IIT-JEE 2009 Paper 1 Offline

Paper was held on
Sun, Apr 12, 2009 3:30 AM

## Chemistry

Given that the abundances of isotopes 54Fe, 56Fe and 57Fe are 5%, 90% and 5%, respectively, the atomic mass of Fe is :

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The compound(s) formed upon combustion of sodium metal in excess air is (are)

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The term that corrects for the attractive forces present in a real gas in the van der Waals equation is

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Among the electrolytes Na$$_2$$SO$$_4$$, CaCl$$_2$$, Al$$_2$$(SO$$_4$$)$$_3$$ and NH$$_4$$Cl, the most effective coagula

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The Henry's law constant for the solubility of N$$_2$$ gas in water at 298 K is 1.0 $$\times$$ 10$$^5$$ atm. The mole fr

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The reaction of P$$_4$$ with X leads selectively to P$$_4$$O$$_6$$. The X is

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The correct acidity order of the following is

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Among cellulose, poly(vinyl chloride), nylon and natural rubber, the polymer in which the intermolecular force of attrac

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The IUPAC name of the following compound is

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The correct statement(s) regarding defects in solids is (are)

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The compound(s) that exhibit(s) geometrical isomerism is(are)

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The correct statement(s) about the compound $$\mathrm{H_3C(HO)HC-CH=CH-CH(OH)CH_3~~(X)}$$ is (are)

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The compound X is

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The compound Y is

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The compound Z is

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The structure of the carbonyl compound P is

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The structures of the products Q and R, respectively, are

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The structure of the product S is

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Match each of the diatomic molecules in Column I with its property/properties in Column II:
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Match each of the compounds in Column I with its characteristic reaction(s) in Column II.
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## Mathematics

Let $$z = x + iy$$ be a complex number where x and y are integers. Then the area of the rectangle whose vertices are the

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Let $$z = \,\cos \,\theta \, + i\,\sin \,\theta $$ . Then the value of $$\sum\limits_{m = 1}^{15} {{\mathop{\rm Im}\noli

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If $${{{{\sin }^4}x} \over 2} + {{{{\cos }^4}x} \over 3} = {1 \over 5},$$ then

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The number of seven digit integers, with sum of the digits equal to 10 and formed by using the digits 1, 2 and 3 only, i

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Tangents drawn from the point P (1, 8) to the circle
$${x^2}\, + \,{y^2}\, - \,6x\, - 4y\, - 11 = 0$$
touch the circl

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The line passing through the extremity $$A$$ of the major axis and extremity $$B$$ of the minor axis of the ellipse $${x

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In a triangle $$ABC$$ with fixed base $$BC$$, the vertex $$A$$ moves such that
$$$\cos \,B + \cos \,C = 4{\sin ^2}{A \o

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Match the conics in Column I with the statements/expressions in Column II :
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Let $$f$$ be a non-negative function defined on the interval $$[0,1]$$.
If $$\int\limits_0^x {\sqrt {1 - {{(f'(t))}^2}d

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Area of the region bounded by the curve $$y = {e^x}$$ and lines $$x=0$$ and $$y=e$$ is

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Match the statements/expressions in Column I with the open intervals in Column II :
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The probability that X = 3 equals

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The conditional probability that $$X\ge6$$ given $$X>3$$ equals :

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The probability that $$X\ge3$$ equals :

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If $$\overrightarrow a ,\overrightarrow b ,\overrightarrow c $$ and $$\overrightarrow d $$ are unit vectors such that $$

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Let $$P(3,2,6)$$ be a point in space and $$Q$$ be a point on the line
$$$\widehat r = \left( {\widehat i - \widehat j +

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Let $$L = \mathop {\lim }\limits_{x \to 0} {{a - \sqrt {{a^2} - {x^2}} - {{{x^2}} \over 4}} \over {{x^4}}},a > 0$$. If

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The number of matrices in A is

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The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{
x \cr
y \cr
z \

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The number of matrices A in A for which the system of linear equations $$A\left[ {\matrix{
x \cr
y \cr
z \

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## Physics

A block of base 10 cm × 10 cm and height 15 cm is kept on an inclined plane. The coefficient of friction
between them is

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Look at the drawing given in the figure below which has been drawn with ink of uniform line-thickness. The mass of ink u

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The figure shows certain wire segments joined together to form a coplanar loop. The loop is placed in a perpendicular ma

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Two small particles of equal masses start moving in opposite directions from a point A in a horizontal circular orbit. T

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A disk of radius $${a \over 4}$$ having a uniformly distributed charge 6C is placed in the xy-plane with its centre at (

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Three concentric metallic spherical shells of radii $$R,2R,3R$$ are given charges $$Q_1,Q_2,Q_3$$, respectively. It is f

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The $$x$$-$$t$$ graph of a particle undergoing simple harmonic motion is shown in the figure. The acceleration of the pa

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A ball is dropped from a height of 20 m above the surface of water in a lake. The refractive index of water is 4/3. A fi

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For the circuit shown in the figure

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$$C_V$$ and $$C_P$$ denote the molar specific heat capacities of a gas at constant volume and constant pressure, respect

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A student performed the experiment of determination of focal length of a concave mirror by $$u$$-$$v$$ method using an o

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If the resultant of all the external forces acting on a system of particles is zero, then from an inertial frame, one ca

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The allowed energy for the particle for a particular value of $$n$$ is proportional to

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If the mass of the particle is $$m=1.0\times10^{-30}$$ kg and $$a=6.6$$ nm, the energy of the particle in its ground sta

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The speed of the particle, that can take discrete values, is proportional to

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In the core of nuclear fusion reactor, the gas becomes plasma because of

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Assume that two deuteron nuclei in the core of fusion reactor at temperature T are moving towards each other, each with

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Results of calculations for four different designs of a fusion reactor using D-D reaction are given below. Which of thes

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Column II shows five systems in which two objects are labelled as X and Y. Also in each case a point P is shown. Column

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Six point charges, each of the same magnitude q, are arranged in different manners as shown in Column II. In each case,

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