JEE Main 2020 (Online) 8th January Evening Slot | Limits, Continuity and Differentiability Question 111 | Mathematics

JEE Main 2020 (Online) 8th January Evening Slot

MCQ (Single Correct Answer)

-1

Let S be the set of all functions ƒ : [0,1] $$ \to $$ R, which are continuous on [0,1] and differentiable on (0,1). Then for every ƒ in S, there exists a c $$ \in $$ (0,1), depending on ƒ, such that

$$\left| {f(c) - f(1)} \right| < \left| {f'(c)} \right|$$

$$\left| {f(c) + f(1)} \right| < \left( {1 + c} \right)\left| {f'(c)} \right|$$

$$\left| {f(c) - f(1)} \right| < \left( {1 - c} \right)\left| {f'(c)} \right|$$

None

JEE Main 2020 (Online) 8th January Evening Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to 0} {{\int_0^x {t\sin \left( {10t} \right)dt} } \over x}$$ is equal to

$$ - {1 \over 5}$$

$$ - {1 \over 10}$$

$$ {1 \over 10}$$

JEE Main 2020 (Online) 8th January Morning Slot

MCQ (Single Correct Answer)

-1

$$\mathop {\lim }\limits_{x \to 0} {\left( {{{3{x^2} + 2} \over {7{x^2} + 2}}} \right)^{{1 \over {{x^2}}}}}$$ is equal to

e²

$${1 \over {{e^2}}}$$

$${1 \over e}$$

JEE Main 2020 (Online) 7th January Evening Slot

MCQ (Single Correct Answer)

-1

The value of c in the Lagrange's mean value theorem for the function
ƒ(x) = x³ - 4x² + 8x + 11, when x $$ \in $$ [0, 1] is:

$${2 \over 3}$$

$${{\sqrt 7 - 2} \over 3}$$

$${{4 - \sqrt 5 } \over 3}$$

$${{4 - \sqrt 7 } \over 3}$$

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