JEE Main 2015 (Offline)

Paper was held on
Sat, Apr 4, 2015 9:30 AM

## Chemistry

Which of the following is the energy of a possible excited state of hydrogen?

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The ionic radii (in Å) of N3–, O2– and F– are respectively:

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The intermolecular interaction that is dependent on the inverse cube of distance between the molecule is:

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The standard Gibbs energy change at 300 K for the reaction 2A $$\leftrightharpoons$$ B + C is 2494.2 J. At a given time,

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The following reaction is performed at 298 K
2NO(g) + O2 (g) $$\leftrightharpoons$$ 2NO2 (g)
The standard free energy

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The molecular formula of a commercial resin used for exchanging ions in water softening is
C8H7SO3Na (Mol. Wt. 206). Wha

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Which one of the following alkaline earth metal sulphates has its hydration enthalpy greater than its lattice
enthalpy?

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From the following statements regarding H2O2, choose the incorrect statement :

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In Carius method of estimation of halogens, 250 mg of an organic compound gave 141 mg of AgBr. The
percentage of bromine

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Which of the following compounds will exhibit geometrical isomerism?

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Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å . The radius of
sodium atom is

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3 g of activated charcoal was added to 50 mL of acetic acid solution (0.06N) in a flask. After an hour it was
filtered a

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The vapour pressure of acetone at 20oC is 185 torr. When 1.2 g of a non-volatile substance was dissolved in
100 g of ace

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Two Faraday of electricity is passed through a solution of CuSO4. The mass of copper deposited at the
cathode is: (at. m

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Higher order (>3) reactions are rare due to

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In the context of the Hall-Heroult process for the extraction of Al, which of the following statements is
false?

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Which among the following is the most reactive?

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Which one has the highest boiling point?

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Assertion : Nitrogen and Oxygen are the main components in the atmosphere but these do not react to
form oxides of nitro

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Which of the following compounds is not colored yellow?

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The colour of KMnO4 is due to :

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The number of geometric isomers that can exist for square planar [Pt (Cl) (py) (NH3) (NH2OH)]+ is (py = pyridine) :

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The synthesis of alkyl fluorides is best accomplished by:

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In the following sequence of reactions:
The product C is

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Which of the vitamins given below is water soluble?

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Which polymer is used in the manufacture of paints and lacquers?

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Which of the following compounds is not an antacid?

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Which compound would give $$5$$ - keto - $$2$$ - methylhexanal upon ozonolysis?

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In the reaction
The product $$E$$ is :

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Match the catalysts to the correct processes :
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## Mathematics

A complex number z is said to be unimodular if $$\,\left| z \right| = 1$$. Suppose $${z_1}$$ and $${z_2}$$ are complex n

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Let $$\alpha $$ and $$\beta $$ be the roots of equation $${x^2} - 6x - 2 = 0$$. If $${a_n} = {\alpha ^n} - {\beta ^n},$$

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The number of integers greater than 6,000 that can be formed, using the digits 3, 5, 6, 7 and 8, without repetition, is:

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The sum of coefficients of integral power of $$x$$ in the binomial expansion $${\left( {1 - 2\sqrt x } \right)^{50}}$$ i

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The sum of first 9 terms of the series.
$${{{1^3}} \over 1} + {{{1^3} + {2^3}} \over {1 + 3}} + {{{1^3} + {2^3} + {3^3}

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If m is the A.M. of two distinct real numbers l and n $$(l,n > 1)$$ and $${G_1},{G_2}$$ and $${G_3}$$ are three geome

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The number of points, having both co-ordinates as integers, that lie in the interior of the triangle with vertices $$(0,

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Locus of the image of the point $$(2, 3)$$ in the line $$\left( {2x - 3y + 4} \right) + k\left( {x - 2y + 3} \right) = 0

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The number of common tangents to the circles $${x^2} + {y^2} - 4x - 6x - 12 = 0$$ and $${x^2} + {y^2} + 6x + 18y + 26 =

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The normal to the curve, $${x^2} + 2xy - 3{y^2} = 0$$, at $$(1,1)$$

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Let $$O$$ be the vertex and $$Q$$ be any point on the parabola, $${{x^2} = 8y}$$. If the point $$P$$ divides the line se

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The area (in sq. units) of the quadrilateral formed by the tangents at the end points of the latera recta to the ellipse

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If the angles of elevation of the top of a tower from three collinear points $$A, B$$ and $$C,$$ on a line leading to th

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Let $${\tan ^{ - 1}}y = {\tan ^{ - 1}}x + {\tan ^{ - 1}}\left( {{{2x} \over {1 - {x^2}}}} \right),$$
where $$\left| x

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Let $$f(x)$$ be a polynomial of degree four having extreme values
at $$x=1$$ and $$x=2$$. If $$\mathop {\lim }\limits_{

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The set of all values of $$\lambda $$ for which the system of linear equations:
$$\matrix{
{2{x_1} - 2{x_2} + {x_3} =

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If $$A = \left[ {\matrix{
1 & 2 & 2 \cr
2 & 1 & { - 2} \cr
a & 2 & b \cr
} } \r

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The integral $$\int {{{dx} \over {{x^2}{{\left( {{x^4} + 1} \right)}^{3/4}}}}} $$ equals :

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The integral
$$\int\limits_2^4 {{{\log \,{x^2}} \over {\log {x^2} + \log \left( {36 - 12x + {x^2}} \right)}}dx} $$ is

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The area (in sq. units) of the region described by
$$\left\{ {\left( {x,y} \right):{y^2} \le 2x} \right.$$ and $$\left.

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Let $$y(x)$$ be the solution of the differential equation
$$\left( {x\,\log x} \right){{dy} \over {dx}} + y = 2x\,\log

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If $$12$$ different balls are to be placed in $$3$$ identical boxes, then the probability that one of the boxes contains

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Let $$\overrightarrow a ,\overrightarrow b $$ and $$\overrightarrow c $$ be three non-zero vectors such that no two of t

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The equation of the plane containing the line $$2x-5y+z=3; x+y+4z=5,$$ and parallel to the plane, $$x+3y+6z=1,$$ is :

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The distance of the point $$(1, 0, 2)$$ from the point of intersection of the line $${{x - 2} \over 3} = {{y + 1} \over

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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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The negation of $$ \sim s \vee \left( { \sim r \wedge s} \right)$$ is equivalent to :

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The mean of the data set comprising of 16 observations is 16. If one of the observation valued 16 is deleted
and three n

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If the function.
$$g\left( x \right) = \left\{ {\matrix{
{k\sqrt {x + 1} ,} & {0 \le x \le 3} \cr
{m\,x + 2,

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Let A and B be two sets containing four and
two elements respectively. Then, the number
of subsets of the set A $\times$

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## Physics

The period of oscillation of a simple pendulum is $$T = 2\pi \sqrt {{L \over g}} $$. Measured value of L is 20.0 cm kno

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A particle of mass $$m$$ moving in the $$x$$ direction with speed $$2v$$ is hit by another particle of mass $$2m$$ movi

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Distance of the center of mass of a solid uniform cone from its vertex is $$z{}_0$$. If the radius of its base is $$R$$

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From a solid sphere of mass $$M$$ and radius $$R$$ a cube of maximum possible volume is cut. Moment of inertia of cube a

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Given in the figure are two blocks $$A$$ and $$B$$ of weight 20 N and 100 N, respectively. These are being pressed again

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A solid body of constant heat capacity $$1$$ $$J/{}^ \circ C$$ is being heated by keeping it in contact with reservoirs

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Consider an ideal gas confined in an isolated closed chamber. As the gas undergoes an adiabatic expansion, the average t

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Consider a spherical shell of radius $$R$$ at temperature $$T$$. The black body radiation inside it can be considered as

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From a solid sphere of mass $$M$$ and radius $$R,$$ a spherical portion of radius $$R/2$$ is removed, as shown in the fi

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A pendulum made of a uniform wire of cross sectional area $$A$$ has time period $$T.$$ When an additional mass $$M$$ is

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For a simple pendulum, a graph is plotted between its kinetic energy $$(KE)$$ and potential energy $$(PE)$$ against its

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A train is moving on a straight track with speed $$20\,m{s^{ - 1}}.$$ It is blowing its whistle at the frequency of $$10

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In the given circuit, charges $${Q_2}$$ on the $$2\mu F$$ capacitor changes as $$C$$ is varied from $$1\,\mu F$$ to $$3\

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A uniformly charged solid sphere of radius $$R$$ has potential $${V_0}$$ (measured with respect to $$\infty $$) on its s

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A long cylindrical shell carries positives surfaces change $$\sigma $$ in the upper half and negative surface charge - $

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When $$5V$$ potential difference is applied across a wire of length $$0.1$$ $$m,$$ the drift speed of electrons is $$2.5

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In the circuit shown, the current in the $$1\Omega $$ resistor is :

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Two long current carrying thin wires, both with current $$I,$$ are held by insulating threads of length $$L$$ and are in

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A rectangular loop of sides $$10$$ $$cm$$ and $$5$$ $$cm$$ carrying a current $$1$$ of $$12A$$ is placed in different or

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Two coaxial solenoids of different radius carry current $$I$$ in the same direction. $$\overrightarrow {{F_1}} $$ be the

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On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the grou

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Assuming human pupil to have a radius of $$0.25$$ $$cm$$ and a comfortable viewing distance of $$25$$ $$cm$$, the minimu

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An $$LCR$$ circuit is equivalent to a damped pendulum. In an $$LCR$$ circuit the capacitor is charged to $${Q_0}$$ and t

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An inductor $$(L=0.03$$ $$H)$$ and a resistor $$\left( {R = 0.15\,k\Omega } \right)$$ are connected in series to a batte

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Monochromatic light is incident on a glass prism of angle $$A$$. If the refractive index of the material of the prism is

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A red $$LED$$ emits light at $$0.1$$ watt uniformly around it. The amplitude of the electric field of the light at a dis

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A signal of $$5$$ $$kHz$$ frequency is amplitude modulated on a carrier wave of frequency $$2$$ $$MHz.$$ The frequencies

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As an electron makes a transition from an excited state to the ground state of a hydrogen - like atom/ion :

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Match List - $${\rm I}$$ (Fundamental Experiment) with List - $${\rm II}$$ (its conclusion) and select the correct optio

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Two stones are thrown up simultaneously from the edge of a cliff $$240$$ $$m$$ high with initial speed of $$10$$ $$m/s$$

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