1

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

If a continuous function $$f$$ defined on the real line $$R$$, assumes positive and negative values in $$R$$ then the equation $$f(x)=0$$ has a root in $$R$$. For example, if it is known that a continuous function $$f$$ on $$R$$ is positive at some point and its minimum value is negative then the equation $$f(x)=0$$ has a root in $$R$$.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

The line $$y=x$$ meets $$y = k{e^x}$$ for $$k \le 0$$ at

2

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

If a continuous function $$f$$ defined on the real line $$R$$, assumes positive and negative values in $$R$$ then the equation $$f(x)=0$$ has a root in $$R$$. For example, if it is known that a continuous function $$f$$ on $$R$$ is positive at some point and its minimum value is negative then the equation $$f(x)=0$$ has a root in $$R$$.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

For $$k>0$$, the set of all values of $$k$$ for which $$k{e^x} - x = 0$$ has two distinct roots is

3

IIT-JEE 2007

MCQ (Single Correct Answer)

+4

-1

If a continuous function $$f$$ defined on the real line $$R$$, assumes positive and negative values in $$R$$ then the equation $$f(x)=0$$ has a root in $$R$$. For example, if it is known that a continuous function $$f$$ on $$R$$ is positive at some point and its minimum value is negative then the equation $$f(x)=0$$ has a root in $$R$$.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

Consider $$f\left( x \right) = k{e^x} - x$$ for all real $$x$$ where $$k$$ is real constant.

The positive value of $$k$$ for which $$k{e^x} - x = 0$$ has only one root is

4

IIT-JEE 2005 Screening

MCQ (Single Correct Answer)

+2

-0.5

If $$P(x)$$ is a polynomial of degree less than or equal to $$2$$ and $$S$$ is the set of all such polynomials so that $$P(0)=0$$, $$P(1)=1$$ and $$P'\left( x \right) > 0\,\,\forall x \in \left[ {0,1} \right],$$ then

Questions Asked from Application of Derivatives (MCQ (Single Correct Answer))

Number in Brackets after Paper Indicates No. of Questions

JEE Advanced 2023 Paper 1 Online (1)
JEE Advanced 2020 Paper 1 Offline (1)
JEE Advanced 2017 Paper 1 Offline (3)
JEE Advanced 2016 Paper 1 Offline (1)
JEE Advanced 2013 Paper 2 Offline (2)
IIT-JEE 2012 Paper 2 Offline (2)
IIT-JEE 2008 Paper 1 Offline (1)
IIT-JEE 2007 (4)
IIT-JEE 2005 Screening (1)
IIT-JEE 2004 Screening (2)
IIT-JEE 2003 Screening (2)
IIT-JEE 2002 Screening (2)
IIT-JEE 2001 Screening (3)
IIT-JEE 2000 Screening (5)
IIT-JEE 1999 (1)
IIT-JEE 1998 (2)
IIT-JEE 1997 (1)
IIT-JEE 1995 Screening (3)
IIT-JEE 1994 (2)
IIT-JEE 1987 (2)
IIT-JEE 1986 (1)
IIT-JEE 1983 (4)

JEE Advanced Subjects

Physics

Mechanics

Units & Measurements Motion Laws of Motion Work Power & Energy Impulse & Momentum Rotational Motion Properties of Matter Heat and Thermodynamics Simple Harmonic Motion Waves Gravitation

Electricity

Electrostatics Current Electricity Capacitor Magnetism Electromagnetic Induction Alternating Current Electromagnetic Waves

Optics

Modern Physics

Chemistry

Physical Chemistry

Some Basic Concepts of Chemistry Structure of Atom Redox Reactions Gaseous State Equilibrium Solutions States of Matter Thermodynamics Chemical Kinetics and Nuclear Chemistry Electrochemistry 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 Salt Analysis

Organic Chemistry

Mathematics

Algebra

Quadratic Equation and Inequalities Sequences and Series Mathematical Induction and Binomial Theorem Matrices and Determinants Permutations and Combinations Probability Vector Algebra and 3D Geometry Statistics Complex Numbers

Trigonometry

Coordinate Geometry

Calculus