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 _____.

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

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

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

View Question 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

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

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

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

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

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

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

View Question The principal quantum number of an atom is related to the

View Question Any p-orbital can accommodate upto

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

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

View Question Carbon tetrachloride has no net dipole moment because of

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

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

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

View Question Heavy water is

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

View Question ## Mathematics

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

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

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

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

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

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

View Question 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

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

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

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

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

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

View Question 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

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

View Question 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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

View Question 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^

View Question 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.

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

View Question ## Physics

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

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

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

View Question 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

View Question