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

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

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

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

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

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

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

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

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

View Question 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.

View Question 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

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

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

View Question 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$

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

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

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

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

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

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

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

View Question Synthesis of each molecule of glucose in photosynthesis involves:

View Question The order of stability of the following carbocations :

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

View Question Arrange the following compounds in order of decreasing acidity :

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

View Question ## Mathematics

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

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

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

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

View Question 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

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

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

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

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

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

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

View Question 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 :

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

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

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

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

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

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

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

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

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

View Question ## Physics

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

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

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

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

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

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

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

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

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

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

View Question 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

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

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

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

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

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

View Question 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

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

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

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

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

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

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

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

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

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

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

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

View Question