Morning Shift (1)
JEE Main 2024 (Online) 1st February Evening Shift (2)
JEE Main 2024 (Online) 1st February Morning Shift (1)
JEE Main 2024 (Online) 31st January Evening Shift (1)
JEE Main 2024 (Online) 31st January Morning Shift (2)
JEE Main 2024 (Online) 27th January Evening Shift (2)
JEE Main 2024 (Online) 27th January Morning Shift (2)
JEE Main 2023 (Online) 15th April Morning Shift (1)
JEE Main 2023 (Online) 13th April Evening Shift (1)
JEE Main 2023 (Online) 11th April Evening Shift (1)
JEE Main 2023 (Online) 11th April Morning Shift (1)
JEE Main 2023 (Online) 8th April Evening Shift (1)
JEE Main 2023 (Online) 8th April Morning Shift (1)
JEE Main 2023 (Online) 6th April Morning Shift (1)
JEE Main 2023 (Online) 31st January Evening Shift (1)
JEE Main 2023 (Online) 30th January Evening Shift (1)
JEE Main 2023 (Online) 30th January Morning Shift (1)
JEE Main 2023 (Online) 29th January Morning Shift (1)
JEE Main 2023 (Online) 25th January Evening Shift (1)
JEE Main 2023 (Online) 25th January Morning Shift (1)
JEE Main 2023 (Online) 24th January Evening Shift (1)
JEE Main 2023 (Online) 24th January Morning Shift (2)
JEE Main 2022 (Online) 29th July Evening Shift (1)
JEE Main 2022 (Online) 29th July Morning Shift (2)
JEE Main 2022 (Online) 28th July Evening Shift (1)
JEE Main 2022 (Online) 27th July Evening Shift (1)
JEE Main 2022 (Online) 26th July Evening Shift (1)
JEE Main 2022 (Online) 26th July Morning Shift (4)
JEE Main 2022 (Online) 25th July Evening Shift (1)
JEE Main 2022 (Online) 25th July Morning Shift (1)
JEE Main 2022 (Online) 29th June Evening Shift (1)
JEE Main 2022 (Online) 28th June Evening Shift (2)
JEE Main 2022 (Online) 28th June Morning Shift (1)
JEE Main 2022 (Online) 27th June Morning Shift (1)
JEE Main 2022 (Online) 26th June Evening Shift (2)
JEE Main 2022 (Online) 26th June Morning Shift (2)
JEE Main 2022 (Online) 25th June Evening Shift (1)
JEE Main 2022 (Online) 25th June Morning Shift (1)
JEE Main 2022 (Online) 24th June Evening Shift (1)
JEE Main 2021 (Online) 31st August Evening Shift (2)
JEE Main 2021 (Online) 31st August Morning Shift (3)
JEE Main 2021 (Online) 27th August Evening Shift (1)
JEE Main 2021 (Online) 27th August Morning Shift (1)
JEE Main 2021 (Online) 26th August Evening Shift (2)
JEE Main 2021 (Online) 27th July Evening Shift (2)
JEE Main 2021 (Online) 27th July Morning Shift (2)
JEE Main 2021 (Online) 25th July Morning Shift (1)
JEE Main 2021 (Online) 22th July Evening Shift (1)
JEE Main 2021 (Online) 20th July Evening Shift (1)
JEE Main 2021 (Online) 20th July Morning Shift (1)
JEE Main 2021 (Online) 18th March Evening Shift (1)
JEE Main 2021 (Online) 18th March Morning Shift (2)
JEE Main 2021 (Online) 17th March Evening Shift (2)
JEE Main 2021 (Online) 17th March Morning Shift (1)
JEE Main 2021 (Online) 16th March Evening Shift (2)
JEE Main 2021 (Online) 16th March Morning Shift (2)
JEE Main 2021 (Online) 26th February Evening Shift (3)
JEE Main 2021 (Online) 26th February Morning Shift (1)
JEE Main 2021 (Online) 25th February Morning Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 6th September Evening Slot (2)
JEE Main 2020 (Online) 5th September Evening Slot (1)
JEE Main 2020 (Online) 5th September Morning Slot (2)
JEE Main 2020 (Online) 4th September Evening Slot (2)
JEE Main 2020 (Online) 3rd September Evening Slot (1)
JEE Main 2020 (Online) 3rd September Morning Slot (1)
JEE Main 2020 (Online) 2nd September Evening Slot (1)
JEE Main 2020 (Online) 2nd September Morning Slot (1)
JEE Main 2020 (Online) 9th January Evening Slot (1)
JEE Main 2020 (Online) 9th January Morning Slot (2)
JEE Main 2020 (Online) 8th January Evening Slot (1)
JEE Main 2020 (Online) 8th January Morning Slot (1)
JEE Main 2019 (Online) 12th April Evening Slot (2)
JEE Main 2019 (Online) 12th April Morning Slot (1)
JEE Main 2019 (Online) 10th April Evening Slot (1)
JEE Main 2019 (Online) 10th April Morning Slot (3)
JEE Main 2019 (Online) 9th April Evening Slot (2)
JEE Main 2019 (Online) 9th April Morning Slot (2)
JEE Main 2019 (Online) 8th April Evening Slot (2)
JEE Main 2019 (Online) 8th April Morning Slot (1)
JEE Main 2019 (Online) 12th January Evening Slot (2)
JEE Main 2019 (Online) 12th January Morning Slot (2)
JEE Main 2019 (Online) 11th January Evening Slot (2)
JEE Main 2019 (Online) 11th January Morning Slot (2)
JEE Main 2019 (Online) 10th January Evening Slot (1)
JEE Main 2019 (Online) 10th January Morning Slot (2)
JEE Main 2019 (Online) 9th January Evening Slot (1)
JEE Main 2019 (Online) 9th January Morning Slot (2)
JEE Main 2018 (Online) 16th April Morning Slot (2)
JEE Main 2018 (Offline) (2)
JEE Main 2018 (Online) 15th April Evening Slot (3)
JEE Main 2018 (Online) 15th April Morning Slot (1)
JEE Main 2017 (Online) 9th April Morning Slot (1)
JEE Main 2017 (Online) 8th April Morning Slot (1)
JEE Main 2017 (Offline) (1)
JEE Main 2016 (Online) 10th April Morning Slot (2)
JEE Main 2016 (Online) 9th April Morning Slot (2)
JEE Main 2016 (Offline) (2)
JEE Main 2015 (Offline) (2)
JEE Main 2014 (Offline) (1)
JEE Main 2013 (Offline) (1)
AIEEE 2012 (2)
AIEEE 2011 (2)
AIEEE 2010 (1)
AIEEE 2009 (1)
AIEEE 2008 (1)
AIEEE 2007 (2)
AIEEE 2006 (1)
AIEEE 2005 (3)
AIEEE 2004 (2)
AIEEE 2003 (4)
AIEEE 2002 (8)

JEE Main Subjects

Physics

Mechanics

Units & Measurements Vector Algebra Motion Circular Motion Laws of Motion Work Power & Energy Center of Mass and Collision Rotational Motion Properties of Matter Heat and Thermodynamics Simple Harmonic Motion Waves Gravitation

Electricity

Electrostatics Current Electricity Capacitor Magnetic Effect of Current Magnetic Properties of Matter Electromagnetic Induction Alternating Current Electromagnetic Waves

Optics

Modern Physics

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Structure of Atom Redox Reactions Gaseous State Chemical Equilibrium Ionic Equilibrium Solutions Thermodynamics Electrochemistry Chemical Kinetics and Nuclear Chemistry Solid State Surface Chemistry

Inorganic Chemistry

Periodic Table & Periodicity Chemical Bonding & Molecular Structure Isolation of Elements Hydrogen s-Block Elements p-Block Elements d and f Block Elements Coordination Compounds Environmental Chemistry

Organic Chemistry

Mathematics

Algebra

Sets and Relations Logarithm Quadratic Equation and Inequalities Sequences and Series Mathematical Induction Binomial Theorem Matrices and Determinants Permutations and Combinations Probability Vector Algebra 3D Geometry Complex Numbers Statistics Mathematical Reasoning

Trigonometry

Trigonometric Ratio and Identites Trigonometric Equations Inverse Trigonometric Functions Properties of Triangle Height and Distance

Coordinate Geometry

Calculus