1
IIT-JEE 2002
MCQ (Single Correct Answer)
+4
-1
The pair of lines represented by
$$3a{x^2} + 5xy + \left( {{a^2} - 2} \right){y^2} = 0$$ are perpendicular to each other for
A
two values of $$a$$
B
$$\forall \,a$$
C
for one values of $$a$$
D
for no values of $$a$$
2
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.
3
IIT-JEE 2002
Subjective
+5
-0
Prove that $$\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \over {{x^2} + 2}}} $$.
4
IIT-JEE 2002
Subjective
+5
-0
For any natural number $$m$$, evaluate
$$\int {\left( {{x^{3m}} + {x^{2m}} + {x^m}} \right){{\left( {2{x^{2m}} + 3{x^m} + 6} \right)}^{l/m}}dx,x > 0.} $$
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