1

IIT-JEE 2008

MCQ (Single Correct Answer)

+4

-1

Let the function $$g:\left( { - \infty ,\infty } \right) \to \left( { - {\pi \over 2},{\pi \over 2}} \right)$$ be given by

$$g\left( u \right) = 2{\tan ^{ - 1}}\left( {{e^u}} \right) - {\pi \over 2}.$$ Then, $$g$$ is

$$g\left( u \right) = 2{\tan ^{ - 1}}\left( {{e^u}} \right) - {\pi \over 2}.$$ Then, $$g$$ is

2

IIT-JEE 2007

MCQ (Single Correct Answer)

+3

-0.75

The tangent to the curve $$y = {e^x}$$ drawn at the point $$\left( {c,{e^c}} \right)$$ intersects the line joining the points $$\left( {c - 1,{e^{c - 1}}} \right)$$ and $$\left( {c + 1,{e^{c + 1}}} \right)$$

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

4

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

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

Number in Brackets after Paper Indicates
No. of Questions

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 (3)
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)

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