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## IIT-JEE 2002

Exam Held on Thu Apr 11 2002 09:00:00 GMT+0000 (Coordinated Universal Time)
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## Mathematics

Let $$\omega$$ $$= - {1 \over 2} + i{{\sqrt 3 } \over 2},$$ then the value of...
Let a complex number $$\alpha ,\,\alpha \ne 1$$, be a root of the equation $${z... Use mathematical induction to show that <br>$${\left( {25} \right)^{n + 1}} - 2...
Let a, b be positive real numbers. If a, $${{A_1},{A_2}}$$, b are in arithmetic ...
A straight line $$L$$ through the origin meets the lines $$x + y = 1$$ and $$x +... A straight line$$L$$with negative slope passes through the point$$(8, 2)$$an... A triangle with vertices$$(4, 0), (-1, -1), (3, 5)$$is Locus of mid point of the portion between the axes of$$x\cos \alpha + y\s...
If the pair of lines $$a{x^2} + 2hxy + b{y^2} + 2gx + 2fy + c = 0$$ intersect on...
The pair of lines represented by <br>$$3a{x^2} + 5xy + \left( {{a^2} - 2} \righ... Prove that, in an ellipse, the perpendicular from a focus upon any tangent and t... Prove that$$\cos \,ta{n^{ - 1}}\sin \,{\cot ^{ - 1}}x = \sqrt {{{{x^2} + 1} \ov...
For any natural number $$m$$, evaluate <br>$$\int {\left( {{x^{3m}} + {x^{2m}} +... Find the area of the region bounded by the curves$$y = {x^2},y = \left| {2 - {x...
A box contains $$N$$ coins, $$m$$ of which are fair and the rest are biased. The...
Let $$V$$ be the volume of the parallelopiped formed by the vectors \overright...

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