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IIT-JEE 1981

Exam Held on Sat Apr 11 1981 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

If 0.50 mol of BaCl<sub>2</sub> is mixed with 0.20 mol of Na<sub>3</sub>PO<sub>4...
1 mole of N<sub>2</sub>H<sub>4</sub> loses 10 moles of electrons to form a new c...
A 1.00 gm sample of H<sub>2</sub>O<sub>2</sub> solution containing X percent H<...
Balance the following Equations:<br><br> <b>(i)</b> Cu<sub>2</sub>O + H<sup>+</s...
Rutherford's experiment on scattering of $$\alpha-particles$$ showed for the fir...
The energy of the electron in the second and the third Bohr's orbits of the hydr...
The correct order of second ionisation potential of carbon, nitrogen, oxygen and...
The angle between two convalent bonds is maximum in ________. (CH<sub>4</sub>, H...
If a molecule MX<sub>3</sub> has zero dipole moment, the sigma bonding orbitals ...
Equal weights of methane and oxygen are mixed in an empty container at 25<sup>o<...
The temperature at which a real gas obeys the ideal gas aws over a wide range of...
The ratio of root mean square velocity to average velocity of a gas molecule at ...
A solution of sodium metal in liquid ammonia is strongly reducing due to the pre...
Give reasons of the following:<br> Sodium carbonate is made by Solvay process bu...
The vapour pressure of pure benzene is 639.7 mm of mercury and the vapour of a s...

Mathematics

Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an...
The general solution of the trigonometric equation sin x+cos x=1 is given by:
For complex number $${z_1} = {x_1} + i{y_1}$$ and $${z_2} = {x_2} + i{y_2},$$ we...
The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - ...
Let the complex number $${{z_1}}$$, $${{z_2}}$$ and $${{z_3}}$$ be the vertices ...
For every integer n &gt; 1, the inequality $${(n!)^{1/n}} &lt; {{n + 1} \over 2}...
Five balls of different colours are to be placed in there boxes of different siz...
The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ i...
Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 =...
Find the equations of the circle passing through (- 4, 3) and touching the lines...
The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r &...
Each of the four inequalties given below defines a region in the $$xy$$ plane. O...
Suppose that the normals drawn at three different points on the parabola $${y^2}...
Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \o...
Let the angles $$A, B, C$$ of a triangle $$ABC$$ be in A.P. and let $$b:c = \sqr...
Let $$a, b, c$$ be positive real numbers Let <br>$$\theta = {\tan ^{ - 1}}\sqr...
Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \righ...
For all $$x$$ in $$\left[ {0,1} \right]$$, let the second derivative $$f''(x)$$ ...
Let $$x$$ and $$y$$ be two real variables such that $$x&gt;0$$ and $$xy=1$$. Fin...
Use the function $$f\left( x \right) = {x^{1/x}},x &gt; 0$$. to determine the bi...
Evaluate $$\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $$
The value of the definite integral $$\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}...
Let $$a, b, c$$ be non-zero real numbers such that <br>$$\int\limits_0^1 {\left...
Find the area bounded by the curve $${x^2} = 4y$$ and the straight
Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} +...
For a biased die the probabilities for the different faces to turn up are given ...
An anti-aircraft gun can take a maximum of four shots at an enemy plane moving a...
Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$ be vectors of l...
Let $$\overrightarrow A ,\overrightarrow B $$ and $${\overrightarrow C }$$ be un...
The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C }...

Physics

A gas bubble, from an explosion under water, oscillates with a period T proporti...
When a person walks on a rough surface, the frictional force exerted by the surf...

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