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IIT-JEE 1983

Exam Held on Mon Apr 11 1983 09:00:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

3 g of a salt of molecular weight 30 is dissolved in 250 g of water. The molali...
The density of a 3 M Sodium thiosulphate solution (Na<sub>2</sub>S<sub>2</sub>O<...
Complete and balance the following equation:<br><br> $$Cr_2O_7^{2-}$$ + C<sub>2<...
Complete and balance the following equation:<br><br> Zn + $$NO_3^- \to$$ Zn<sup>...
Complete and balance the following equation:<br><br> Ce<sup>3+</sup> + $$S_2O_8^...
4.08 g of a mixture of BaO and an unknown carbonate MCO<sub>3</sub> was heated s...
Complete and balance the following equation:<br><br> HNO<sub>3</sub> + HCl $$\to...
Complete and balance the following equations:<br><br> Cl<sub>2</sub> + OH<sup>-<...
Elements of the same mass number but of different atomic numbers are known as __...
Gamma rays are electromagnetic radiations of wavelengths of 10<sup>-6</sup> to 1...
The energy of the electron in the 3d-orbital is less than that in the 4s-orbital...
Any p-orbital can accommodate upto
The principal quantum number of an atom is related to the
Rutherford's scattering experiment is related to the size of the
Linear overlap of two atomic p-orbitals leads to a sigma bond.
Carbon tetrachloride has no net dipole moment because of
Which one among the following does not have the hydrogen bond?
The types of bonds present in CuSO<sub>4</sub>.5H<sub>2</sub>O are only
The absorption of hydrogen by palladium is commonly known as ______.
Heavy water is
An organic compound C<sub>x</sub>H<sub>2y</sub>O<sub>y</sub> was burnt with twic...

Mathematics

If $$\tan \,A = \left( {1 - \cos B} \right)/\sin B,$$ then $$tan2A = tan\,B$$. ...
If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right)...
The points z<sub>1</sub>, z<sub>2</sub>, z<sub>3</sub>, z<sub>4</sub> in the co...
Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an e...
Find all solutions of $$4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x$$
Show that $$$16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \...
If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$...
Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 &gt; 0$$ and $${x^2...
The equation $$2{x^2} + 3x + 1 = 0$$ has an irrational root.
If $${\left( {1 + ax} \right)^n} = 1 + 8x + 24{x^2} + .....$$ then $$a=............
Given positive integers $$r &gt; 1,\,n &gt; 2$$ and that the coefficient of $$\l...
The coefficient of $${x^4}$$ in $${\left( {{x \over 2} - {3 \over {{x^2}}}} \rig...
If $${\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ..... + {C_n}{x^...
Use mathematical Induction to prove : If $$n$$ is any odd positive integer, then...
m men and n women are to be seated in a row so that no two women sit together. I...
The rational number, which equals the number $$2\overline {357} $$ with recurrin...
Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that <br>(i) their s...
Given the points $$A\left( {0,4} \right)$$ and $$B\left( {0, - 4} \right)$$, the...
The straight line $$5x + 4y = 0$$ passes through the point of intersection of th...
The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triang...
The vertices of a triangle are <br>$$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t...
The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, ...
The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon ...
The point of intersection of the line 4x - 3y - 10 = 0 and the circle $${x^2} + ...
The centre of the circle passing through the point (0, 1) and touching the curve...
The equation of the circle passing through (1, 1) and the points of intersectio...
Through a fixed point (h, k) secants are drawn to the circle $$\,{x^2}\, + \,{y^...
The derivative of an even function is always an odd function.
From the top of a light-house 60 metres high with its base at the sea-level, the...
The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its ...
The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\ta...
Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$
The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\co...
The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing f...
If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has
If $$x-r$$ is a factor of the polynomial $$f\left( x \right) = {a_n}{x^4} + .......
$$AB$$ is a diameter of a circle and $$C$$ is any point on the circumference of ...
The normal to the curve $$\,x = a\left( {\cos \theta + \theta \sin \theta } \ri...
If $$y = a\,\,In\,x + b{x^2} + x$$ has its extreamum values at $$x=-1$$ and $$x=...
Show that $$1+x$$ $$In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^...
Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$ <b...
Evaluate : $$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right...
The value of the integral $$\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\s...
Evaluate : $$\int\limits_0^{\pi /4} {{{\sin x + \cos x} \over {9 + 16\sin 2x}}dx...
Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 ...
If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \o...
If the letters of the word "Assassin" are written down at random in a row, the p...
Fifteen coupons are numbered $$1, 2 ........15,$$ respectively. Seven coupons ar...
$$A, B, C$$ are events such that <br>$$P\left( A \right) = 0.3,P\left( B \right)...
Cards are drawn one by one at random from a well - shuffled full pack of $$52$$ ...
The unit vector perpendicular to the plane determined by $$P\left( {1, - 1,2} \r...
The area of the triangle whose vertices are $$A(1, -1, 2), B(2, 1, -1), C(3, -1,...
If $$X.A=0, X.B=0, X.C=0$$ for some non-zero vector $$X,$$ then $$\left[ {A\,B\,...
The volume of the parallelopiped whose sides are given by <br>$$\overrightarrow...
The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinea...
A vector $$\overrightarrow A $$ has components $${A_1},{A_2},{A_3}$$ in a right ...

Physics

Match the physical quantities given in column I with dimension expressed in term...
A particle moves in a circle of radius R. In half the period of revolution its d...
Two balls of different masses are thrown vertically upwards with the same speed....
A river is flowing from west to east at a speed of 5 meters per minute. A man on...

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