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## IIT-JEE 1997

Exam Held on Fri Apr 11 1997 09:00:00 GMT+0000 (Coordinated Universal Time)
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## Chemistry

For a d-electron the orbital angular momentum is
Which one of the following compounds has sp<sup>2</sup> hybridization?
Which contains both polar and non-polar bonds?
The critical temperature of water is higher than that of O<sub>2</sub> because t...
A compound of vanadium has a magnetic moment of 1.73 BM. Work out the electronic...
Give reasons of the following:<br> The crystalline salts of alkaline earth metal...
To a 25ml H<sub>2</sub>O<sub>2</sub> solution, excess of acidified solution of p...
Element A burns in nitrogen to give an ionic compound B. Compound B reacts with ...
Give reactions for the oxidation of hydrogen peroxide with potassium permanganat...
Arrange the following sulphates of Alkaline earth metals in order of decreasing ...
How many grams of silver could be plated out on a serving tray by electrolysis o...
Calculate the equilibrium constant for the reaction<br> Fe<sup>2+</sup> + Ce<sup...

## Mathematics

The real roots of the equation $$\,{\cos ^7}x + {\sin ^4}x = 1$$ in the interval...
Let $${z_1}$$ and $${z_2}$$ be roots of the equation $${z^2} + pz + q = 0\,$$ , ...
Prove that the values of the function $${{\sin x\cos 3x} \over {\sin 3x\cos x}}... Prove that$$\sum\limits_{k = 1}^{n - 1} {\left( {n - k} \right)\,\cos \,{{2k\pi...
Let $$S$$ be a square of unit area. Consider any quadrilateral which has one ver...
The sum of all the real roots of the equation $${\left| {x - 2} \right|^2} + \le... The sum of the rational terms in the expansion of$${\left( {\sqrt 2 + {3^{1/5}...
Let $$0 &lt; {A_i} &lt; n$$ for $$i = 1,\,2....,\,n.$$ Use mathematical inductio...
Let $$p$$ and $$q$$ be roots of the equation $${x^2} - 2x + A = 0$$ and let $$r... For each natural number k, let$${C_k}$$denote the circle with radius k centime... The chords of contact of the pair of tangents drawn from each point on the line ... Let C be any circle with centre$$\,\left( {0\, , \sqrt {2} } \right)$$. Prove t... A tangent to the ellipse x<sup>2</sup> + 4y<sup>2</sup> = 4 meets the ellipse x<... If$$f\left( x \right) = {x \over {\sin x}}$$and$$g\left( x \right) = {x \over...
Let $$a+b=4$$, where $$a&lt;2,$$ and let $$g(x)$$ be a differentiable function. ...
The value of $$\int_1^{{e^{37}}} {{{\pi \sin \left( {\pi In\,x} \right)} \over x... Let$${d \over {dx}}\,F\left( x \right) = {{{e^{\sin x}}} \over x},\,x &gt; 0.$$... If$$g\left( x \right) = \int_0^x {{{\cos }^4}t\,dt,} $$then$$g\left( {x + \pi...
Let $$f(x)= Maximum$$ $$\,\left\{ {{x^2},{{\left( {1 - x} \right)}^2},2x\left(... Determine the value of$$\int_\pi ^\pi {{{2x\left( {1 + \sin x} \right)} \over ...
Let $$u(x)$$ and $$v(x)$$ satisfy the differential equation $${{du} \over {dx}} ... If$$p$$and$$q$$are chosen randomly from the set$$\left\{ {1,2,3,4,5,6,7,8,9...
Let $$OA=a,$$ $$OB=10a+2b$$ and $$OC=b$$ where $$O,A$$ and $$C$$ are non-colline...
If $$A,B$$ and $$C$$ are vectors such that $$\left| B \right| = \left| C \right|... ## Physics The equation of state for real gas is given by$$\left( {P + {a \over {{V^2}}}} ...

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