JEE Main 2018 (Offline) | Limits, Continuity and Differentiability Question 156 | Mathematics | JEE Main - ExamSIDE.com

Joint Entrance Examination

Graduate Aptitude Test in Engineering

Medical

1

JEE Main 2018 (Offline)

MCQ (Single Correct Answer)

+4

-1

For each t $$ \in R$$, let [t] be the greatest integer less than or equal to t.

Then $$\mathop {\lim }\limits_{x \to {0^ + }} x\left( {\left[ {{1 \over x}} \right] + \left[ {{2 \over x}} \right] + ..... + \left[ {{{15} \over x}} \right]} \right)$$

A

does not exist in R

B

is equal to 0

C

is equal to 15

D

is equal to 120

2

JEE Main 2018 (Online) 15th April Evening Slot

MCQ (Single Correct Answer)

+4

-1

$$\mathop {\lim }\limits_{x \to 0} {{x\tan 2x - 2x\tan x} \over {{{\left( {1 - \cos 2x} \right)}^2}}}$$ equals :

A

$${1 \over 4}$$

B

1

C

$${1 \over 2}$$

D

$$-$$ $${1 \over 2}$$

3

JEE Main 2018 (Online) 15th April Evening Slot

MCQ (Single Correct Answer)

+4

-1

Let f(x) = $$\left\{ {\matrix{ {{{\left( {x - 1} \right)}^{{1 \over {2 - x}}}},} & {x > 1,x \ne 2} \cr {k\,\,\,\,\,\,\,\,\,\,\,\,\,\,} & {,x = 2} \cr } } \right.$$

Thevaue of k for which f s continuous at x = 2 is :

A

1

B

e

C

e^-1

D

e^-2

4

JEE Main 2018 (Online) 15th April Evening Slot

MCQ (Single Correct Answer)

+4

-1

If f(x) = sin^-1 $$\left( {{{2 \times {3^x}} \over {1 + {9^x}}}} \right),$$ then f'$$\left( { - {1 \over 2}} \right)$$ equals :

A

$$ - \sqrt 3 {\log _e}\sqrt 3 $$

B

$$ \sqrt 3 {\log _e}\sqrt 3 $$

C

$$ - \sqrt 3 {\log _e}\, 3 $$

D

$$ \sqrt 3 {\log _e}\, 3 $$

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 Main JEE Advanced WB JEE

Graduate Aptitude Test in Engineering

GATE CSE GATE ECE GATE EE GATE ME GATE CE GATE PI GATE IN

Medical

NEET