IIT-JEE 1990

Paper was held on
Wed, Apr 11, 1990 9:00 AM

## Chemistry

The oxidation number of phosphorus in Ba(H2PO2) is :

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A mixture of H2C2O4 (oxalic acid) and NaHC2O4 weighing 2.02 g was dissolved in water and solution made upto one litre. T

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A solid mixture (5.0 g) consisting of lead nitrate and sodium nitrate was headed below 600oC until the weight of the res

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Calculate the molality of 1 litre solution of 93% H2SO4 (weight/volume). The density of the solution is 1.84 g/ml

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According to Bohr's theory, the electronic energy of hydrogen atom in the nth Bohr's orbit is given by $${E_n} = {{ - 21

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Amongst the following elements (whose electronic configuration are given below), the one having the highest ionization e

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The shape of [CH3]+ is _____.

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The presence of polar bonds in a poly-atomic molecule suggests that the molecule has non-zero dipole moment.

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When zeolite, which is hydrated sodium aluminium silicate is treated with hard water the sodium ions are exchanged with

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The freezing point of equimolal aqueous solutions will be highest for

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The vapour pressure of pure benzene at a certain temperature is 640 mm Hg. A non-volatile non-electrolyte solid weighing

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Give the IUPAC name of the following compound :

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## Mathematics

The equation $$\left( {\cos p - 1} \right){x^2} + \left( {\cos p} \right)x + \sin p = 0\,$$
In the variable x, has real

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Let $${z_1}$$ = 10 + 6i and $${z_2}$$ = 4 + 6i. If Z is any complex number such that the argument of $${{(z - {z_1})} \o

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$$ABC$$ is a triangle such that
$$$\sin \left( {2A + B} \right) = \sin \left( {C - A} \right) = \, - \sin \left( {B + 2

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If $$\,x < 0,\,\,y < 0,\,\,x + y + {x \over y} = {1 \over 2}$$ and $$(x + y)\,{x \over y} = - {1 \over 2}$$, then

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The number of solutions of the equation sin$${(e)^x} = {5^x} + {5^{ - x}}$$ is

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Prove that $${{{n^7}} \over 7} + {{{n^5}} \over 5} + {{2{n^3}} \over 3} - {n \over {105}}$$ is an integer for every posi

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The number $${\log _2}\,7$$ is

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If $${\log _3}\,2\,,\,\,{\log _3}\,({2^x} - 5)\,,\,and\,\,{\log _3}\,\left( {{2^x} - {7 \over 2}} \right)$$ are in arith

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Line $$L$$ has intercepts $$a$$ and $$b$$ on the coordinate axes. When the axes are rotated through a given angle, keepi

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Straight lines $$3x + 4y = 5$$ and $$4x - 3y = 15$$ intersect at the point $$A$$. Points $$B$$ and $$C$$ are choosen on

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A line cuts the $$x$$-axis at $$A (7, 0)$$ and the $$y$$-axis at $$B (0, -5)$$. A variable line $$PQ$$ is drawn perpendi

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A circle touches the line y = x at a point P such that OP = $${4\sqrt 2 \,}$$, where O is the origin. The circle contain

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If $$f\left( x \right) = \left| {x - 2} \right|$$ and $$g\left( x \right) = f\left[ {f\left( x \right)} \right]$$, then

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Let $$f(x)$$ be a quadratic expression which is positive for all the real values of $$x$$. If $$g(x)=f(x)+f''(x)$$, then

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In a triangle $$ABC$$, angle $$A$$ is greater than angle $$B$$. If the measures of angles $$A$$ and $$B$$ satify the equ

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A vertical tower $$PQ$$ stands at a point $$P$$. Points $$A$$ and $$B$$ are located to the South and East of $$P$$ respe

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Show that $$2\sin x + \tan x \ge 3x$$ where $$0 \le x < {\pi \over 2}$$.

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A point $$P$$ is given on the circumference of a circle of radius $$r$$. Chord $$QR$$ is parallel to the tangent at $$P$

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If $$\int {{{4{e^x} + 6{e^{ - x}}} \over {9{e^x} - 4{e^{ - x}}}}\,dx = Ax + B\,\,\log \left( {9{e^{2x}} - 4} \right) + C

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Let $$f:R \to R$$ and $$\,\,g:R \to R$$ be continuous functions. Then the value of the integral
$$\int\limits_{ - \pi

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Prove that for any positive integer $$k$$,
$${{\sin 2kx} \over {\sin x}} = 2\left[ {\cos x + \cos 3x + ......... + \cos

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Compute the area of the region bounded by the curves $$\,y = ex\,\ln x$$ and $$y = {{\ln x} \over {ex}}$$ where $$ln$$ $

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Show that $$\int\limits_0^{\pi /2} {f\left( {\sin 2x} \right)\sin x\,dx = \sqrt 2 } \int\limits_0^{\pi /4} {f\left( {\co

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Let $$A$$ and $$B$$ be two events such that $$P\,\,\left( A \right)\,\, = \,\,0.3$$ and $$P\left( {A \cup B} \right) = 0

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A is a set containing $$n$$ elements. $$A$$ subset $$P$$ of $$A$$ is chosen at random. The set $$A$$ is reconstructed by

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Let $$\overrightarrow A = 2\overrightarrow i + \overrightarrow k ,\,\overrightarrow B = \overrightarrow i + \overrig

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## Physics

Column - I gives the three physical quantities. Select the appropriate units for the choices given in Column - II. Some

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