JEE Main 2013 (Offline)

Paper was held on
Sun, Apr 7, 2013 9:30 AM

## Chemistry

Consider the following reaction:
$$xMnO_4^- + yC_2O_4^{2-}$$ + zH+ $$\to$$ xMn2+ + 2yCO2 + $${z \over 2}{H_2}O$$
The val

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A gaseous hydrocarbon gives upon combustion 0.72 g of water and 3.08 g of CO2. The empirical formula of the hydrocarbon

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Experimentally it was found that a metal oxide has formula M0.98O. Metal M, present as M2+ and M3+ in its oxide. Fractio

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Energy of an electron is given by $$E = - 2.178 \times {10^{ - 18}}J\left( {{{{Z^2}} \over {{n^2}}}} \right)$$. Wavelen

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Which of the following represents the correct order of increasing first ionization enthalpy for Ca, Ba, S, Se
and Ar?

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The first ionization potential of Na is 5.1 eV. The value of electron gain enthalpy of Na+
will be:

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Which one of the following molecules is expected to exhibit diamagnetic behaviour?

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Which of the following is the wrong statement?

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In which of the following pairs of molecules/ions, both the species are not likely to exist?

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Stability of the species Li2, $$Li_2^−$$ and $$Li_2^+$$ increases in the order of:

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For gaseous state, if most probable speed is denoted by C*, average speed by $$\mathop C\limits^{\_\_} $$ and mean squa

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A piston filled with 0.04 mol of an ideal gas expands reversibly from 50.0 mL to 375 mL at a constant
temperature of 37.

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How many litres of water must be added to 1 litre of an aqueous solution of HCl with a pH of 1 to create an
aqueous solu

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A solution of (–$$l$$) – chloro –1 – phenylethane in toluene racemises slowly in the presence of a small
amount of SbCl5

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Which of the following exists as covalent crystals in the solid state?

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The coagulating power of electrolytes having ions Na+, Al3+ and Ba2+ for arsenic sulphide sol increases in the order:

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The molarity of a solution obtained by mixing 750 mL of 0.5 (M) HCl with 250 mL of 2(M) HCl will be:

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Given
$$E_{C{r^{2 + }}/Cr}^o$$ = -0.74 V; $$E_{MnO_4^ - /M{n^{2 + }}}^o$$ = 1.51 V
$$E_{C{r_2}O_7^{2 - }/C{r^{3 + }}}^o$

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The rate of a reaction doubles when its temperature changes from 300K to 310K. Activation energy of such
a reaction will

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Which of the following arrangements does not represent the correct order of the property stated against it?

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Four successive members of the first row transition elements are listed below with atomic numbers. Which
one of them is

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Which of the following complex species is not expected to exhibit optical isomerism?

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An unknown alcohol is treated with the “Lucas reagent” to determine whether the alcohol is primary,
secondary or tertiar

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A compound with molecular mass 180 is acylated with CH3COCl to get a compound with molecular mass
390. The number of ami

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The gas leaked from a storage tank of the Union Carbide plant in Bhopal gas tragedy was:

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Synthesis of each molecule of glucose in photosynthesis involves:

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The order of stability of the following carbocations :

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Compound $$\left( A \right),\,{C_8}{H_9}Br,\,\,\,$$ gives a white precipitate when warmed with alcoholic $$AgN{O_3}.$$

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Arrange the following compounds in order of decreasing acidity :

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An organic compound A upon reacting with $$N{H_3}$$ gives $$B.$$ On heating $$B$$ gives $$C.$$ $$C$$ in presence of $$KO

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## Mathematics

The expression $${{\tan {\rm A}} \over {1 - \cot {\rm A}}} + {{\cot {\rm A}} \over {1 - \tan {\rm A}}}$$ can be written

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$$ABCD$$ is a trapezium such that $$AB$$ and $$CD$$ are parallel and $$BC \bot CD.$$ If $$\angle ADB = \theta ,\,BC = p$

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If z is a complex number of unit modulus and argument $$\theta $$, then arg $$\left( {{{1 + z} \over {1 + \overline z }}

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The number of values of $$k$$, for which the system of equations : $$$\matrix{
{\left( {k + 1} \right)x + 8y = 4k} \

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The real number $$k$$ for which the equation, $$2{x^3} + 3x + k = 0$$ has two distinct real roots in $$\left[ {0,\,1} \r

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If the equations $${x^2} + 2x + 3 = 0$$ and $$a{x^2} + bx + c = 0,$$ $$a,\,b,\,c\, \in \,R,$$ have a common root, then

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Let $${T_n}$$ be the number of all possible triangles formed by joining vertices of an n-sided regular polygon. If $${T_

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The term independent of $$x$$ in expansion of
$${\left( {{{x + 1} \over {{x^{2/3}} - {x^{1/3}} + 1}} - {{x - 1} \over

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The sum of first 20 terms of the sequence 0.7, 0.77, 0.777,........,is

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A ray of light along $$x + \sqrt 3 y = \sqrt 3 $$ gets reflected upon reaching $$X$$-axis, the equation of the reflected

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The $$x$$-coordinate of the incentre of the triangle that has the coordinates of mid points of its sides as $$(0, 1) (1,

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The circle passing through $$(1, -2)$$ and touching the axis of $$x$$ at $$(3, 0)$$ also passes through the point :

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The equation of the circle passing through the foci of the ellipse $${{{x^2}} \over {16}} + {{{y^2}} \over 9} = 1$$, and

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Given : A circle, $$2{x^2} + 2{y^2} = 5$$ and a parabola, $${y^2} = 4\sqrt 5 x$$.
Statement-1 : An equation of a common

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If $$y = \sec \left( {{{\tan }^{ - 1}}x} \right),$$ then $${{{dy} \over {dx}}}$$ at $$x=1$$ is equal to :

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If $$x, y, z$$ are in A.P. and $${\tan ^{ - 1}}x,{\tan ^{ - 1}}y$$ and $${\tan ^{ - 1}}z$$ are also in A.P., then :

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The intercepts on $$x$$-axis made by tangents to the curve,
$$y = \int\limits_0^x {\left| t \right|dt,x \in R,} $$ whic

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If $$P = \left[ {\matrix{
1 & \alpha & 3 \cr
1 & 3 & 3 \cr
2 & 4 & 4 \cr
} } \

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If $$\int {f\left( x \right)dx = \psi \left( x \right),} $$ then $$\int {{x^5}f\left( {{x^3}} \right)dx} $$ is equal to

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Statement-1 : The value of the integral
$$\int\limits_{\pi /6}^{\pi /3} {{{dx} \over {1 + \sqrt {\tan \,x} }}} $$ is eq

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The area (in square units) bounded by the curves $$y = \sqrt {x,} $$ $$2y - x + 3 = 0,$$ $$x$$-axis, and lying in the f

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At present, a firm is manufacturing $$2000$$ items. It is estimated that the rate of change of production P w.r.t. add

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A multiple choice examination has $$5$$ questions. Each question has three alternative answers of which exactly one is c

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Distance between two parallel planes $$2x+y+2z=8$$ and $$4x+2y+4z+5=0$$ is :

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If the lines $${{x - 2} \over 1} = {{y - 3} \over 1} = {{z - 4} \over { - k}}$$ and $${{x - 1} \over k} = {{y - 4} \over

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If the vectors $$\overrightarrow {AB} = 3\widehat i + 4\widehat k$$ and $$\overrightarrow {AC} = 5\widehat i - 2\wideh

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$$\mathop {\lim }\limits_{x \to 0} {{\left( {1 - \cos 2x} \right)\left( {3 + \cos x} \right)} \over {x\tan 4x}}$$ is equ

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Consider :
Statement − I : $$\left( {p \wedge \sim q} \right) \wedge \left( { \sim p \wedge q} \right)$$ is a fallacy.

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All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10
to each of th

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Let A and B be two sets containing 2 elements and
4 elements respectively. The number of subsets of
A $$ \times $$ B hav

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## Physics

Let [$${\varepsilon _0}$$] denote the dimensional formula of the permittivity of vacuum. If M = mass, L = length, T = ti

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A projectile is given an initial velocity of $$\left( {\widehat i + 2\widehat j} \right)$$ m/s, where $${\widehat i}$$ i

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This question has statement $${\rm I}$$ and statement $${\rm I}$$$${\rm I}$$. Of the four choices given after the statem

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A hoop of radius $$r$$ and mass $$m$$ rotating with an angular velocity $${\omega _0}$$ is placed on a rough horizontal

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What is the minimum energy required to launch a satellite of mass $$m$$ from the surface of a planet of mass $$M$$ and r

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A uniform cylinder of length $$L$$ and mass $$M$$ having cross-sectional area $$A$$ is suspended, with its length vertic

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Assume that a drop of liquid evaporates by decreases in its surface energy, so that its temperature remains unchanged. W

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The above $$p$$-$$v$$ diagram represents the thermodynamic cycle of an engine, operating with an ideal monatomic gas.

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If a piece of metal is heated to temperature $$\theta $$ and then allowed to cool in a room which is at temperature $${\

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An ideal gas enclosed in a vertical cylindrical container supports a freely moving piston of mass $$M.$$ The piston and

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The amplitude of a damped oscillator decreases to $$0.9$$ times its original magnitude in $$5s$$. In another $$10s$$ it

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A sonometer wire of length $$1.5$$ $$m$$ is made of steel. The tension in it produces an elastic strain of $$1\% $$. Wh

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Two charges, each equals to $$q,$$ are kept at $$x=-a$$ and $$x=a$$ on the $$x$$-axis. A particle of mass $$m$$ and char

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Two capacitors $${C_1}$$ and $${C_2}$$ are charged to $$120$$ $$V$$ and $$200$$ $$V$$ respectively. It is found that con

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A charge $$Q$$ is uniformly distributed over a long rod $$AB$$ of length $$L$$ as shown in the figure. The electric pote

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The supply voltage to room is $$120V.$$ The resistance of the lead wires is $$6\Omega $$. A $$60$$ $$W$$ bulb is already

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This questions has Statement - $${\rm I}$$ and Statement - $${\rm I}$$$${\rm I}$$. Of the four choices given after the S

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Two short bar magnets of length $$1$$ $$cm$$ each have magnetic moments $$1.20$$ $$A{m^2}$$ and $$1.00$$ $$A{m^2}$$ res

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A circular loop of radius $$0.3$$ $$cm$$ lies center of the small loop is on the axis of the bigger loop. The distance b

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Diameter of a plano-convex lens is $$6$$ $$cm$$ and thickness at the center is $$3mm$$. If speed of light in material of

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A beam of unpolarised light of intensity $${{\rm I}_0}$$ is passed through a polaroid $$A$$ and then through another pol

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A metallic rod of length $$'\ell '$$ is tied to a string of length $$2$$$$\ell $$ and made to rotate with angular speed

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In an $$LCR$$ circuit as shown below both switches are open initially. Now switch $${S_1}$$ is closed, $${S_2}$$ kept op

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Two coherent point sources $${S_1}$$ and $${S_2}$$ are separated by a small distance $$'d'$$ as shown. The fringes obtai

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The graph between angle of deviation $$\left( \delta \right)$$ and angle of incidence $$(i)$$ for a triangular prism is

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A diode detector is used to detect an amplitude modulated wave of $$60\% $$ modulation by using a condenser of capacity

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The magnetic field in a travelling electromagnetic wave has a peak value of $$20$$ $$n$$$$T$$. The peak value of electri

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In a hydrogen like atom electron make transition from an energy level with quantum number $$n$$ to another with quantum

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The anode voltage of a photocell is kept fixed. The wavelength $$\lambda $$ of the light falling on the cathode is gradu

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The $${\rm I}$$-$$V$$ characteristic of an $$LED$$ is

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