IIT-JEE 1993

Paper was held on
Sun, Apr 11, 1993 9:00 AM

## Chemistry

Upon mixing 45.0 ml. of 0.25 M lead nitrate solution with 25.0 ml. of 0.10M chromic sulphate solution, precipitation of

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The light radiations with discrete quantities of energy are called ______.

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Wave functions of electrons in atoms and molecules are called ______.

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The 2px, 2py and 2pz orbitals of atom have identical shapes but differ in their _____.

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In a given electric field, $$\beta-particles $$ are deflected more than $$\alpha-particles$$ in spite of $$\alpha-partic

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Estimate the difference in energy between 1st and 2nd Bohr orbit for a hydrogen atom. At what minimum atomic number, a t

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What transition in the hydrogen spectrum would have the same wavelength as the Balmer transition n = 4 to n = 2 of He+ s

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The decreasing order of electron affinity of F, Cl, Br is F > Cl >Br

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The basic nature of the hydroxides of group 13 (Gr. III B) decreases progressively down the group.

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The dipole moment of CH3F is greater than of CH3Cl

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Pick out the isoelectronic structures from the following
I. $$CH_3^+$$ II. $$H_3O^+$$
III. $$NH_3$$
IV. $$CH_3^-$$

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The dipole moment of KCl is 3.336 $$\times$$ 10-29 Coulomb meters which indicates that it is a highly polar molecule. Th

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In the van der Waal's equation (P + $${{{n^2}a} \over {{V^2}}}$$)(V - nb) = nRT the constant 'a' reflects the actual vol

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A gas bulb of 1 litre capacity contains 2.0 $$\times$$ 1021 molecules of nitrogen exerting a pressure of 7.57 $$\times$

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Ca2+ has a small ionic radius than K+ because it has ______.

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Give briefly the isolation of magnesium from sea water by the Dow process. Give equations for the steps involved.

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What weight of the non-volatile solute, urea(NH2 - CO - NH2) needs to be dissolved in 100g of water, in order to decreas

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The standard reduction potential for the half-cell
$$NO_3^-$$ + 2H+ (aq) + e $$\to$$ NO2 (g) + H2O is 0.78 V
(i) Calcula

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Chromium metal can be plated out from an acidic solution containing CrO3 according to the following equation
CrO3 (aq)

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A first order reaction A $$\to$$ B, requires activation energy of 70 kJ mol-1. When 20% solution of A was kept at 25oC f

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## Mathematics

If $$K = \sin \left( {\pi /18} \right)\sin \left( {5\pi /18} \right)\sin \left( {7\pi /18} \right),$$ then the numerica

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If $$A > 0,B > 0\,$$ and $$A + B = \pi /3,$$ then the maximum value of tan A tan B is _______.

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Number of solutions of the equation $$\tan x + \sec x = 2\cos x\,$$ lying in the interval $$\left[ {0,2\pi } \right]$$ i

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$$ABCD$$ is a rhombus. Its diagonals $$AC$$ and $$BD$$ intersect at the point $$M$$ and satisfy $$BD$$ = 2$$AC$$. If the

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Determine the smallest positive value of number $$x$$ (in degrees) for which
$$$\tan \left( {x + {{100}^ \circ }} \rig

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Using mathematical induction, prove that
$${\tan ^{ - 1}}\left( {1/3} \right) + {\tan ^{ - 1}}\left( {1/7} \right) + ..

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Prove that $$\sum\limits_{r = 1}^k {{{\left( { - 3} \right)}^{r - 1}}\,\,{}^{3n}{C_{2r - 1}} = 0,} $$ where $$k = \left(

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For $$0 < \phi < \pi /2,$$ if
$$x = $$$$\sum\limits_{n = 0}^\infty {{{\cos }^{2n}}\phi ,y = \sum\limits_{n = 0}

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The vertices of a triangle are $$A\left( { - 1, - 7} \right)B\left( {5,\,1} \right)$$ and $$C\left( {1,\,4} \right).$$ T

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Tagent at a point $${P_1}$$ {other than $$(0, 0)$$} on the curve $$y = {x^3}$$ meets the curve again at $${P_2}$$. The t

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A line through $$A (-5, -4)$$ meets the line $$x + 3y + 2 = 0,$$ $$2x + y + 4 = 0$$ and $$x - y - 5 = 0$$ at the points

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The equation of the locus of the mid-points of the circle $$4{x^2} + 4{y^2} - 12x + 4y + 1 = 0$$ that subtend an angle

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The locus of the centre of a circle, which touches externally the circle $${x^2} + {y^2} - 6x - 6y + 14 = 0$$ and also t

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Find the coordinates of the point at which the circles $${x^2}\, + \,{y^2} - \,4x - \,2y = - 4\,\,and\,\,{x^2}\, + \,{y

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Consider a family of circles passing through two fixed points A (3, 7) and B (6, 5). Show that the chords on which the c

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If in a triangle $$ABC$$, $${{2\cos A} \over a} + {{\cos B} \over b} + {{2\cos C} \over c} = {a \over {bc}} + {b \over {

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An observer at $$O$$ notices that the angle of elevation of the top of a tower is $${30^ \circ }$$. The line joining $$O

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If $$f\left( x \right) = \left\{ {\matrix{
{3{x^2} + 12x - 1,} & { - 1 \le x \le 2} \cr
{37 - x} & {2 &l

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Find the equation of the normal to the curve
$$y = {\left( {1 + x} \right)^y} + {\sin ^{ - 1}}\left( {{{\sin }^2}x} \ri

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Let $$f\left( x \right) = \left\{ {\matrix{
{ - {x^3} + {{\left( {{b^3} - {b^2} + b - 1} \right)} \over {\left( {{b^2

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The value of $$\int\limits_{\pi /4}^{3\pi /4} {{\phi \over {1 + \sin \phi }}d\phi } $$ is ..............

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The value of $$\int\limits_0^{\pi /2} {{{dx} \over {1 + {{\tan }^3}\,x}}} $$ is

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Evaluate $$\int_2^3 {{{2{x^5} + {x^4} - 2{x^3} + 2{x^2} + 1} \over {\left( {{x^2} + 1} \right)\left( {{x^4} - 1} \right)

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An unbiased die with faces marked $$1,2,3,4,5$$ and $$6$$ is rolled four times. Out of four face values obtained, the pr

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$$E$$ and $$F$$ are two independent events. The probability that both $$E$$ and $$F$$ happen is $$1/12$$ and the probabi

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Numbers are selected at random, one at a time, from the two- digit numbers $$00, 01, 02 ......, 99$$ with replacement. A

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Let $$a, b, c$$ be distinct non-negative numbers. If the vectors $$a\widehat i + a\widehat j + c\widehat k,\widehat i +

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Let $$\vec a = 2\hat i - \hat j + \hat k,\vec b = \hat i + 2\hat j - \hat k$$ and $$\overrightarrow c = \widehat i + \

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In a triangle $$ABC, D$$ and $$E$$ are points on $$BC$$ and $$AC$$ respectively, such that $$BD=2DC$$ and $$AE=3EC.$$ Le

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## Physics

A particle of mass m moves on the x-axis as follows: it starts from rest at t = 0 from the point x = 0, and come to rest

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A uniform rod of length L and density $$\rho $$ is being pulled along a smooth floor with a horizontal acceleration $$\a

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