IIT-JEE 1994

Paper was held on
Mon, Apr 11, 1994 9:00 AM

## Chemistry

The compound YBa2Cu3O7, which shows superconductivity, has copper in oxidation state ______ assume that the rare earth

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The composition of a sample of Wustite is Fe0.93O1.00 what percentage of the iron is present in the form of Fe(III)?

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8.0575 $$\times$$ 10-2 kg of Glauber's salt is dissolved in water to obtain 1 dm3 of a solution of density 1077.2 kg.m-3

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The outermost electronic configuration of Cr is _______.

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Find out the number of waves made by a Bohr electron in once complete revolution in its 3rd orbit?

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The two types of bond present in B2H6 are covalent and _______.

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Using the VSEPR theory, identify the type of hybridization and draw the structure of OF2. What are the oxidation states

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A 4 : 1 molar mixture of He and CH4 is contained in a vessel at 20 bar pressure. Due to a hole in the vessel the gas mix

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An LPG (liquefied petroleum gas) cylinder weighs 14.8 kg when empty. When full, it weighs 29.0 kg and shows a pressure o

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Complete and balance the following reactions:
Ca5(PO4)3F + H2SO4 + H2O $$\buildrel {Heat} \over
\longrightarrow $$ ....

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Statement (S) The alkali metals can form ionic hydrides which contain the hydride ion H-.
Explanation (E) The alkali met

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The IUPAC name of succinic acid is _______.

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The standard reduction potential of the Ag+/Ag electrode at 298 K is 0.799V. Given that for AgI, Ksp = 8.7 $$\times$$ 10

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The Edison storage cells is represented as
Fe(s) | FeO(s) | KOH (aq) | Ni2O3(s) | Ni(s)
The half-cell reactions are:
Ni2

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A is binary compound of a univalent metal. 1.422 g of A
reacts completely with 0.321 g of sulphur in an evacuated
and se

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## Mathematics

Let $$0 < x < {\pi \over 4}$$ then $$\left( {\sec 2x - \tan 2x} \right)$$ equals

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Let $$n$$ be a positive integer such that $$\sin {\pi \over {2n}} + \cos {\pi \over {2n}} = {{\sqrt n } \over 2}.$$ T

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If $$\omega \,$$ is an imaginary cube root of unity then the value of $$\sin \left\{ {\left( {{\omega ^{10}} + {\omega ^

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Suppose Z1, Z2, Z3 are the vertices of an equilateral triangle inscribed in the circle $$\left| Z \right| = 2.$$ If Z1 =

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Let $$2{\sin ^2}x + 3\sin x - 2 > 0$$ and $${x^2} - x - 2 < 0$$ ($$x$$ is measured in radians). Then $$x$$ lies in

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The number of points of intersection of two curves y = 2 sin x and y $$ = 5{x^2} + 2x + 3$$ is

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If p, q, r are + ve and are on A.P., the roots of quadratic equation $$p{x^2} + qx + r = 0$$ are all real for

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Let $$p,q \in \left\{ {1,2,3,4} \right\}\,$$. The number of equations of the form $$p{x^2} + qx + 1 = 0$$ having real ro

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Let $$n$$ be positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of $${\left( {1 + x} \rig

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If $$x$$ is not an integral multiple of $$2\pi $$ use mathematical induction to prove that :
$$$\cos x + \cos 2x + ....

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Let $$n$$ be a positive integer and $${\left( {1 + x + {x^2}} \right)^n} = {a_0} + {a_1}x + ............ + {a_{2n}}{x^{2

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A committee of 12 is to be formed from 9 women and 8 men. In how many ways this can be done if at least five women have

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If $$In\left( {a + c} \right),In\left( {a - c} \right),In\left( {a - 2b + c} \right)$$ are in A.P., then

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The locus of a variable point whose distance from $$\left( { - 2,\,0} \right)$$ is $$2/3$$ times its distance from the

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The equations to a pair of opposites sides of parallelogram are $${x^2} - 5x + 6 = 0$$ and $${y^2} - 6y + 5 = 0,$$ the e

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The circles $${x^2} + {y^2} - 10x + 16 = 0$$ and $${x^2} + {y^2} = {r^2}$$ intersect each other in two distinct points i

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The point of intersection of the tangents at the ends of the latus rectum of the parabola $${y^2} = 4x$$ is ...... .

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The equation $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$ represents

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Let $$E$$ be the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 4} = 1$$ and $$C$$ be the circle $${x^2} + {y^2} = 9$$. Le

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Through the vertex $$O$$ of parabola $${y^2} = 4x$$, chords $$OP$$ and $$OQ$$ are drawn at right angles to one another .

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If $$y = {\left( {\sin x} \right)^{\tan x}},$$ then $${{dy} \over {dx}}$$ is equal to

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In a triangle $$ABC$$, $$AD$$ is the altitude from $$A$$. Given $$b>c$$, $$\angle C = {23^ \circ }$$ and $$AD = {{abc

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A circle is inscribed in an equilateral triangle of side $$a$$. The area of any square inscribed in this circle is ....

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If the lengths of the sides of triangle are $$3, 5, 7$$ then the largest angle of the triangle is

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A tower $$AB$$ leans towards west making an angle $$\alpha $$ with the vertical. The angular elevation of $$B$$, the top

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Let $${A_1},{A_2},........,{A_n}$$ be the vertices of an $$n$$-sided regular polygon such that $${1 \over {{A_1}{A_2}}}

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Consider the following statements connecting a triangle $$ABC$$
(i) The sides $$a, b, c$$ and area $$\Delta $$ are rati

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If we consider only the principle values of the inverse trigonometric functions then the value of
$$\tan \left( {{{\cos

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Let $$C$$ be the curve $${y^3} - 3xy + 2 = 0$$. If $$H$$ is the set of points on the curve $$C$$ where the tangent is ho

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Let $$P$$ be a variable point on the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ with foci $${F_1}

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Which one of the following curves cut the parabola $${y^2} = 4ax$$ at right angles?

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The function defined by $$f\left( x \right) = \left( {x + 2} \right){e^{ - x}}$$

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The curve $$y = a{x^3} + b{x^2} + cx + 5$$, touches the $$x$$-axis at $$P(-2, 0)$$ and cuts the $$y$$ axis at a point $$

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The circle $${x^2} + {y^2} = 1$$ cuts the $$x$$-axis at $$P$$ and $$Q$$. Another circle with centre at $$Q$$ and variabl

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Find the indefinite integral $$\,\int {\cos 2\theta {\mkern 1mu} ln\left( {{{\cos \theta + \sin \theta } \over {\cos \t

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The value of $$\int\limits_2^3 {{{\sqrt x } \over {\sqrt {3 - x} + \sqrt x }}} dx$$ is ...........

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Show that $$\int\limits_0^{n\pi + v} {\left| {\sin x} \right|dx = 2n + 1 - \cos \,v} $$ where $$n$$ is a positive integ

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In what ratio does the $$x$$-axis divide the area of the region
bounded by the parabolas $$y = 4x - {x^2}$$ and $$y = {

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A normal is drawn at a point $$P(x,y)$$ of a curve. It meets the $$x$$-axis at $$Q.$$ If $$PQ$$ is of constant length $$

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If two events $$A$$ and $$B$$ are such that $$P\,\,\left( {{A^c}} \right)\,\, = \,\,0.3,\,\,P\left( B \right) = 0.4$$ an

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Let $$A, B, C$$ be three mutually independent events. Consider the two statements $${S_1}$$ and $${S_2}$$
$${S_1}\,:\,A$

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An unbiased coin is tossed. If the result is a head, a pair of unbiased dice is rolled and the number obtained by adding

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

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Let $$\alpha ,\beta ,\gamma $$ be distinct real numbers. The points with position
vectors $$\alpha \widehat i + \beta \

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Let $$\overrightarrow p $$ and $$\overrightarrow q $$ be the position vectors of $$P$$ and $$Q$$ respectively, with resp

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The vector $$\,{1 \over 3}\left( {2\widehat i - 2\widehat j + \widehat k} \right)$$ is

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If the vectors $$\overrightarrow b ,\overrightarrow c ,\overrightarrow d ,$$ are not coplanar, then prove that the vecto

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## Physics

A block of mass 0.1 is held against a wall applying a horizontal force of 5 N on the block. If the coefficient of fricti

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A particle of mass m is moving in a circular path of constant radius r such that its centripetal acceleration $${a_c}$$

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An object of mass 0.2 kg executes simple harmonic oscillation along the x-axis with a frequency of $$\left( {{{25} \over

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