IIT-JEE 1981

Paper was held on
Sat, Apr 11, 1981 9:00 AM

## Chemistry

If 0.50 mol of BaCl2 is mixed with 0.20 mol of Na3PO4, the maximum amount of Ba3(PO4)2 that can be formed is

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1 mole of N2H4 loses 10 moles of electrons to form a new compound Y. assuming that all nitrogen appears in the new compo

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Balance the following Equations:
(i) Cu2O + H+ + $$NO_3^ - \to $$ Cu2+ + NO + H2O
(ii) K4[Fe(CN)6] + H2SO4 + H2O $$\to$

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A 1.00 gm sample of H2O2 solution containing X percent H2O2 by weight requires X ml of a KMnO4 solution for complete ox

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Rutherford's experiment on scattering of $$\alpha-particles$$ showed for the first time that the atom has

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The energy of the electron in the second and the third Bohr's orbits of the hydrogen atom is -5.42 $$\times$$ 10-12 erg

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The correct order of second ionisation potential of carbon, nitrogen, oxygen and fluorine is

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The angle between two convalent bonds is maximum in ________. (CH4, H2O, CO2)

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If a molecule MX3 has zero dipole moment, the sigma bonding orbitals used by M (atomic number < 21) are

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Equal weights of methane and oxygen are mixed in an empty container at 25oC. The fraction of the total pressure exerted

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The temperature at which a real gas obeys the ideal gas aws over a wide range of pressure is

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The ratio of root mean square velocity to average velocity of a gas molecule at a particular temperature is

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A solution of sodium metal in liquid ammonia is strongly reducing due to the presence of

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Give reasons of the following:
Sodium carbonate is made by Solvay process but the same process is not extended to the ma

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The vapour pressure of pure benzene is 639.7 mm of mercury and the vapour of a solution of a solute in benzene at the sa

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## Mathematics

Suppose $${\sin ^3}\,x\sin 3x = \sum\limits_{m = 0}^n {{C_m}\cos \,mx} $$ is an identity in x, where C0, C1 ,....Cn are

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The general solution of the trigonometric equation sin x+cos x=1 is given by:

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For complex number $${z_1} = {x_1} + i{y_1}$$ and $${z_2} = {x_2} + i{y_2},$$ we write $${z_1} \cap {z_2},\,\,if\,\,{x_1

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The complex numbers $$z = x + iy$$ which satisfy the equation $$\,\left| {{{z - 5i} \over {z + 5i}}} \right| = 1$$ lie o

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Let the complex number $${{z_1}}$$, $${{z_2}}$$ and $${{z_3}}$$ be the vertices of an equilateral triangle. Let $${{z_0}

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For every integer n > 1, the inequality $${(n!)^{1/n}} < {{n + 1} \over 2}$$ holds.

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Five balls of different colours are to be placed in there boxes of different size. Each box can hold all five. In how ma

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The area enclosed within the curve $$\left| x \right| + \left| y \right| = 1$$ is .................

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Let A be the centre of the circle $${x^2}\, + \,{y^2}\, - \,2x\,\, - 4y\, - 20 = 0\,$$. Suppose that the tangents at the

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Find the equations of the circle passing through (- 4, 3) and touching the lines x + y = 2 and x - y = 2.

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The equation $${{{x^2}} \over {1 - r}} - {{{y^2}} \over {1 + r}} = 1,\,\,\,\,r > 1$$ represents

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Each of the four inequalties given below defines a region in the $$xy$$ plane. One of these four regions does not have t

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Suppose that the normals drawn at three different points on the parabola $${y^2} = 4x$$ pass through the point $$(h, k)$

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Let $$y = {e^{x\,\sin \,{x^3}}} + {\left( {\tan x} \right)^x}$$. Find $${{dy} \over {dx}}$$

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Let the angles $$A, B, C$$ of a triangle $$ABC$$ be in A.P. and let $$b:c = \sqrt 3 :\sqrt 2 $$. Find the angle $$A$$.

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Let $$a, b, c$$ be positive real numbers Let
$$\theta = {\tan ^{ - 1}}\sqrt {{{a\left( {a + b + c} \right)} \over {bc}

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Find the value of : $$\cos \left( {2{{\cos }^{ - 1}}x + {{\sin }^{ - 1}}x} \right)$$ at $$x = {1 \over 5}$$, where
$$0

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Use the function $$f\left( x \right) = {x^{1/x}},x > 0$$. to determine the bigger of the two numbers $${e^\pi }$$ and

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Let $$x$$ and $$y$$ be two real variables such that $$x>0$$ and $$xy=1$$. Find the minimum value of $$x+y$$.

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For all $$x$$ in $$\left[ {0,1} \right]$$, let the second derivative $$f''(x)$$ of a function $$f(x)$$ exist and satisfy

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Evaluate $$\int {\left( {{e^{\log x}} + \sin x} \right)\cos x\,\,dx.} $$

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The value of the definite integral $$\int\limits_0^1 {\left( {1 + {e^{ - {x^2}}}} \right)} \,\,dx$$

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Let $$a, b, c$$ be non-zero real numbers such that
$$\int\limits_0^1 {\left( {1 + {{\cos }^8}x} \right)\left( {a{x^2} +

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Find the area bounded by the curve $${x^2} = 4y$$ and the straight

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Show that : $$\mathop {\lim }\limits_{n \to \infty } \left( {{1 \over {n + 1}} + {1 \over {n + 2}} + .... + {1 \over {6n

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For a biased die the probabilities for the different faces to turn up are given below :
This die tossed and you are to

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An anti-aircraft gun can take a maximum of four shots at an enemy plane moving away from it. The probabilities of hitti

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Let $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$ be vectors of length $$3, 4, 5$$ respectively. Let $$\o

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Let $$\overrightarrow A ,\overrightarrow B $$ and $${\overrightarrow C }$$ be unit vectors suppose that $$\overrightarro

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The scalar $$\overrightarrow A .\left( {\overrightarrow B + \overrightarrow C } \right) \times \left( {\overrightarrow

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## Physics

A gas bubble, from an explosion under water, oscillates with a period T proportional to padbEc. Where 'P' is the static

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When a person walks on a rough surface, the frictional force exerted by the surface on the person is opposite to the di

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