JEE Main 2014 (Offline)

Paper was held on
Sat, Apr 6, 2013 9:30 AM

## Chemistry

The correct set of four quantum numbers for the valence elections of rubidium atom (Z= 37) is:

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If Z is a compressibility factor, van der Waals equation at low pressure can be written as:

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The ratio of masses of oxygen and nitrogen in a particular gaseous mixture is 1 : 4. The ratio of number of
their molecu

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For complete combustion of ethanol, C2H5OH(l) + 3O2(g) $$\to$$ 2CO2(g) + 3H2O(l) the amount of heat
produced as measure

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For the reaction SO2 (g) + $${1 \over 2} O_2(g) \leftrightharpoons$$ SO3(g).
if KP = KC(RT)x where the symbols have us

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In which of the following reactions H2O2 acts as a reducing agent?
1. H2O2 + 2H+ + 2e- $$\to$$ 2H2O
2. H2O2 - 2e- $$\to$

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For the estimation of nitrogen, 1.4 g of organic compound was digested by Kjeldahl method and the
evolved ammonia was ab

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CsCl crystallises in body centred cubic lattice. If ‘a’ is its edge length then which of the following
expressions is co

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Consider separate solutions of 0.500 M C2H5OH(aq), 0.100 M Mg3(PO4)2(aq), 0.250 M KBr(aq) and 0.125
M Na3PO4(aq) at 25oC

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Resistance of 0.2 M solution of an electrolyte is 50 $$\Omega$$. The specific conductance of the solution is 1.4 S m-1.

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Given below are the half-cell reactions:
Mn2+ + 2e- $$\to$$ Mn; Eo = -1.18 V
2(Mn3+ + e- $$\to$$ Mn2+); Eo = +1.51 V
The

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The equivalent conductance of NaCl at concentration C and at infinite dilution are $${\lambda _C}$$ and $${\lambda _\in

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For the non – stoichiometre reaction 2A + B $$\to$$ C + D, the following kinetic data were obtained in three
separate ex

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The metal that cannot be obtained by electrolysis of an aqueous solution of its salts is :

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Among the following oxoacids, the correct decreasing order of acid strength is :

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Which one of the following properties is not shown by NO?

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The correct statement for the molecule, CsI3 is :

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Which series of reactions correctly represents chemical relations related to iron and its compound?

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The octahedral complex of a metal ion M3+ with four monodentate ligands L1, L2, L3 and L4 absorb wavelengths in the regi

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The equation which is balanced and represents the correct product(s) is :

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In SN2 reactions, the correct order of reactivity for the following compounds:
CH3Cl, CH3CH
2Cl, (CH3)2CHCl and (CH3)3CC

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The major organic compound formed by the reaction of 1, 1, 1– trichloroethane with silver powder is:

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In the reaction,
the product C is:

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The most suitable reagent for the conversion of R - CH2 - OH $$\to$$ R - CHO is:

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On heating an aliphatic primary amine with chloroform and ethanolic potassium hydroxide, the organic
compound formed is:

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Considering the basic strength of amines in aqueous solution, which one has the smallest pKb value?

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Which one is classified as a condensation polymer?

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Which one of the following bases is not present in DNA?

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Sodium phenoxide when heated with $$C{O_2}$$ under pressure at $${125^ \circ }C$$ yields a product which on acetylation

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## Mathematics

Let $$f_k\left( x \right) = {1 \over k}\left( {{{\sin }^k}x + {{\cos }^k}x} \right)$$ where $$x \in R$$ and $$k \ge \,1.

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If z is a complex number such that $$\,\left| z \right| \ge 2\,$$, then the minimum value of $$\,\,\left| {z + {1 \over

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If $$a \in R$$ and the equation $$ - 3{\left( {x - \left[ x \right]} \right)^2} + 2\left( {x - \left[ x \right]} \right)

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Let $$\alpha $$ and $$\beta $$ be the roots of equation $$p{x^2} + qx + r = 0,$$ $$p \ne 0.$$ If $$p,\,q,\,r$$ in A.P. a

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If the coefficints of $${x^3}$$ and $${x^4}$$ in the expansion of $$\left( {1 + ax + b{x^2}} \right){\left( {1 - 2x} \ri

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Three positive numbers form an increasing G.P. If the middle term in this G.P. is doubled, the new numbers are in A.P. t

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If $${(10)^9} + 2{(11)^1}\,({10^8}) + 3{(11)^2}\,{(10)^7} + ......... + 10{(11)^9} = k{(10)^9},$$, then k is equal to :

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Let $$PS$$ be the median of the triangle with vertices $$P(2, 2)$$, $$Q(6, -1)$$ and $$R(7, 3)$$. The equation of the li

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Let $$a, b, c$$ and $$d$$ be non-zero numbers. If the point of intersection of the lines $$4ax + 2ay + c = 0$$ and $$5bx

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Let $$C$$ be the circle with centre at $$(1, 1)$$ and radius $$=$$ $$1$$. If $$T$$ is the circle centred at $$(0, y)$$,

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The locus of the foot of perpendicular drawn from the centre of the ellipse $${x^2} + 3{y^2} = 6$$ on any tangent to it

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The slope of the line touching both the parabolas $${y^2} = 4x$$ and $${x^2} = - 32y$$ is

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If $$x=-1$$ and $$x=2$$ are extreme points of $$f\left( x \right) = \alpha \,\log \left| x \right|+\beta {x^2} + x$$ the

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If $$g$$ is the inverse of a function $$f$$ and $$f'\left( x \right) = {1 \over {1 + {x^5}}},$$ then $$g'\left( x \right

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A bird is sitting on the top of a vertical pole $$20$$ m high and its elevation from a point $$O$$ on the ground is $${4

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If $$f$$ and $$g$$ are differentiable functions in $$\left[ {0,1} \right]$$ satisfying
$$f\left( 0 \right) = 2 = g\left

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If $$\alpha ,\beta \ne 0,$$ and $$f\left( n \right) = {\alpha ^n} + {\beta ^n}$$ and
$$$\left| {\matrix{
3 & {1

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If $$A$$ is a $$3 \times 3$$ non-singular matrix such that $$AA'=A'A$$ and
$$B = {A^{ - 1}}A',$$ then $$BB'$$ equals:

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The integral $$\int {\left( {1 + x - {1 \over x}} \right){e^{x + {1 \over x}}}dx} $$ is equal to

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The area of the region described by
$$A = \left\{ {\left( {x,y} \right):{x^2} + {y^2} \le 1} \right.$$ and $$\left. {{y

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The integral $$\int\limits_0^\pi {\sqrt {1 + 4{{\sin }^2}{x \over 2} - 4\sin {x \over 2}{\mkern 1mu} } } dx$$ equals:

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Let the population of rabbits surviving at time $$t$$ be governed by the differential equation $${{dp\left( t \right)}

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Let $$A$$ and $$B$$ be two events such that $$P\left( {\overline {A \cup B} } \right) = {1 \over 6},\,P\left( { {A \cap

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The image of the line $${{x - 1} \over 3} = {{y - 3} \over 1} = {{z - 4} \over { - 5}}\,$$ in the plane $$2x-y+z+3=0$$ i

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The angle between the lines whose direction cosines satisfy the equations $$l+m+n=0$$ and $${l^2} = {m^2} + {n^2}$$ is :

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If $$\left[ {\overrightarrow a \times \overrightarrow b \,\,\,\,\overrightarrow b \times \overrightarrow c \,\,\,\,\ov

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$$\mathop {\lim }\limits_{x \to 0} {{\sin \left( {\pi {{\cos }^2}x} \right)} \over {{x^2}}}$$ is equal to :

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The statement $$ \sim \left( {p \leftrightarrow \sim q} \right)$$ is :

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The variance of first 50 even natural numbers is

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## Physics

A student measured the length of a rod and wrote it as 3.50 cm. Which instrument did he use to measure it?

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From a tower of height H, a particle is thrown vertically upwards with a speed u. The time taken by the
particle, to hit

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A block of mass $$m$$ is placed on a surface with a vertical cross section given by $$y = {{{x^3}} \over 6}.$$ If the co

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When a rubber-band is stretched by a distance $$x$$, it exerts restoring force of magnitude $$F = ax + b{x^2}$$ where $$

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A bob of mass $$m$$ attached to an inextensible string of length $$l$$ is suspended from a vertical support. The bob rot

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Four particles, each of mass $$M$$ and equidistant from each other, move along a circle of radius $$R$$ under the action

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An open glass tube is immersed in mercury in such a way that a length of $$8$$ $$cm$$ extends above the mercury level. T

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A mass $$'m'$$ is supported by a massless string wound around a uniform hollow cylinder of mass $$m$$ and radius $$R.$$

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The pressure that has to be applied to the ends of a steel wire of length $$10$$ $$cm$$ to keep its length constant when

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Three rods of Copper, Brass and Steel are welded together to form a $$Y$$ shaped structure. Area of cross - section of e

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On heating water, bubbles being formed at the bottom of the vessel detach and rise. Take the bubbles to be spheres of ra

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One mole of a diatomic ideal gas undergoes a cyclic process $$ABC$$ as shown in figure. The process $$BC$$ is adiabatic.

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There is a circular tube in a vertical plane. Two liquids which do not mix and of densities $${d_1}$$ and $${d_2}$$ are

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A particle moves with simple harmonic motion in a straight line. In first $$\tau s,$$ after starting from rest it travel

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A pipe of length $$85$$ $$cm$$ is closed from one end. Find the number of possible natural oscillations of air column in

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Assume that an electric field $$\overrightarrow E = 30{x^2}\widehat i$$ exists in space. Then the potential difference

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A parallel plate capacitor is made of two circular plates separated by a distance $$5$$ $$mm$$ and with a dielectric of

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In a large building, three are $$15$$ bulbs of $$40$$ $$W$$, $$5$$ bulbs of $$100$$ $$W$$, $$5$$ fans of $$80$$ $$W$$ an

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The coercivity of a small magnet where the ferromagnet gets demagnetized is $$3 \times {10^3}\,A{m^{ - 1}}.$$ The curren

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A conductor lies along the $$z$$-axis at $$ - 1.5 \le z < 1.5\,m$$ and carries a fixed current of $$10.0$$ $$A$$ in $

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A thin convex lens made from crown glass $$\left( {\mu = {3 \over 2}} \right)$$ has focal length $$f$$. When it is meas

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Two beams, $$A$$ and $$B$$, of plane polarized light with mutually perpendicular planes of polarization are seen through

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A green light is incident from the water to the air - water interface at the critical angle $$\left( \theta \right)$$.

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In the circuit shown here, the point $$'C'$$ is kept connected to point $$'A'$$ till the current flowing through the ci

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The current voltage relation of diode is given by $${\rm I} = \left( {{e^{100V/T}} - 1} \right)mA,$$ where the applied v

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During the propagation of electromagnetic waves in a medium:

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The radiation corresponding to $$3 \to 2$$ transition of hydrogen atom falls on a metal surface to produce photoelectron

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Hydrogen $$\left( {{}_1{H^1}} \right)$$, Deuterium $$\left( {{}_1{H^2}} \right)$$, singly ionised Helium $${\left( {{}_2

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Match List - $$1$$ (Electromagnetic wave type ) with List - $$2$$ (Its association/application) and select the correct

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The forward biased diode connection is:

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