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## IIT-JEE 1990

Exam Held on Wed Apr 11 1990 09:00:00 GMT+0000 (Coordinated Universal Time)
Click View All Questions to see questions one by one or you can choose a single question from below.

## 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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