1

JEE Main 2021 (Online) 27th July Evening Shift

Numerical

+4

-1

If $$\int_0^\pi {({{\sin }^3}x){e^{ - {{\sin }^2}x}}dx = \alpha - {\beta \over e}\int_0^1 {\sqrt t {e^t}dt} } $$, then $$\alpha$$ + $$\beta$$ is equal to ____________.

Your input ____

2

JEE Main 2021 (Online) 27th July Morning Shift

Numerical

+4

-1

Let the domain of the function

$$f(x) = {\log _4}\left( {{{\log }_5}\left( {{{\log }_3}(18x - {x^2} - 77)} \right)} \right)$$ be (a, b). Then the value of the integral $$\int\limits_a^b {{{{{\sin }^3}x} \over {({{\sin }^3}x + {{\sin }^3}(a + b - x)}}} dx$$ is equal to _____________.

$$f(x) = {\log _4}\left( {{{\log }_5}\left( {{{\log }_3}(18x - {x^2} - 77)} \right)} \right)$$ be (a, b). Then the value of the integral $$\int\limits_a^b {{{{{\sin }^3}x} \over {({{\sin }^3}x + {{\sin }^3}(a + b - x)}}} dx$$ is equal to _____________.

Your input ____

3

JEE Main 2021 (Online) 27th July Morning Shift

Numerical

+4

-1

Let $$F:[3,5] \to R$$ be a twice differentiable function on (3, 5) such that

$$F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt} $$. If $$F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}$$, then $$\alpha$$ + $$\beta$$ is equal to _______________.

$$F(x) = {e^{ - x}}\int\limits_3^x {(3{t^2} + 2t + 4F'(t))dt} $$. If $$F'(4) = {{\alpha {e^\beta } - 224} \over {{{({e^\beta } - 4)}^2}}}$$, then $$\alpha$$ + $$\beta$$ is equal to _______________.

Your input ____

4

JEE Main 2021 (Online) 18th March Evening Shift

Numerical

+4

-1

Let P(x) be a real polynomial of degree 3 which vanishes at x = $$-$$3. Let P(x) have local minima at x = 1, local maxima at x = $$-$$1 and $$\int\limits_{ - 1}^1 {P(x)dx} $$ = 18, then the sum of all the coefficients of the polynomial P(x) is equal to _________.

Your input ____

Questions Asked from Definite Integration (Numerical)

Number in Brackets after Paper Indicates No. of Questions

JEE Main 2024 (Online) 1st February Evening Shift (1)
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 (3)
JEE Main 2024 (Online) 30th January Morning Shift (1)
JEE Main 2024 (Online) 29th January Evening Shift (2)
JEE Main 2024 (Online) 27th January Evening Shift (1)
JEE Main 2024 (Online) 27th January Morning Shift (1)
JEE Main 2023 (Online) 13th April Evening Shift (1)
JEE Main 2023 (Online) 13th April Morning Shift (1)
JEE Main 2023 (Online) 12th April Morning 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 Evening Shift (1)
JEE Main 2023 (Online) 1st February Evening Shift (1)
JEE Main 2023 (Online) 1st February Morning Shift (2)
JEE Main 2023 (Online) 30th January Morning Shift (1)
JEE Main 2023 (Online) 25th January Evening Shift (1)
JEE Main 2023 (Online) 24th January Evening Shift (1)
JEE Main 2023 (Online) 24th January Morning Shift (2)
JEE Main 2022 (Online) 28th July Evening Shift (1)
JEE Main 2022 (Online) 28th July Morning Shift (1)
JEE Main 2022 (Online) 27th July Evening Shift (2)
JEE Main 2022 (Online) 26th July Morning Shift (1)
JEE Main 2022 (Online) 25th July Evening Shift (2)
JEE Main 2022 (Online) 25th July Morning Shift (1)
JEE Main 2022 (Online) 30th 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 (1)
JEE Main 2022 (Online) 24th June Morning Shift (2)
JEE Main 2021 (Online) 31st August Morning Shift (2)
JEE Main 2021 (Online) 27th July Evening Shift (1)
JEE Main 2021 (Online) 27th July Morning Shift (2)
JEE Main 2021 (Online) 18th March Evening Shift (1)
JEE Main 2021 (Online) 18th March Morning Shift (1)
JEE Main 2021 (Online) 17th March Evening Shift (1)
JEE Main 2021 (Online) 17th March Morning Shift (1)
JEE Main 2021 (Online) 16th March Morning Shift (3)
JEE Main 2021 (Online) 26th February Evening Shift (1)
JEE Main 2021 (Online) 26th February Morning Shift (1)
JEE Main 2021 (Online) 25th February Evening Shift (1)
JEE Main 2021 (Online) 24th February Morning Shift (1)
JEE Main 2020 (Online) 4th September Evening Slot (1)
JEE Main 2020 (Online) 2nd September Evening Slot (1)
JEE Main 2020 (Online) 2nd September Morning Slot (1)

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