1
JEE Advanced 2015 Paper 1 Offline
Numerical
+4
-0
A cylindrical container is to be made from certain solid material with the following constraints: It has a fixed inner volume of $$V$$ $$m{m^3}$$, has a $$2$$ mm thick solid wall and is open at the top. The bottom of the container is a solid circular disc of thickness $$2$$ mm and is of radius equal to the outer radius of the container.

If the volume of the material used to make the container is minimum when the inner radius of the container is $$10 $$ mm,
then the value of $${V \over {250\pi }}$$ is

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2
JEE Advanced 2014 Paper 1 Offline
Numerical
+3
-0
The slope of the tangent to the curve $${\left( {y - {x^5}} \right)^2} = x{\left( {1 + {x^2}} \right)^2}$$ at the point $$(1, 3)$$ is
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3
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
Let $$p(x)$$ be a real polynomial of least degree which has a local maximum at $$x=1$$ and a local minimum at $$x=3$$. If $$p(1)=6$$ and $$p(3)=2$$, then $$p'(0)$$ is
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4
IIT-JEE 2012 Paper 1 Offline
Numerical
+4
-0
Let $$f:IR \to IR$$ be defined as $$f\left( x \right) = \left| x \right| + \left| {{x^2} - 1} \right|.$$ The total number of points at which $$f$$ attains either a local maximum or a local minimum is
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