1

AIEEE 2010

MCQ (Single Correct Answer)

+4

-1

Let $$f:R \to R$$ be a continuous function defined by
$$$f\left( x \right) = {1 \over {{e^x} + 2{e^{ - x}}}}$$$

**Statement - 1 :** $$f\left( c \right) = {1 \over 3},$$ for some $$c \in R$$.

**Statement - 2 :** $$0 < f\left( x \right) \le {1 \over {2\sqrt 2 }},$$ for all $$x \in R$$

2

AIEEE 2009

MCQ (Single Correct Answer)

+4

-1

Let $$f\left( x \right) = x\left| x \right|$$ and $$g\left( x \right) = \sin x.$$

**Statement-1:**gof is differentiable at $$x=0$$ and its derivative is continuous at that point.**Statement-2:**gof is twice differentiable at $$x=0$$.3

AIEEE 2009

MCQ (Single Correct Answer)

+4

-1

Given $$P\left( x \right) = {x^4} + a{x^3} + b{x^2} + cx + d$$ such that $$x=0$$ is the only

real root of $$P'\,\left( x \right) = 0.$$ If $$P\left( { - 1} \right) < P\left( 1 \right),$$ then in the interval $$\left[ { - 1,1} \right]:$$

real root of $$P'\,\left( x \right) = 0.$$ If $$P\left( { - 1} \right) < P\left( 1 \right),$$ then in the interval $$\left[ { - 1,1} \right]:$$

4

AIEEE 2008

MCQ (Single Correct Answer)

+4

-1

Suppose the cubic $${x^3} - px + q$$ has three distinct real roots

where $$p>0$$ and $$q>0$$. Then which one of the following holds?

where $$p>0$$ and $$q>0$$. Then which one of the following holds?

Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

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

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
Magnetics
Alternating Current and Electromagnetic Induction

Optics

Modern Physics

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry
Structure of Atom
Redox Reactions
Gaseous State
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
Quadratic Equation and Inequalities
Sequences and Series
Mathematical Induction and Binomial Theorem
Matrices and Determinants
Permutations and Combinations
Probability
Vector Algebra
3D Geometry
Complex Numbers
Statistics
Mathematical Reasoning

Trigonometry

Coordinate Geometry

Calculus