IIT-JEE 1996

Paper was held on
Thu, Apr 11, 1996 9:00 AM

## Chemistry

A 3.00 g sample containing Fe3O4, Fe2O3 and an inert impure substance is treated with excess of KI solution in presence

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The orbital angular momentum of an electron in 2s orbital is

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Calculate the wave number for the shortest wavelength transition in the Balmer series of atomic hydrogen.

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Consider the hydrogen atom to be a proton embedded in a cavity of radius a0 (Bohr radius) whose charge is neutralised by

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Which of the following has the maximum number of unpaired electrons?

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When N2, the N-N bond distance _____ and when O2 goes to $$O_2^+$$ the O-O bond distance ___.

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The number and type of bonds between two carbon atoms in CaC2 are:

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Among the following species, identity the isostructural pairs NF3, $$NO_3^-$$, BF3, H3O+ , HN3

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A mixture of ideal gas is cooled upto liquid helium temperature (4.22K) to form an ideal solution

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The following compounds have been arranged in order of their increasing thermal stabilities. Identify the correct order

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Explain the difference in the nature of bonding in LiF and LiI.

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The molar volume of liquid benzene (density = 0.877 g mL-1) increases by a factor of 2750 as it vaporises at 20oC and th

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The standard reduction potential for Cu2+|Cu is +0.34 V. Calculate the reduction potential at pH = 14 for the above coup

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The ionisation constant of $$NH_4^+$$ in water is 5.6 $$\times$$ 10-10 at 25oC. The rate constant for the reaction of $$

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## Mathematics

General value of $$\theta $$ satisfying the equation $${\tan ^2}\theta + \sec \,2\,\theta = 1$$ is _________.

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$${\sec ^2}\theta = {{4xy} \over {{{\left( {x + y} \right)}^2}}}\,$$ is true if and only if

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The value of the expression
$$1 \bullet \left( {2 - \omega } \right)\left( {2 - {\omega ^2}} \right) + 2 \bullet \left(

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For positive integers $${n_1},\,{n_2}$$ the value of the expression $${\left( {1 + i} \right)^{^{{n_1}}}} + {\left( {1 +

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Find all non-zero complex numbers Z satisfying $$\overline Z = i{Z^2}$$.

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Find all values of $$\theta $$ in the interval $$\left( { - {\pi \over 2},{\pi \over 2}} \right)$$ satisfying the equ

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Let n and k be positive such that $$n \ge {{k(k + 1)} \over 2}$$ . The number of solutions $$\,({x_1},\,{x_2},\,.....{x_

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Using mathematical induction prove that for every integer $$n \ge 1,\,\,\left( {{3^{2n}} - 1} \right)$$ is divisible by

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For any odd integer $$n$$ $$ \ge 1,\,\,{n^3} - {\left( {n - 1} \right)^3} + .... + {\left( { - 1} \right)^{n - 1}}\,{1^3

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The real numbers $${x_1}$$, $${x_2}$$, $${x_3}$$ satisfying the equation $${x^3} - {x^2} + \beta x + \gamma = 0$$ are i

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A rectangle $$PQRS$$ has its side $$PQ$$ parallel to the line $$y = mx$$ and vertices $$P, Q$$ and $$S$$ on the lines $$

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The intercept on the line y = x by the circle $${x^2} + {y^2} - 2x = 0$$ is AB. Equation of the circle with AB as a dia

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The angle between a pair of tangents drawn from a point P to the circle $${x^2}\, + \,{y^2}\, + \,\,4x\, - \,6\,y\, + \,

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A circle passes through three points A, B and C with the line segment AC as its diameter. A line passing through A angle

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Find the intervals of value of a for which the line y + x = 0 bisects two chords drawn from a point $$\left( {{{1\, + \,

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An ellipse has eccentricity $${1 \over 2}$$ and one focus at the point $$P\left( {{1 \over 2},1} \right)$$. Its one dire

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Points $$A, B$$ and $$C$$ lie on the parabola $${y^2} = 4ax$$. The tangents to the parabola at $$A, B$$ and $$C$$, taken

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From a point $$A$$ common tangents are drawn to the circle $${x^2} + {y^2} = {a^2}/2$$ and parabola $${y^2} = 4ax$$. Fin

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If $$x{e^{xy}} = y + {\sin ^2}x,$$ then at $$x = 0,{{dy} \over {dx}} = ..............$$

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In a triangle $$ABC$$, $$a:b:c=4:5:6$$. The ratio of the radius of the circumcircle to that of the incircle is .........

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A curve $$y=f(x)$$ passes through the point $$P(1, 1)$$. The normal to the curve at $$P$$ is $$a(y-1)+(x-1)=0$$. If the

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Determine the points of maxima and minima of the function
$$f\left( x \right) = {1 \over 8}\ell n\,x - bx + {x^2},x >

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Let $$f\left( x \right) = \left\{ {\matrix{
{x{e^{ax}},\,\,\,\,\,\,\,x \le 0} \cr
{x + a{x^2} - {x^3},\,x > 0

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Evaluate $$\int {{{\left( {x + 1} \right)} \over {x{{\left( {1 + x{e^x}} \right)}^2}}}dx} $$.

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If for nonzero $$x$$, $$af(x)+$$ $$bf\left( {{1 \over x}} \right) = {1 \over x} - 5$$ where $$a \ne b,$$ then
$$\int_1^

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For $$n>0,$$ $$\int_0^{2\pi } {{{x{{\sin }^{2n}}x} \over {{{\sin }^{2n}}x + {{\cos }^{2n}}x}}} dx = $$

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Let $${A_n}$$ be the area bounded by the curve $$y = {\left( {\tan x} \right)^n}$$ and the
lines $$x=0,$$ $$y=0,$$ and

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Determine the equation of the curve passing through the origin, in the form $$y=f(x),$$ which satisfies the differential

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For the three events $$A, B,$$ and $$C,P$$ (exactly one of the events $$A$$ or $$B$$ occurs) $$=P$$ (exactly one of the

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In how many ways three girls and nine boys can be seated in two vans, each having numbered seats, $$3$$ in the front an

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A nonzero vector $$\overrightarrow a $$ is parallel to the line of intersection of the plane determined by the vectors $

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If $$\overrightarrow b \,$$ and $$\overrightarrow c \,$$ are two non-collinear unit vectors and $$\overrightarrow a \,$$

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The position vectors of the vertices $$A, B$$ and $$C$$ of a tetrahedron $$ABCD$$ are $$\widehat i + \widehat j + \wideh

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## Physics

Two guns, situated on the top of a hill of height 10 m, fire one shot each with the same speed $$5\sqrt 3 $$ m s-1 at so

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