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## IIT-JEE 1982

Exam Held on Sun Apr 11 1982 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 carbon in CH<sub>2</sub>O is
Hydroxylamine reduces iron (III) according to the equation: <br><br> 2NH<sub>2</...
The mass of a hydrogen atom is ______ kg.
Isotopes of an element differ in the number of ______ in their nuclei.
When there are two electrons in the same orbital, they have _____ spins.
The outer electronic configuration of the ground state chromium atom is 3d<sup>4...
Calculate the wavelength in Angstrom of the photon that is emitted when an elect...
The energy released when an electron is added to a neutral gaseous atom is calle...
The element with the highest first ionization potential is
There are ______ $$\pi$$ bonds in a nitrogen molecule.
____ hybrid orbitals of nitrogen atom are involved in the formation of ammonium ...
The ion that is isoelectronic with CO is
Among the following, the molecule that is linear is
The compound with no dipole moment is
Helium atom is two times heavier than a hydrogen molecule. At 298 K, the average...
At room temparature, ammonia gas at 1 atm pressure and hydrogen chloride gas at ...
MgCl<sub>2</sub>.6H<sub>2</sub>O on heating give anhydrous MgCl<sub>2</sub>
How will you prepare bleaching powder from slaked lime.
Write down the balanced equations for the reaction when:<br> An alkaline solutio...

## Mathematics

If $$z = {\left( {{{\sqrt 3 } \over 2} + {i \over 2}} \right)^5} + {\left( {{{\s... The inequality |z-4| &lt; |z-2| represents the region given by Without using tables, prove that$$\left( {\sin \,{{12}^ \circ }} \right)\left(...
Show that the equation $${e^{\sin x}} - {e^{ - \sin x}} - 4 = 0$$ has no real so...
$$mn$$ squares of equal size are arranged to from a rectangle of dimension $$m$$...
The coeffcient of $${x^{99}}$$ in the polynomial (x -1) (x - 2)...(x - 100) is ....
If $$2 + i\sqrt 3$$ is root of the equation $${x^2} + px + q = 0$$, where p and...
The number of real solutions of the equation $${\left| x \right|^2} - 3\left| x ... Two towns A and B are 60 km apart. A school is to be built to serve 150 students... If p, q, r are any real numbers, then The largest interval for which$${x^{12}} - {x^9} + {x^4} - x + 1 &gt; 0$$is The larger of$${99^{50}} + {100^{50}}$$and$${101^{50}}$$is .............. The sum of the coefficients of the plynomial$${\left( {1 + x - 3{x^2}} \right)^...
In a certain test, $${a_i}$$ students gave wrong answers to atleast i questions,...
Prove that $${7^{2n}} + \left( {{2^{3n - 3}}} \right)\left( {3n - 1} \right)$$ i...
Ten different letters of an alphabet are given. Words with five letters are form...
Eight chairs are numbered 1 to 8. Two women and three men wish to occupy one cha...
The value of the expression $$\,{}^{47}{C_4} + \sum\limits_{j = 1}^5 {^{52 - j}\... The third term of a geometric progression is 4. The product of the first five te... If$$x,\,y$$and$$z$$are$$pth$$,$$qth$$and$$rth$$terms respectively of an... Does there exist a geometric progression containing$$27, 8$$and$$12$$as thre...$$y = {10^x}$$is the reflection of$${\log _{10}}\,x$$in the line whose equati... The set of lines$$ax + by + c = 0,$$where$$3a + 2b + 4c = 0$$is concurrent a... If A and B are points in the plane such that PA/PB = k (constant) for all P on a...$$A$$is point on the parabola$${y^2} = 4ax$$. The normal at$$A$$cuts the par... If$$y = f\left( {{{2x - 1} \over {{x^2} + 1}}} \right)$$and$$f'\left( x \ri...
Let $$f$$ be a twice differentiable function such that <p>$$f''\left( x \right)... A vertical pole stands at a point$$Q$$on a horizontal ground.$$A$$and$$B$$... If$$f(x)$$and$$g(x)$$are differentiable function for$$0 \le x \le 1$$such ... If$$a{x^2} + {b \over x} \ge c$$for all positive$$x$$where$$a&gt;0$$and$$...
The area bounded by the curves $$y=f(x)$$, the $$x$$-axis and the ordinates $$x=... Show that$$\int\limits_0^\pi {xf\left( {\sin x} \right)dx} = {\pi \over 2}\i...
Find the value of $$\int\limits_{ - 1}^{3/2} {\left| {x\sin \,\pi \,x} \right|\,... For any real$$t,\,x = {{{e^t} + {e^{ - t}}} \over 2},\,\,y = {{{e^t} - {e^{ - t...
If $$A$$ and $$B$$ are two events such that $$P\left( A \right) &gt; 0,$$ and $$...$$A$$and$$B$$are two candidates seeking admission in$$IIT.$$The probability... For non-zero vectors$${\overrightarrow a ,\,\overrightarrow b ,\overrightarrow ...
$${A_1},{A_2},.................{A_n}$$ are the vertices of a regular plane polyg...
Find all values of $$\lambda$$ such that $$x, y, z,$$$$\, \ne$$$$(0,0,0)$$ and...

## Physics

Write the dimensions of the followings in terms of mass, time, length and charge...
A particle is moving eastwards with a velocity of 5 m/s. In 10s the velocity cha...
In the arrangement shown in Fig. the ends P and Q of an unstretchable string mov...

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