IIT-JEE 1991

Paper was held on
Thu, Apr 11, 1991 9:00 AM

## Chemistry

The weight of $$1 \times 10^{22}$$ molecules of CuSO4.5H2O is ____.

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The oxidation state of the most electronegative element in the products of the reaction. BaO2 with dil. H2SO4 are

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A 1.0 g sample of Fe2O3 solid of 55.2% purity is dissolved in acid and reduced by heating the solution with zinc dust. T

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A solution of 0.2 g of a compound containing Cu2+ and $$C_2O_4^{2-}$$ ions on titration with 0.02M $$KMnO_4$$ in presenc

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Read the following statement and explanation and answer as per the options given below:
STATEMENT (S): In the titration

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Arrange of the following in :
Increasing order of ionic size:
N3-, Na+, F-, O2-, Mg2+

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Arrange of the following in :
Increasing order of basic character
MgO, SrO, K2O, NiO, Cs2O

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Arrange of the following in :
Arrange the following ions in order of their increasing radii:
Li+, Mg2+, K+, Al3+

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The linear structure is assumed by

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Arrange the following :
Increasing strength of hydrogen bonding (X-H-X):
O, S, F, Cl, N

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Calculate the volume occupied by 5.0 g of acetylene gas at 50oC and 740 mm pressure.

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The volume strength of 1.5 N H2O2 solution is

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Write down the balanced equation for the reaction when:
Carbon dioxide is passed through a suspension of lime stone in w

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The hybridization of carbon atoms in C-C single bond of HC $$ \equiv $$ C - CH = CH2 is

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The degree of dissociation of calcium nitrate in a dilute aqueous solution, containing 7.0 g. of the salt per 100 gm of

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Zinc granules are added in excess to a 500 ml. of 1.0 M nickel nitrate solution at 25oC until the equilibrium is reached

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The current of 1.70 A is passed through 300.0 ml of 0.160 M solution of a ZnSO4 for 230 sec. with a current efficiency o

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The decomposition of N2O5 according to the equation:
2N2O5 (g) $$\to$$ 4NO2(g) + O2(g)
is a first order reaction. After

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Write the IUPAC name for the following :

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## Mathematics

The value of
$$\sin {\pi \over {14}}\sin {{3\pi } \over {14}}\sin {{5\pi } \over {14}}\sin {{7\pi } \over {14}}\sin {{

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If $$\exp \,\,\,\left\{ {\left( {\left( {{{\sin }^2}x + {{\sin }^4}x + {{\sin }^6}x + \,\,\,..............\infty } \righ

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The product of $$n$$ positive numbers is unity. Then their sum is

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Using induction or otherwise, prove that for any non-negative integers $$m$$, $$n$$, $$r$$ and $$k$$ ,
$$\sum\limits_{m

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Eighteen guests have to be seated, half on each side of a long table. Four particular guests desire to sit on one partic

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Let p be the first of the n arithmetic means between two numbers and q the first of n harmonic means between the same nu

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If $${S_1}$$, $${S_2}$$, $${S_3}$$,.............,$${S_n}$$ are the sums of infinite geometric series whose first terms a

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Let the algebraic sum of the perpendicular distances from the points $$\left( {2,0} \right),\,\left( {0,\,2} \right)$$ $

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Show that all chords of the curve $$3{x^2} - {y^2} - 2x + 4y = 0,$$ which subtend a right angle at the origin, pass thro

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If a circle passes through the points of intersection of the coordinate axes with the lines $$\lambda \,x - y + 1 = 0$$

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Find the equation of the line passing through the point $$(2, 3)$$ and making intercept of length 2 units between the li

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Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangent is 4x + 3y = 10

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Three normals are drawn from the point $$(c, 0)$$ to the curve $${y^2} = x.$$ Show that $$c$$ must be greater than $$1/2

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Find $${{{dy} \over {dx}}}$$ at $$x=-1$$, when
$${\left( {\sin y} \right)^{\sin \left( {{\pi \over 2}x} \right)}} + {{

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A man notices two objects in a straight line due west. After walking a distance $$c$$ due north he observes that the obj

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In a triangle of base a the ratio of the other two sides is $$r\left( { < 1} \right)$$. Show that the altitude of the

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The sides of a triangle are three consecutive natural numbers and its largest angle is twice the smallest one. Determine

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A window of perimeter $$P$$ (including the base of the arch) is in the form of a rectangle surmounded by a semi circle.

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

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Evaluate $$\,\int\limits_0^\pi {{{x\,\sin \,2x\,\sin \left( {{\pi \over 2}\cos x} \right)} \over {2x - \pi }}dx} $$

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If $$'f$$ is a continuous function with $$\int\limits_0^x {f\left( t \right)dt \to \infty } $$ as $$\left| x \right| \to

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If the mean and the variance of binomial variate $$X$$ are $$2$$ and $$1$$ respectively, then the probability that $$X$$

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For any two events $$A$$ and $$B$$ in a simple space

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In a test an examine either guesses or copies or knows the answer to a multiple choice question with four choices. The p

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Given that $$\overrightarrow a = \left( {1,1,1} \right),\,\,\overrightarrow c = \left( {0,1, - 1} \right),\,\overright

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Determine the value of $$'c'$$ so that for all real $$x,$$ the vector
$$cx\widehat i - 6\widehat j - 3\widehat k$$ and

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