1
IIT-JEE 2005
Subjective
+4
-0
If length of tangent at any point on the curve $$y=f(x)$$ intecepted between the point and the $$x$$-axis is length $$1.$$ Find the equation of the curve.
2
IIT-JEE 2004
Subjective
+4
-0
A curve $$'C''$$ passes through $$(2,0)$$ and the slope at $$(x,y|)$$ as $$\,{{{{\left( {x + 1} \right)}^2} + \left( {y - 3} \right)} \over {x + 3}}$$. Find the equation of the curve. Find the area bounded by curve and $$x$$-axis in fourth quadrant.
3
IIT-JEE 2003
Subjective
+4
-0
A right circular cone with radius $$R$$ and height $$H$$ contains a liquid which eveporates at a rate proportional to its surface area in contact with air (proportionality constant $$= k > 0$$. Find the time after which the come is empty.
4
IIT-JEE 2001
Subjective
+10
-0
A hemispherical tank of radius $$2$$ metres is initially full of water and has an outlet of $$12$$ cm2 cross-sectional area at the bottom. The outlet is opened at some instant. The flow through the outlet is according to the law $$v(t)=0.6$$ $$\sqrt {2gh\left( t \right),}$$ where $$v(t)$$ and $$h(t)$$ are respectively the velocity of the flow through the outlet and the height of water level above the outlet at time $$t,$$ and $$g$$ is the acceleration due to gravity. Find the time it takes to empty the tank. (Hint: From a differential equation by relasing the decreases of water level to the outflow).
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