IIT-JEE 2004

Paper was held on
Sun, Apr 11, 2004 9:00 AM

## Chemistry

(a) The Schrodinger wave equation for hydrogen atom is
$$$\psi = {1 \over {4\sqrt {2\pi } }}{\left( {{1 \over {{a_0}}}}

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A ball of mass 100 g is moving with 100 ms-1. Find it's wavelength.

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Arrange the following :
In the decreasing order of the O - O bond length present in them
O2, KO2 and O2[AsF4]

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Draw the structure of XeF4 and OSF4 according to VSEPR theory clearly indicating the state of hybridisation of the centr

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A compound AB has rock salt type structure. The formula weight of AB is 6.023 Y amu, and the closest A - B distance is Y

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1.22 g of benzoic acid is dissolved in 100 g of acetone and 100 g of benzene separately. Boiling point of the solution i

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Find the equilibrium constant for the reaction,
In2+ + Cu2+ $$\to$$ In3+ + Cu+ at 298 K given
$$E_{C{u^{2 + }}/C{u^ + }}

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For the given reactions, A + B $$\to$$ Products, following data were obtained
.tg {border-collapse:collapse;border-sp

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## Mathematics

Find the centre and radius of circle given by $$\,\left| {{{z - \alpha } \over {z - \beta }}} \right| = k,k \ne 1\,$$

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If $$a,\,b,c$$ are positive real numbers. Then prove that
$$${\left( {a + 1} \right)^7}{\left( {b + 1} \right)^7}{\left

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Prove by permulation or otherwise $${{({n^2})!} \over {{{(n!)}^n}}}$$ is an integer $$(n \in {1^ + })$$.

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Find the equation of circle touching the line 2x + 3y + 1 = 0 at (1, -1) and cutting orthogonally the circle having line

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Tangent is drawn to parabola $${y^2} - 2y - 4x + 5 = 0$$ at a point $$P$$ which cuts the directrix at the point $$Q$$. $

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Using Rolle's theorem, prove that there is at least one root
in $$\left( {{{45}^{1/100}},46} \right)$$ of the polynomia

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Prove that for $$x \in \left[ {0,{\pi \over 2}} \right],$$ $$\sin x + 2x \ge {{3x\left( {x + 1} \right)} \over \pi }$$.

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If $$y\left( x \right) = \int\limits_{{x^2}/16}^{{x^2}} {{{\cos x\cos \sqrt \theta } \over {1 + {{\sin }^2}\sqrt \theta

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Find the value of $$\int\limits_{ - \pi /3}^{\pi /3} {{{\pi + 4{x^3}} \over {2 - \cos \left( {\left| x \right| + {\pi

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A curve $$'C''$$ passes through $$(2,0)$$ and the slope at $$(x,y|)$$ as $$\,{{{{\left( {x + 1} \right)}^2} + \left( {y

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$$A$$ and $$B$$ are two independent events. $$C$$ is even in which exactly one of $$A$$ or $$B$$ occurs. Prove that $$P\

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A box contains $$12$$ red and $$6$$ white balls. Balls are drawn from the box one at a time without replacement. If in $

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Find the equation of plane passing through $$(1, 1, 1)$$ & parallel to the lines $${L_1},{L_2}$$ having direction ra

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A parallelopiped $$'S'$$ has base points $$A, B, C$$ and $$D$$ and upper face points $$A',$$ $$B',$$ $$C'$$ and $$D'.$$

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If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ and $$\overrightarrow d $$ are distinct vectors such tha

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$${P_1}$$ and $${P_2}$$ are planes passing through origin. $${L_1}$$ and $${L_2}$$ are two line on $${P_1}$$ and $${P_2}

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## Physics

A screw gauge having 100 equal divisions and a pitch of length 1 mm is used to measure the diameter of a wire of length

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In Searle's experiment, which is used to find Young's Modulus of elasticity, the diameter of experimental wire is D = 0.

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