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IIT-JEE 1993

Exam Held on Sun Apr 11 1993 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

Upon mixing 45.0 ml. of 0.25 M lead nitrate solution with 25.0 ml. of 0.10M chro...
The light radiations with discrete quantities of energy are called ______.
Wave functions of electrons in atoms and molecules are called ______.
The 2p<sub>x</sub>, 2p<sub>y</sub> and 2p<sub>z</sub> orbitals of atom have iden...
In a given electric field, $$\beta-particles $$ are deflected more than $$\alpha...
Estimate the difference in energy between 1st and 2nd Bohr orbit for a hydrogen ...
What transition in the hydrogen spectrum would have the same wavelength as the B...
The decreasing order of electron affinity of F, Cl, Br is F &gt; Cl &gt;Br
The basic nature of the hydroxides of group 13 (Gr. III B) decreases progressive...
The dipole moment of CH<sub>3</sub>F is greater than of CH<sub>3</sub>Cl
Pick out the isoelectronic structures from the following<br> I. $$CH_3^+$$ <br> ...
The dipole moment of KCl is 3.336 $$\times$$ 10<sup>-29</sup> Coulomb meters whi...
In the van der Waal's equation (P + $${{{n^2}a} \over {{V^2}}}$$)(V - nb) = nRT ...
A gas bulb of 1 litre capacity contains 2.0 $$\times$$ 10<sup>21</sup> molecules...
Ca<sup>2+</sup> has a small ionic radius than K<sup>+</sup> because it has _____...
Give briefly the isolation of magnesium from sea water by the Dow process. Give ...
What weight of the non-volatile solute, urea(NH<sub>2</sub> - CO - NH<sub>2</sub...
The standard reduction potential for the half-cell<br> $$NO_3^-$$ + 2H<sup>+</su...
Chromium metal can be plated out from an acidic solution containing CrO<sub>3</s...
A first order reaction A $$\to$$ B, requires activation energy of 70 kJ mol<sup>...

Mathematics

If $$K = \sin \left( {\pi /18} \right)\sin \left( {5\pi /18} \right)\sin \left( ...
If $$A &gt; 0,B &gt; 0\,$$ and $$A + B = \pi /3,$$ then the maximum value of tan...
Number of solutions of the equation $$\tan x + \sec x = 2\cos x\,$$ lying in the...
$$ABCD$$ is a rhombus. Its diagonals $$AC$$ and $$BD$$ intersect at the point $$...
Determine the smallest positive value of number $$x$$ (in degrees) for which $...
Prove that $$\sum\limits_{r = 1}^k {{{\left( { - 3} \right)}^{r - 1}}\,\,{}^{3n}...
Using mathematical induction, prove that <br>$${\tan ^{ - 1}}\left( {1/3} \righ...
For $$0 &lt; \phi &lt; \pi /2,$$ if <br>$$x = $$$$\sum\limits_{n = 0}^\infty ...
The vertices of a triangle are $$A\left( { - 1, - 7} \right)B\left( {5,\,1} \rig...
A line through $$A (-5, -4)$$ meets the line $$x + 3y + 2 = 0,$$ $$2x + y + 4 =...
Tagent at a point $${P_1}$$ {other than $$(0, 0)$$} on the curve $$y = {x^3}$$ m...
The equation of the locus of the mid-points of the circle $$4{x^2} + 4{y^2} - 1...
The locus of the centre of a circle, which touches externally the circle $${x^2}...
Find the coordinates of the point at which the circles $${x^2}\, + \,{y^2} - \,4...
Consider a family of circles passing through two fixed points A (3, 7) and B (6,...
If in a triangle $$ABC$$, $${{2\cos A} \over a} + {{\cos B} \over b} + {{2\cos C...
An observer at $$O$$ notices that the angle of elevation of the top of a tower i...
If $$f\left( x \right) = \left\{ {\matrix{ {3{x^2} + 12x - 1,} &amp; { - 1 \l...
Find the equation of the normal to the curve <br>$$y = {\left( {1 + x} \right)^...
Let $$f\left( x \right) = \left\{ {\matrix{ { - {x^3} + {{\left( {{b^3} - {b^...
The value of $$\int\limits_{\pi /4}^{3\pi /4} {{\phi \over {1 + \sin \phi }}d\p...
The value of $$\int\limits_0^{\pi /2} {{{dx} \over {1 + {{\tan }^3}\,x}}} $$ is ...
Evaluate $$\int_2^3 {{{2{x^5} + {x^4} - 2{x^3} + 2{x^2} + 1} \over {\left( {{x^2...
An unbiased die with faces marked $$1,2,3,4,5$$ and $$6$$ is rolled four times. ...
$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and ...
Numbers are selected at random, one at a time, from the two- digit numbers $$00,...
Let $$a, b, c$$ be distinct non-negative numbers. If the vectors $$a\widehat i +...
Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ a...
In a triangle $$ABC, D$$ and $$E$$ are points on $$BC$$ and $$AC$$ respectively,...

Physics

A particle of mass m moves on the x-axis as follows: it starts from rest at t = ...
A uniform rod of length L and density $$\rho $$ is being pulled along a smooth f...

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