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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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