1
IIT-JEE 2002
Subjective
+5
-0
Prove that, in an ellipse, the perpendicular from a focus upon any tangent and the line joining the centre of the ellipse to the point of contact meet on the corresponding directrix.
2
IIT-JEE 2002
Subjective
+5
-0
Prove that $$\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \over {{x^2} + 2}}} $$.
3
IIT-JEE 2002
Subjective
+5
-0
For any natural number $$m$$, evaluate
$$\int {\left( {{x^{3m}} + {x^{2m}} + {x^m}} \right){{\left( {2{x^{2m}} + 3{x^m} + 6} \right)}^{l/m}}dx,x > 0.} $$
4
IIT-JEE 2002
Subjective
+5
-0
Find the area of the region bounded by the curves $$y = {x^2},y = \left| {2 - {x^2}} \right|$$ and $$y=2,$$ which lies to the right of the line $$x=1.$$
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