IIT-JEE 2003
Paper was held on Fri, Apr 11, 2003 9:00 AM
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Chemistry

Calculate the molarity of water if it's density is 1000 kg/m3
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Wavelength of high energy transition of H-atoms is 91.2 nm. Calculate the corresponding wavelength of He atoms.
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Using VSEPR theory deduce the structures of PCl5 and BrF5
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1 gm of charcoal adsorbs 100 ml 0.5 M CH3COOH to form a monolayer, and thereby the molarity of CH3COOH reduces to 0.49.
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Two students use the same stock solution of ZnSO4 and solution of CuSO4. The emf of one cell is 0.03 V higher than other
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Mathematics

If $${z_1}$$ and $${z_2}$$ are two complex numbers such that $$\,\left| {{z_1}} \right| < 1 < \left| {{z_2}} \righ
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Prove that there exists no complex number z such that $$\left| z \right| < {1 \over 3}\,and\,\sum\limits_{r = 1}^n {{
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If $${x^2} + \left( {a - b} \right)x + \left( {1 - a - b} \right) = 0$$ where $$a,\,b\, \in \,R$$ then find the values o
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Prove that $${2^k}\left( {\matrix{ n \cr 0 \cr } } \right)\left( {\matrix{ n \cr k \cr } } \rig
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If a, b, c are in A.P., $${a^2}$$, $${b^2}$$, $${c^2}$$ are in H.P., then prove that either a = b = c or a, b, $${ - {c
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For the circle $${x^2}\, + \,{y^2} = {r^2}$$, find the value of r for which the area enclosed by the tangents drawn from
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Normals are drawn from the point $$P$$ with slopes $${m_1}$$, $${m_2}$$, $${m_3}$$ to the parabola $${y^2} = 4x$$. If lo
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If $${I_n}$$ is the area of $$n$$ sided regular polygon inscribed in a circle of unit radius and $${O_n}$$ be the area o
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Using the relation $$2\left( {1 - \cos x} \right) < {x^2},\,x \ne 0$$ or otherwise, prove that $$\sin \left( {\tan x
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Find a point on the curve $${x^2} + 2{y^2} = 6$$ whose distance from the line $$x+y=7$$, is minimum.
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If the function $$f:\left[ {0,4} \right] \to R$$ is differentiable then show that (i)$$\,\,\,\,\,$$ For $$a, b$$$$\,\,$
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If $$P(1)=0$$ and $${{dp\left( x \right)} \over {dx}} > P\left( x \right)$$ for all $$x \ge 1$$ then prove that $$P(
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If $$f$$ is an even function then prove that $$\int\limits_0^{\pi /2} {f\left( {\cos 2x} \right)\cos x\,dx = \sqrt 2 }
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A right circular cone with radius $$R$$ and height $$H$$ contains a liquid which eveporates at a rate proportional to it
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$$A$$ is targeting to $$B, B$$ and $$C$$ are targeting to $$A.$$ Probability of hitting the target by $$A,B$$ and $$C$$
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For a student to qualify, he must pass at least two out of three exams. The probability that he will pass the 1st exam i
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If $$\overrightarrow u ,\overrightarrow v ,\overrightarrow w ,$$ are three non-coplanar unit vectors and $$\alpha ,\beta
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(i) Find the equation of the plane passing through the points $$(2, 1, 0), (5, 0, 1)$$ and $$(4, 1, 1).$$ (ii) If $$P$$
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Physics

If nth divisions of the main scale coincide with (n+1)th divisions of vernier scale. Given one main scale division is eq
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