1

JEE Main 2013 (Offline)

MCQ (Single Correct Answer)

+4

-1

The intercepts on $$x$$-axis made by tangents to the curve,

$$y = \int\limits_0^x {\left| t \right|dt,x \in R,} $$ which are parallel to the line $$y=2x$$, are equal to :

$$y = \int\limits_0^x {\left| t \right|dt,x \in R,} $$ which are parallel to the line $$y=2x$$, are equal to :

2

AIEEE 2012

MCQ (Single Correct Answer)

+4

-1

Let $$a,b \in R$$ be such that the function $$f$$ given by $$f\left( x \right) = In\left| x \right| + b{x^2} + ax,\,x \ne 0$$ has extreme values at $$x=-1$$ and $$x=2$$

**Statement-1 :** $$f$$ has local maximum at $$x=-1$$ and at $$x=2$$.

**Statement-2 :** $$a = {1 \over 2}$$ and $$b = {-1 \over 4}$$

3

AIEEE 2012

MCQ (Single Correct Answer)

+4

-1

A spherical balloon is filled with $$4500\pi $$ cubic meters of helium gas. If a leak in the balloon causes the gas to escape at the rate of $$72\pi $$ cubic meters per minute, then the rate (in meters per minute) at which the radius of the balloon decreases $$49$$ minutes after the leakage began is :

4

AIEEE 2012

MCQ (Single Correct Answer)

+4

-1

A line is drawn through the point $$(1, 2)$$ to meet the coordinate axes at $$P$$ and $$Q$$ such that it forms a triangle $$OPQ,$$ where $$O$$ is the origin. If the area of the triangle $$OPQ$$ is least, then the slope of the line $$PQ$$ is :

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

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