ExamSIDE
Questions
PREVIOUS NEXT
1
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
The value of $$\int\limits_{{{ - 1} \over {\sqrt 2 }}}^{{1 \over {\sqrt 2 }}} {{{\left( {{{\left( {{{x + 1} \over {x - 1}}} \right)}^2} + {{\left( {{{x - 1} \over {x + 1}}} \right)}^2} - 2} \right)}^{{1 \over 2}}}dx} $$ is :
A
loge 4
B
loge 16
C
2loge 16
D
4loge (3 + 2$${\sqrt 2 }$$)
2
JEE Main 2021 (Online) 26th August Morning Shift
MCQ (Single Correct Answer)
+4
-1
The value of

$$\mathop {\lim }\limits_{n \to \infty } {1 \over n}\sum\limits_{r = 0}^{2n - 1} {{{{n^2}} \over {{n^2} + 4{r^2}}}} $$ is :
A
$${1 \over 2}{\tan ^{ - 1}}(2)$$
B
$${1 \over 2}{\tan ^{ - 1}}(4)$$
C
$${\tan ^{ - 1}}(4)$$
D
$${1 \over 4}{\tan ^{ - 1}}(4)$$
3
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
The area of the region bounded by y $$-$$ x = 2 and x2 = y is equal to :
A
$${{16} \over 3}$$
B
$${{2} \over 3}$$
C
$${{9} \over 2}$$
D
$${{4} \over 3}$$
4
JEE Main 2021 (Online) 27th July Evening Shift
MCQ (Single Correct Answer)
+4
-1
Let f : (a, b) $$\to$$ R be twice differentiable function such that $$f(x) = \int_a^x {g(t)dt} $$ for a differentiable function g(x). If f(x) = 0 has exactly five distinct roots in (a, b), then g(x)g'(x) = 0 has at least :
A
twelve roots in (a, b)
B
five roots in (a, b)
C
seven roots in (a, b)
D
three roots in (a, b)
PREVIOUS NEXT
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
Ray & Wave Optics
Modern Physics
Atoms and Nuclei Dual Nature of Radiation Semiconductor Communication Systems
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
Basics of Organic Chemistry Hydrocarbons Haloalkanes and Haloarenes Alcohols, Phenols and Ethers Aldehydes, Ketones and Carboxylic Acids Compounds Containing Nitrogen Polymers Biomolecules Chemistry in Everyday Life Practical 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
Trigonometric Functions & Equations Inverse Trigonometric Functions Properties of Triangle
Coordinate Geometry
Straight Lines and Pair of Straight Lines Circle Conic Sections
Calculus
Functions Limits, Continuity and Differentiability Differentiation Application of Derivatives Indefinite Integrals Definite Integrals and Applications of Integrals Differential Equations
EXAM MAP
Joint Entrance Examination
JEE MainJEE AdvancedWB JEE
Graduate Aptitude Test in Engineering
GATE CSEGATE ECEGATE EEGATE MEGATE CEGATE PIGATE IN
Medical
NEET