IIT-JEE 1983

Paper was held on
Mon, Apr 11, 1983 9:00 AM

## Chemistry

3 g of a salt of molecular weight 30 is dissolved in 250 g of water. The molality if the solution is _____.

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The density of a 3 M Sodium thiosulphate solution (Na2S2O3) is 1.25 g per ml. Calculate (i) the percentage by weight of

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Complete and balance the following equation:
Ce3+ + $$S_2O_8^{-2} \to $$ $$SO_4^{-2}$$ + Ce4+

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Complete and balance the following equation:
$$Cr_2O_7^{2-}$$ + C2H4O $$\to$$ C2H4O2 + Cr3+

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4.08 g of a mixture of BaO and an unknown carbonate MCO3 was heated strongly. The residue weighed 3.64 g. This was disso

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Complete and balance the following equation:
Zn + $$NO_3^- \to$$ Zn2+ + $$NH_4^+$$

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Complete and balance the following equation:
HNO3 + HCl $$\to$$ NO + Cl2

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Complete and balance the following equations:
Cl2 + OH- $$\to$$ Cl- + ClO-

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Elements of the same mass number but of different atomic numbers are known as ____.

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Gamma rays are electromagnetic radiations of wavelengths of 10-6 to 10-5 cm

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The energy of the electron in the 3d-orbital is less than that in the 4s-orbital in the hydrogen atom.

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The principal quantum number of an atom is related to the

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Any p-orbital can accommodate upto

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Rutherford's scattering experiment is related to the size of the

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Linear overlap of two atomic p-orbitals leads to a sigma bond.

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Carbon tetrachloride has no net dipole moment because of

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The types of bonds present in CuSO4.5H2O are only

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Which one among the following does not have the hydrogen bond?

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The absorption of hydrogen by palladium is commonly known as ______.

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Heavy water is

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An organic compound CxH2yOy was burnt with twice the amount of oxygen needed for complete combustion of CO2 and H2O. The

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## Mathematics

If $$\tan \,A = \left( {1 - \cos B} \right)/\sin B,$$ then $$tan2A = tan\,B$$.

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If $$z = x + iy$$ and $$\omega = \left( {1 - iz} \right)/\left( {z - i} \right),$$ then $$\,\left| \omega \right| = 1

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The points z1, z2, z3, z4 in the complex plane are the vertices of a parallelogram taken in order if and only if

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Prove that the complex numbers $${{z_1}}$$, $${{z_2}}$$ and the origin form an equilateral triangle only if $$z_1^2 + z_

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Find all solutions of $$4{\cos ^2}\,x\sin x - 2{\sin ^2}x = 3\sin x$$

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Show that $$$16\cos \left( {{{2\pi } \over {15}}} \right)\cos \left( {{{4\pi } \over {15}}} \right)\cos \left( {{{8\pi }

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If one root of the quadratic equation $$a{x^2} + bx + c = 0$$ is equal to the $$n$$-th power of the other, then show tha

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Find all real values of $$x$$ which satisfy $${x^2} - 3x + 2 > 0$$ and $${x^2} - 2x - 4 \le 0$$

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The equation $$2{x^2} + 3x + 1 = 0$$ has an irrational root.

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If $${\left( {1 + ax} \right)^n} = 1 + 8x + 24{x^2} + .....$$ then $$a=..........$$ and $$n =............$$

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Given positive integers $$r > 1,\,n > 2$$ and that the coefficient of $$\left( {3r} \right)$$th and $$\left( {r +

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The coefficient of $${x^4}$$ in $${\left( {{x \over 2} - {3 \over {{x^2}}}} \right)^{10}}$$ is

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If $${\left( {1 + x} \right)^n} = {C_0} + {C_1}x + {C_2}{x^2} + ..... + {C_n}{x^n}$$ then show that the sum of the produ

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Use mathematical Induction to prove : If $$n$$ is any odd positive integer, then $$n\left( {{n^2} - 1} \right)$$ is divi

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m men and n women are to be seated in a row so that no two women sit together. If $$m > n$$, then show that the numbe

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The rational number, which equals the number $$2\overline {357} $$ with recurring decimal is

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Find three numbers $$a,b,c$$ between $$2$$ and $$18$$ such that
(i) their sum is $$25$$
(ii) the numbers $$2,$$ $$a, b$

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Given the points $$A\left( {0,4} \right)$$ and $$B\left( {0, - 4} \right)$$, the equation of the locus of the point $$P\

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The straight line $$5x + 4y = 0$$ passes through the point of intersection of the straight lines $$x + 2y - 10 = 0$$ and

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The straight lines $$x + y = 0,\,3x + y - 4 = 0,\,x + 3y - 4 = 0$$ form a triangle which is

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The vertices of a triangle are $$\left[ {a{t_1}{t_2},\,\,a\left( {{t_1} + {t_2}} \right)} \right],\,\,\left[ {a{t_2}{t_3

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The coordinates of $$A, B, C$$ are $$(6, 3), (-3, 5), (4, -2)$$ respectively, and $$P$$ is any point $$(x, y)$$. Show

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The end $$A, B$$ of a straight line segment of constant length $$c$$ slide upon the fixed rectangular axes $$OX, OY$$ re

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The point of intersection of the line 4x - 3y - 10 = 0 and the circle $${x^2} + {y^2} - 2x + 4y - 20 = 0$$ are .........

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The centre of the circle passing through the point (0, 1) and touching the curve $$\,y = {x^2}$$ at (2, 4) is

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The equation of the circle passing through (1, 1) and the points of intersection of $${x^2} + {y^2} + 13x - 3y = 0$$ an

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Through a fixed point (h, k) secants are drawn to the circle $$\,{x^2}\, + \,{y^2} = \,{r^2}$$. Show that the locus of t

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The derivative of an even function is always an odd function.

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From the top of a light-house 60 metres high with its base at the sea-level, the angle of depression of a boat is $${15^

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The ex-radii $${r_1},{r_2},{r_3}$$ of $$\Delta $$$$ABC$$ are H.P. Show that its sides $$a, b, c$$ are in A.P.

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The value of $$\tan \left[ {{{\cos }^{ - 1}}\left( {{4 \over 5}} \right) + {{\tan }^{ - 1}}\left( {{2 \over 3}} \right)}

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Find all the solution of $$4$$ $${\cos ^2}x\sin x - 2{\sin ^2}x = 3\sin x$$

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The larger of $$\cos \left( {In\,\,\theta } \right)$$ and $$In $$ $$\left( {\cos \,\,\theta } \right)$$ If $${e^{ - \pi

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The function $$y = 2{x^2} - In\,\left| x \right|$$ is monotonically increasing for values of $$x\left( {x \ne 0} \right)

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If $$a+b+c=0$$, then the quadratic equation $$3a{x^2} + 2bx + c = 0$$ has

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If $$x-r$$ is a factor of the polynomial $$f\left( x \right) = {a_n}{x^4} + ..... + {a_0},$$ repeated $$m$$ times $$\lef

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$$AB$$ is a diameter of a circle and $$C$$ is any point on the circumference of the circle. Then

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The normal to the curve $$\,x = a\left( {\cos \theta + \theta \sin \theta } \right)$$, $$y = a\left( {\sin \theta - \t

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If $$y = a\,\,In\,x + b{x^2} + x$$ has its extreamum values at $$x=-1$$ and $$x=2$$, then

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Show that $$1+x$$ $$In\left( {x + \sqrt {{x^2} + 1} } \right) \ge \sqrt {1 + {x^2}} $$ for all $$x \ge 0$$

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Find the coordinates of the point on the curve $$y = {x \over {1 + {x^2}}}$$
where the tangent to the curve has the gre

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Evaluate : $$\int {{{\left( {x - 1} \right){e^x}} \over {{{\left( {x + 1} \right)}^3}}}dx} $$

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The value of the integral $$\int\limits_0^{\pi /2} {{{\sqrt {\cot x} } \over {\sqrt {\cot x} + \sqrt {\tan x} }}dx} $$

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Evaluate : $$\int\limits_0^{\pi /4} {{{\sin x + \cos x} \over {9 + 16\sin 2x}}dx} $$

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Find the area bounded by the $$x$$-axis, part of the curve $$y = \left( {1 + {8 \over {{x^2}}}} \right)$$ and
the ordin

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If $$\left( {a + bx} \right){e^{y/x}} = x,$$ then prove that $${x^3}{{{d^2}y} \over {d{x^2}}} = {\left( {x{{dy} \over {d

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If the letters of the word "Assassin" are written down at random in a row, the probability that no two S's occur togethe

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Fifteen coupons are numbered $$1, 2 ........15,$$ respectively. Seven coupons are selected at random one at a time with

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Cards are drawn one by one at random from a well - shuffled full pack of $$52$$ playing cards until $$2$$ aces are obtai

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$$A, B, C$$ are events such that
$$P\left( A \right) = 0.3,P\left( B \right) = 0.4,P\left( C \right) = 0.8$$
$$P\left( {

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The unit vector perpendicular to the plane determined by $$P\left( {1, - 1,2} \right),\,Q\left( {2,0, - 1} \right)$$ and

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The area of the triangle whose vertices are $$A(1, -1, 2), B(2, 1, -1), C(3, -1, 2)$$ is ..........

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If $$X.A=0, X.B=0, X.C=0$$ for some non-zero vector $$X,$$ then $$\left[ {A\,B\,C} \right] = 0$$

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The points with position vectors $$60i+3j,$$ $$40i-8j,$$ $$ai-52j$$ are collinear if

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The volume of the parallelopiped whose sides are given by
$$\overrightarrow {OA} = 2i - 2j,\,\overrightarrow {OB} = i

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A vector $$\overrightarrow A $$ has components $${A_1},{A_2},{A_3}$$ in a right -handed rectangular Cartesian coordinate

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## Physics

Match the physical quantities given in column I with dimension expressed in terms of mass (M), length (L), time (T), and

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A particle moves in a circle of radius R. In half the period of revolution its displacement is ________ and distance cov

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Two balls of different masses are thrown vertically upwards with the same speed. They pass through the point of projecti

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A river is flowing from west to east at a speed of 5 meters per minute. A man on the south bank of the river, capable of

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