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.

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

2

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

3

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

+2

-0.5

If $$f\left( x \right) = {x^3} + b{x^2} + cx + d$$ and $$0 < {b^2} < c,$$ then in $$\left( { - \infty ,\infty } \right)$$

4

IIT-JEE 2004 Screening

MCQ (Single Correct Answer)

+2

-0.5

If $$f\left( x \right) = {x^a}\log x$$ and $$f\left( 0 \right) = 0,$$ then the value of $$\alpha $$ for which Rolle's theorem can be applied in $$\left[ {0,1} \right]$$ 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 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)

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