1

IIT-JEE 2012 Paper 2 Offline

MCQ (Single Correct Answer)

+4

-1

Let $$f\left( x \right) = {\left( {1 - x} \right)^2}\,\,{\sin ^2}\,\,x + {x^2}$$ for all $$x \in IR$$ and let

$$g\left( x \right) = \int\limits_1^x {\left( {{{2\left( {t - 1} \right)} \over {t + 1}} - In\,t} \right)f\left( t \right)dt} $$ for all $$x \in \left( {1,\,\infty } \right)$$.

$$g\left( x \right) = \int\limits_1^x {\left( {{{2\left( {t - 1} \right)} \over {t + 1}} - In\,t} \right)f\left( t \right)dt} $$ for all $$x \in \left( {1,\,\infty } \right)$$.

Consider the statements:

$$P:$$ There exists some $$x \in R$$ such that $$f\left( x \right) + 2x = 2\left( {1 + {x^2}} \right)$$

$$Q:\,\,$$ There exists some $$x \in R$$ such that $$2\,f\left( x \right) + 1 = 2x\left( {1 + x} \right)$$

Then

2

IIT-JEE 2008 Paper 1 Offline

MCQ (Single Correct Answer)

+3

-1

The total number of local maxima and local minima of the function

$$f(x) = \left\{ {\matrix{
{{{(2 + x)}^3},} & { - 3 < x \le - 1} \cr
{{x^{2/3}},} & { - 1 < x < 2} \cr
} } \right.$$ is

3

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 $$\left( {c + 1,{e^{c + 1}}} \right)$$

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

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

Number in Brackets after Paper Indicates No. of Questions

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