1

JEE Advanced 2022 Paper 2 Online

MCQ (More than One Correct Answer)

+4

-2

Let

$$ \alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)} $$

Let $g:[0,1] \rightarrow \mathbb{R}$ be the function defined by

$$ g(x)=2^{\alpha x}+2^{\alpha(1-x)} . $$

Then, which of the following statements is/are TRUE ?

$$ \alpha=\sum\limits_{k = 1}^\infty {{{\sin }^{2k}}\left( {{\pi \over 6}} \right)} $$

Let $g:[0,1] \rightarrow \mathbb{R}$ be the function defined by

$$ g(x)=2^{\alpha x}+2^{\alpha(1-x)} . $$

Then, which of the following statements is/are TRUE ?

2

JEE Advanced 2019 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-1

Let f : R $$ \to $$ R be given by

$$f(x) = (x - 1)(x - 2)(x - 5)$$. Define

$$F(x) = \int\limits_0^x {f(t)dt} $$, x > 0

Then which of the following options is/are correct?

$$f(x) = (x - 1)(x - 2)(x - 5)$$. Define

$$F(x) = \int\limits_0^x {f(t)dt} $$, x > 0

Then which of the following options is/are correct?

3

JEE Advanced 2019 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-1

Let, $$f(x) = {{\sin \pi x} \over {{x^2}}}$$, x > 0

Let x

Then which of the following options is/are correct?

Let x

_{1}< x_{2}< x_{3}< ... < x_{n}< ... be all the points of local maximum of f and y_{1}< y_{2}< y_{3}< ... < y_{n}< ... be all the points of local minimum of f.Then which of the following options is/are correct?

4

JEE Advanced 2017 Paper 2 Offline

MCQ (More than One Correct Answer)

+4

-2

f : R $$ \to $$ R is a differentiable function such that f'(x) > 2f(x) for all x$$ \in $$R, and f(0) = 1 then

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

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2022 Paper 2 Online (1)
JEE Advanced 2019 Paper 2 Offline (2)
JEE Advanced 2017 Paper 2 Offline (2)
JEE Advanced 2016 Paper 2 Offline (1)
JEE Advanced 2015 Paper 2 Offline (1)
JEE Advanced 2013 Paper 2 Offline (1)
JEE Advanced 2013 Paper 1 Offline (1)
IIT-JEE 2012 Paper 2 Offline (1)
IIT-JEE 2009 Paper 2 Offline (1)
IIT-JEE 2006 (2)
IIT-JEE 1999 (1)
IIT-JEE 1998 (1)
IIT-JEE 1993 (1)
IIT-JEE 1986 (1)

JEE Advanced Subjects

Physics

Mechanics

Units & Measurements Motion Laws of Motion Work Power & Energy Impulse & Momentum Rotational Motion Properties of Matter Heat and Thermodynamics Simple Harmonic Motion Waves Gravitation

Electricity

Electrostatics Current Electricity Capacitor Magnetism 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 Chemical Kinetics and Nuclear Chemistry Electrochemistry 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 Salt Analysis

Organic Chemistry

Mathematics

Algebra

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

Trigonometry

Coordinate Geometry

Calculus