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IIT-JEE 1990

Exam Held on Wed Apr 11 1990 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

The oxidation number of phosphorus in Ba(H<sub>2</sub>PO<sub>2</sub>) is :
A mixture of H<sub>2</sub>C<sub>2</sub>O<sub>4</sub> (oxalic acid) and NaHC<sub>...
A solid mixture (5.0 g) consisting of lead nitrate and sodium nitrate was headed...
Calculate the molality of 1 litre solution of 93% H<sub>2</sub>SO<sub>4</sub> (w...
According to Bohr's theory, the electronic energy of hydrogen atom in the n<sup>...
Amongst the following elements (whose electronic configuration are given below),...
The shape of [CH<sub>3</sub>]<sup>+</sup> is _____.
The presence of polar bonds in a poly-atomic molecule suggests that the molecule...
When zeolite, which is hydrated sodium aluminium silicate is treated with hard w...
The vapour pressure of pure benzene at a certain temperature is 640 mm Hg. A non...

Mathematics

The equation $$\left( {\cos p - 1} \right){x^2} + \left( {\cos p} \right)x + \si...
Let $${z_1}$$ = 10 + 6i and $${z_2}$$ = 4 + 6i. If Z is any complex number such ...
$$ABC$$ is a triangle such that $$$\sin \left( {2A + B} \right) = \sin \left( {...
If $$\,x &lt; 0,\,\,y &lt; 0,\,\,x + y + {x \over y} = {1 \over 2}$$ and $$(x + ...
The number of solutions of the equation sin$${(e)^x} = {5^x} + {5^{ - x}}$$ is
Prove that $${{{n^7}} \over 7} + {{{n^5}} \over 5} + {{2{n^3}} \over 3} - {n \ov...
The number $${\log _2}\,7$$ is
If $${\log _3}\,2\,,\,\,{\log _3}\,({2^x} - 5)\,,\,and\,\,{\log _3}\,\left( {{2^...
Line $$L$$ has intercepts $$a$$ and $$b$$ on the coordinate axes. When the axes ...
Straight lines $$3x + 4y = 5$$ and $$4x - 3y = 15$$ intersect at the point $$A$$...
A line cuts the $$x$$-axis at $$A (7, 0)$$ and the $$y$$-axis at $$B (0, -5)$$. ...
A circle touches the line y = x at a point P such that OP = $${4\sqrt 2 \,}$$, w...
If $$f\left( x \right) = \left| {x - 2} \right|$$ and $$g\left( x \right) = f\le...
Let $$f(x)$$ be a quadratic expression which is positive for all the real values...
In a triangle $$ABC$$, angle $$A$$ is greater than angle $$B$$. If the measures ...
A vertical tower $$PQ$$ stands at a point $$P$$. Points $$A$$ and $$B$$ are loca...
Show that $$2\sin x + \tan x \ge 3x$$ where $$0 \le x &lt; {\pi \over 2}$$.
A point $$P$$ is given on the circumference of a circle of radius $$r$$. Chord $...
If $$\int {{{4{e^x} + 6{e^{ - x}}} \over {9{e^x} - 4{e^{ - x}}}}\,dx = Ax + B\,\...
Let $$f:R \to R$$ and $$\,\,g:R \to R$$ be continuous functions. Then the valu...
Prove that for any positive integer $$k$$, <br>$${{\sin 2kx} \over {\sin x}} = 2...
Compute the area of the region bounded by the curves $$\,y = ex\,\ln x$$ and $$y...
Show that $$\int\limits_0^{\pi /2} {f\left( {\sin 2x} \right)\sin x\,dx = \sqrt ...
Let $$A$$ and $$B$$ be two events such that $$P\,\,\left( A \right)\,\, = \,\,0....
A is a set containing $$n$$ elements. $$A$$ subset $$P$$ of $$A$$ is chosen at r...
Let $$\overrightarrow A = 2\overrightarrow i + \overrightarrow k ,\,\overright...

Physics

<p>Column - I gives the three physical quantities. Select the appropriate units ...

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