1

JEE Main 2021 (Online) 20th July Morning Shift

Numerical

+4

-1

If the value of $$\mathop {\lim }\limits_{x \to 0} {(2 - \cos x\sqrt {\cos 2x} )^{\left( {{{x + 2} \over {{x^2}}}} \right)}}$$ is equal to e

^{a}, then a is equal to __________.Your input ____

2

JEE Main 2021 (Online) 18th March Evening Shift

Numerical

+4

-1

Let f : R $$ \to $$ R satisfy the equation f(x + y) = f(x) . f(y) for all x, y $$\in$$R and f(x) $$\ne$$ 0 for any x$$\in$$R. If the function f is differentiable at x = 0 and f'(0) = 3, then

$$\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) - 1)$$ is equal to ____________.

$$\mathop {\lim }\limits_{h \to 0} {1 \over h}(f(h) - 1)$$ is equal to ____________.

Your input ____

3

JEE Main 2021 (Online) 17th March Morning Shift

Numerical

+4

-1

If the function $$f(x) = {{\cos (\sin x) - \cos x} \over {{x^4}}}$$ is continuous at each point in its domain and $$f(0) = {1 \over k}$$, then k is ____________.

Your input ____

4

JEE Main 2021 (Online) 16th March Evening Shift

Numerical

+4

-1

Let f : R $$ \to $$ R and g : R $$ \to $$ R be defined as

$$f(x) = \left\{ {\matrix{ {x + a,} & {x < 0} \cr {|x - 1|,} & {x \ge 0} \cr } } \right.$$ and

$$g(x) = \left\{ {\matrix{ {x + 1,} & {x < 0} \cr {{{(x - 1)}^2} + b,} & {x \ge 0} \cr } } \right.$$,

where a, b are non-negative real numbers. If (gof) (x) is continuous for all x $$\in$$ R, then a + b is equal to ____________.

$$f(x) = \left\{ {\matrix{ {x + a,} & {x < 0} \cr {|x - 1|,} & {x \ge 0} \cr } } \right.$$ and

$$g(x) = \left\{ {\matrix{ {x + 1,} & {x < 0} \cr {{{(x - 1)}^2} + b,} & {x \ge 0} \cr } } \right.$$,

where a, b are non-negative real numbers. If (gof) (x) is continuous for all x $$\in$$ R, then a + b is equal to ____________.

Your input ____

Questions Asked from Limits, Continuity and Differentiability (Numerical)

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2024 (Online) 9th April Morning Shift (2)
JEE Main 2024 (Online) 8th April Evening Shift (1)
JEE Main 2024 (Online) 4th April Morning Shift (1)
JEE Main 2024 (Online) 1st February Morning Shift (1)
JEE Main 2024 (Online) 31st January Evening Shift (1)
JEE Main 2024 (Online) 30th January Morning Shift (1)
JEE Main 2024 (Online) 29th January Evening Shift (1)
JEE Main 2023 (Online) 12th April Morning Shift (1)
JEE Main 2023 (Online) 10th April Morning Shift (1)
JEE Main 2023 (Online) 8th April Evening Shift (1)
JEE Main 2023 (Online) 6th April Morning Shift (1)
JEE Main 2022 (Online) 29th July Evening Shift (1)
JEE Main 2022 (Online) 28th July Morning Shift (2)
JEE Main 2022 (Online) 25th July Morning Shift (1)
JEE Main 2022 (Online) 30th June Morning Shift (1)
JEE Main 2022 (Online) 28th June Evening Shift (1)
JEE Main 2022 (Online) 27th June Evening Shift (1)
JEE Main 2022 (Online) 25th June Evening Shift (1)
JEE Main 2022 (Online) 24th June Morning Shift (1)
JEE Main 2021 (Online) 1st September Evening Shift (2)
JEE Main 2021 (Online) 26th August Morning Shift (1)
JEE Main 2021 (Online) 27th July Morning Shift (1)
JEE Main 2021 (Online) 25th July Evening Shift (1)
JEE Main 2021 (Online) 22th July Evening Shift (1)
JEE Main 2021 (Online) 20th July Evening Shift (2)
JEE Main 2021 (Online) 20th July Morning Shift (1)
JEE Main 2021 (Online) 18th March Evening Shift (1)
JEE Main 2021 (Online) 17th March Morning Shift (1)
JEE Main 2021 (Online) 16th March Evening Shift (1)
JEE Main 2021 (Online) 16th March Morning Shift (1)
JEE Main 2021 (Online) 25th February Evening Shift (2)
JEE Main 2021 (Online) 25th February Morning Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 6th September Morning Slot (1)
JEE Main 2020 (Online) 5th September Morning Slot (1)
JEE Main 2020 (Online) 4th September Morning Slot (1)
JEE Main 2020 (Online) 3rd September Morning Slot (1)
JEE Main 2020 (Online) 2nd September Morning Slot (1)
JEE Main 2020 (Online) 7th January Evening Slot (1)
JEE Main 2020 (Online) 7th January Morning Slot (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 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