IIT-JEE 1989

Paper was held on
Tue, Apr 11, 1989 9:00 AM

## Chemistry

An equal volume of a reducing agent is titrated separately with 1M KMnO4 in acid neutral and alkaline media. The volume

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The correct set of quantum numbers for the unpaired electron of chlorine atom is

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The correct ground state electronic configuration of chromium atom is

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Which one of the following is the smallest in size?

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Which one of the following is the strongest base?

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Sodium sulphate is soluble in water whereas barium sulphate is sparingly soluble because

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The molecule which has zero dipole moment is:

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The molecule which has pyramidal shape is

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The compound in which $$\mathop C\limits^* $$ uses its sp3 hybrid orbitals for bond formation is

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Which of the following is paramagnetic?

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Eight gram each of oxygen and hydrogen at 27oC will have the total kinetic energy in the ratio of _______.

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The electrolysis of molten sodium hydride liberates ____ gas at the _____

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Write down the balanced equation for the reaction when:
Potassium ferricyanide reacts with hydrogen peroxide in basic so

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n-Butane is produced by the monobromination of ethane followed by the Wurtz reaction. Calculate the volume of ethane at

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The vapour pressure of a dilute aqueous solution of glucose (C6H12O6) is 750 mm of mercury at 373 K. Calculate (i) molal

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## Mathematics

The general solutions of $$\,\sin x - 3\sin 2x + \sin 3x = \cos x - 3\cos 2x + \cos 3x$$ is

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If $$a,\,b,\,c,$$ are the numbers between 0 and 1 such that the ponts $${z_1} = a + i,{z_2} = 1 + bi$$ and $${z_3} = 0$$

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The equation $${x^{3/4{{\left( {{{\log }_2}\,\,x} \right)}^2} + {{\log }_2}\,\,x - 5/4}} = \sqrt 2 $$ has

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If x and y are positive real numbers and m, n are any positive integers, then $${{{x^n}\,{y^m}} \over {(1 + {x^{2n}})\,(

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If $$\alpha $$ and $$\beta $$ are the roots of $${x^2}$$+ px + q = 0 and $${\alpha ^4},{\beta ^4}$$ are the roots of $$\

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Let a, b, c be real numbers, $$a \ne 0$$. If $$\alpha \,$$ is a root of $${a^2}{x^2} + bx + c = 0$$. $$\beta \,$$ is the

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A five-digit numbers divisible by 3 is to be formed using the numerals 0, 1, 2, 3, 4 and 5, without repetition. The tota

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Using mathematical induction, prove that $${}^m{C_0}{}^n{C_k} + {}^m{C_1}{}^n{C_{k - 1}}\,\,\, + .....{}^m{C_k}{}^n{C_0}

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Prove that
$${C_0} - {2^2}{C_1} + {3^2}{C_2}\,\, - \,..... + {\left( { - 1} \right)^n}{\left( {n + 1} \right)^2}{C_n}

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Let $$ABC$$ be a triangle with $$AB = AC$$. If $$D$$ is the midpoint of $$BC, E$$ is the foot of the perpendicular drawn

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The line x + 3y = 0 is a diameter of the circle $${x^2} + {y^2} - 6x + 2y = 0\,$$.

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The area of the triangle formed by the positive x-axis and the normal and the tangent to the circle $${x^2} + {y^2} = 4\

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If the two circles $${(x - 1)^2} + {(y - 3)^2} = {r^2}$$ and $${x^2} + {y^2} - 8x + 2y + 8 = 0$$ intersect in two distin

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The lines 2x - 3y = 5 and 3x - 4y = 7 are diameters of a circle of area 154 sq. units. Then the equation of this circle

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If $$\left( {{m_i},{1 \over {{m_i}}}} \right),\,{m_i}\, > \,0,\,i\, = 1,\,2,\,3,\,4$$ are four distinct points on a c

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If $$x = \sec \theta - \cos \theta $$ and $$y = {\sec ^n}\theta - {\cos ^n}\theta $$, then show
that $$\left( {{x^2}

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$$ABC$$ is a triangular park with $$AB=AC=100$$ $$m$$. A television tower stands at the midpoint of $$BC$$. The angles o

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The greater of the two angles $$A = 2{\tan ^{ - 1}}\left( {2\sqrt 2 - 1} \right)$$ and $$B = 3{\sin ^{ - 1}}\left( {1/3

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Find all maxima and minima of the function
$$$y = x{\left( {x - 1} \right)^2},0 \le x \le 2$$$
Also determine the area

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Evaluate $$\int {\left( {\sqrt {\tan x} + \sqrt {\cot x} } \right)dx} $$

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The value of $$\int\limits_{ - 2}^2 {\left| {1 - {x^2}} \right|dx} $$ is ...............

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If $$f$$ and $$g$$ are continuous function on $$\left[ {0,a} \right]$$ satisfying
$$f\left( x \right) = f\left( {a - x}

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A pair of fair dice is rolled together till a sum of either $$5$$ or $$7$$ is obtained. Then the probability that $$5$$

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If the probability for $$A$$ to fail in an examination is $$0.2$$ and that for $$B$$ is $$0.3$$, then the probability th

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If $$E$$ and $$F$$ are independent events such that $$0 < P\left( E \right) < 1$$ and $$0 < P\left( F \right) &

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Suppose the probability for A to win a game against B is $$0.4.$$ If $$A$$ has an option of playing either a "best of $$

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For any three vectors $${\overrightarrow a ,\,\overrightarrow b ,}$$ and $${\overrightarrow c ,}$$
$$\left( {\overright

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If vectors $$\overrightarrow A ,\overrightarrow B ,\overrightarrow C $$ are coplanar, show that
$$$\left| {\matrix{

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In a triangle $$OAB,E$$ is the midpoint of $$BO$$ and $$D$$ is a point on $$AB$$ such that $$AD:DB=2:1.$$ If $$OD$$ and

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