IIT-JEE 1997

Paper was held on
Fri, Apr 11, 1997 9:00 AM

## Chemistry

For a d-electron the orbital angular momentum is

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Which one of the following compounds has sp2 hybridization?

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Which contains both polar and non-polar bonds?

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The critical temperature of water is higher than that of O2 because the H2O molecule has

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A compound of vanadium has a magnetic moment of 1.73 BM. Work out the electronic configuration of the vanadium ion in th

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Give reasons of the following:
The crystalline salts of alkaline earth metals contain more water of crystallisation than

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To a 25ml H2O2 solution, excess of acidified solution of potassium iodide was added. The iodine liberated required 20 ml

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Element A burns in nitrogen to give an ionic compound B. Compound B reacts with water to give C and D. A solution of C b

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Give reactions for the oxidation of hydrogen peroxide with potassium permanganate in acidic medium.

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Arrange the following sulphates of Alkaline earth metals in order of decreasing thermal stability : BeSO4, MgSO4, CaSO4,

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How many grams of silver could be plated out on a serving tray by electrolysis of a solution containing silver in +1 oxi

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Calculate the equilibrium constant for the reaction
Fe2+ + Ce4+ $$\leftrightharpoons$$ Fe3+ + Ce3+
(given $$E_{C{e^{4 +

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## Mathematics

The real roots of the equation $$\,{\cos ^7}x + {\sin ^4}x = 1$$ in the interval $$\left( { - \pi ,\pi } \right)$$ are .

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Let $${z_1}$$ and $${z_2}$$ be roots of the equation $${z^2} + pz + q = 0\,$$ , where the coefficients p and q may be co

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Prove that the values of the function $${{\sin x\cos 3x} \over {\sin 3x\cos x}}$$ do not lie between $${1 \over 3}$$ and

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Prove that $$\sum\limits_{k = 1}^{n - 1} {\left( {n - k} \right)\,\cos \,{{2k\pi } \over n} = - {n \over 2},} $$ where

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Let $$S$$ be a square of unit area. Consider any quadrilateral which has one vertex on each side of $$S$$. If $$a,\,b,\,

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The sum of all the real roots of the equation $${\left| {x - 2} \right|^2} + \left| {x - 2} \right| - 2 = 0$$ is .......

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The sum of the rational terms in the expansion of $${\left( {\sqrt 2 + {3^{1/5}}} \right)^{10}}$$ is ...............

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Let $$0 < {A_i} < n$$ for $$i = 1,\,2....,\,n.$$ Use mathematical induction to prove that
$$$\sin {A_1} + \sin {A

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Let $$p$$ and $$q$$ be roots of the equation $${x^2} - 2x + A = 0$$ and let $$r$$ and $$s$$ be the roots of the equation

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For each natural number k, let $${C_k}$$ denote the circle with radius k centimetres and centre at the origin. On the ci

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The chords of contact of the pair of tangents drawn from each point on the line 2x + y = 4 to circle $${x^2} + {y^2} = 1

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Let C be any circle with centre $$\,\left( {0\, , \sqrt {2} } \right)$$. Prove that at the most two rational points can

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A tangent to the ellipse x2 + 4y2 = 4 meets the ellipse x2 + 2y2 = 6 at P and Q. Prove that the tangents at P and Q of t

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If $$f\left( x \right) = {x \over {\sin x}}$$ and $$g\left( x \right) = {x \over {\tan x}}$$, where $$0 < x \le 1$$,

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Let $$a+b=4$$, where $$a<2,$$ and let $$g(x)$$ be a differentiable function.
If $${{dg} \over {dx}} > 0$$ for all

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The value of $$\int_1^{{e^{37}}} {{{\pi \sin \left( {\pi In\,x} \right)} \over x}\,dx} $$ is ...............

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Let $${d \over {dx}}\,F\left( x \right) = {{{e^{\sin x}}} \over x},\,x > 0.$$ If $$\int_1^4 {{{2{e^{\sin {x^2}}}} \ov

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If $$g\left( x \right) = \int_0^x {{{\cos }^4}t\,dt,} $$ then $$g\left( {x + \pi } \right)$$ equals

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Let $$f(x)= Maximum $$ $$\,\left\{ {{x^2},{{\left( {1 - x} \right)}^2},2x\left( {1 - x} \right)} \right\},$$ where $$0

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Determine the value of $$\int_\pi ^\pi {{{2x\left( {1 + \sin x} \right)} \over {1 + {{\cos }^2}x}}} \,dx.$$

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Let $$u(x)$$ and $$v(x)$$ satisfy the differential equation $${{du} \over {dx}} + p\left( x \right)u = f\left( x \right)

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If $$p$$ and $$q$$ are chosen randomly from the set $$\left\{ {1,2,3,4,5,6,7,8,9,10} \right\},$$ with replacement, deter

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Let $$OA=a,$$ $$OB=10a+2b$$ and $$OC=b$$ where $$O,A$$ and $$C$$ are non-collinear points. Let $$p$$ denote the area of

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If $$A,B$$ and $$C$$ are vectors such that $$\left| B \right| = \left| C \right|.$$ Prove that
$$\left[ {\left( {A + B}

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## Physics

The equation of state for real gas is given by $$\left( {P + {a \over {{V^2}}}} \right)\left( {V - b} \right) = RT$$. Th

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