IIT-JEE 1992

Paper was held on
Sat, Apr 11, 1992 9:00 AM

## Chemistry

For the redox reaction:
$$MnO_4^ - + {C_2}O_4^{ - 2} + {H^ + }$$ $$ \to M{n^{2 + }} + C{O_2} + {H_2}O$$
The correct coe

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A 2.0 g sample of a mixture containing sodium carbonate, sodium bicarbonate and sodium suplphate is gently heated till t

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One gram of commercial AgNO3 is dissolved in 50 ml. of water. It is treated with 50 ml. of a KI solution. The silver iod

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Which of the following relates to photons both as wave motion and as a stream of particles?

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Which of the following does not characterise X-rays?

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The statement that is not correct for the periodic classification of element is

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The maximum number of hydrogen bonds a water molecule can form is

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The cyanide ion, CN- and N2 are isoelectronic, But in contrast to CN-, N2 is chemically inert, because of

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The type of hybrid orbitals used by the chlorine atom in $$ClO_2^-$$ is

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Which of the following have identical bond order?

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The molecules that will have dipole moment are

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At 27oC, hydrogen is leaked through a tiny hole into a vessel for 20 minutes. Another unknown gas at the same temperatur

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At room temperature the following reacton is procedd nearly to completion:
2NO + O2 $$\to$$ 2NO2 $$\to$$ N2O4
The dim

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The species that do not contain peroxide ions are

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Give reasons of the following:
Hydrogen peroxide acts as an oxidising as well as a reducing agent.

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For the galvanic cell
Ag | AgCl(s), KCl (0.2M) || KBr (0.001M), AgBr(s) | Ag
Calculate the EMF generated and assign corr

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An aqueous solution of NaCl on electrolysis gives H2(g), Cl2(g) and NaOH according to the reaction:
2Cl- (aq) + 2H2O = 2

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## Mathematics

In this questions there are entries in columns 1 and 2. Each entry in column 1 is related to exactly one entry in column

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$${\rm{z }} \ne {\rm{0}}$$ is a complex number
Column I
(A) Re z = 0
(B) Arg $$z = {\pi \over 4}$$
Column II

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Show that the value of $${{\tan x} \over {\tan 3x}},$$ wherever defined never lies between $${1 \over 3}$$ and 3.

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Let $$\alpha \,,\,\beta $$ be the roots of the equation (x - a) (x - b) = c, $$c \ne 0$$. Then the roots of the equation

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The expansion $${\left( {x + {{\left( {{x^3} - 1} \right)}^{{1 \over 2}}}} \right)^5} + {\left( {x - {{\left( {{x^3} - 1

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If $$\sum\limits_{r = 0}^{2n} {{a_r}{{\left( {x - 2} \right)}^r}\,\, = \sum\limits_{r = 0}^{2n} {{b_r}{{\left( {x - 3} \

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Let $$p \ge 3$$ be an integer and $$\alpha $$, $$\beta $$ be the roots of $${x^2} - \left( {p + 1} \right)x + 1 = 0$$ us

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Let the harmonic mean and geometric mean of two positive numbers be the ratio 4 : 5. Then the two number are in the rati

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If the sum of the distances of a point from two perpendicular lines in a plane is 1, then its locus is

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Determine all values of $$\alpha $$ for which the point $$\left( {\alpha ,\,{\alpha ^2}} \right)$$ lies insides the tria

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The centre of a circle passing through the points (0, 0), (1, 0) and touching the circle $${x^2} + {y^2} = 9$$is

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Let a circle be given by 2x (x - a) + y (2y - b) = 0, $$(a\, \ne \,0,\,\,b\, \ne 0)$$. Find the condition on a abd b if

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Three circles touch the one another externally. The tangent at their point of contact meet at a point whose distance fro

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A cubic $$f(x)$$ vanishes at $$x=2$$ and has relative minimum / maximum at $$x=-1$$ and $$x = {1 \over 3}$$ if $$\int\li

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What normal to the curve $$y = {x^2}$$ forms the shortest chord?

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In this questions there are entries in columns $$I$$ and $$II$$. Each entry in column $$I$$ is related to exactly one en

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Find the indefinite integral $$\int {\left( {{1 \over {\root 3 \of x + \root 4 \of 4 }} + {{In\left( {1 + \root 6 \of x

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Sketch the region bounded by the curves $$y = {x^2}$$ and
$$y = {2 \over {1 + {x^2}}}.$$ Find the area.

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Determine a positive integer $$n \le 5,$$ such that
$$$\int\limits_0^1 {{e^x}{{\left( {x - 1} \right)}^n}dx = 16 - 6e}

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Three faces of a fair die are yellow, two faces red and one blue. The die is tossed three times. The probability that t

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India plays two matches each with West Indies and Australia. In any match the probabilities of India getting, points $$0

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A lot contains $$50$$ defective and $$50$$ non defective bulbs. Two bulbs are drawn at random, one at a time, with repla

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A unit vector coplanar with $$\overrightarrow i + \overrightarrow j + 2\overrightarrow k $$ and $$\overrightarrow i +

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