JEE Advanced 2013 Paper 1 Offline

Paper was held on
Sat, Jun 1, 2013 9:00 PM

## Chemistry

The atomic masses of He and Ne are 4 and 20 a.m.u., respectively. The value of the de Broglie wavelength
of He gas at –7

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The total number of lone-pairs of electrons in melamine is

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The standard enthalpies of formation of CO2(g), H2O(l) and glucose(s) at 25oC are –400 kJ/mol,
–300 kJ/mol and –1300 kJ/

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The initial rate of hydrolysis of methyl acetate (1M) by a weak acid (HA, 1M) is 1/100th of that of a strong acid (HX, 1

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The hyperconjugative stabilities of tert-butyl cation and 2-butene, respectively, are due to

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Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 25oC. For this process, the
correct stat

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Benzene and naphthalene form an ideal solution at room temperature. For this process, the true statement(s)
is(are)

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Sulphide ores are common for the metals

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KI in acetone undergoes SN2 reaction with each of P, Q, R and S. The rates of the reaction vary as

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The compound that does NOT liberate CO2, on treatment with aqueous sodium bicarbonate solution, is

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Consider the following complex ions : P, Q and R.
$$P = {[Fe{F_6}]^{3 - }}$$, $$Q = {[V{({H_2}O)_6}]^{2 + }}$$ and $$R =

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In the reaction, P + Q $$\to$$ R + S, the time taken for 75% reaction of P is twice the time taken for 50% reaction of P

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Concentrated nitric acid, upon long standing, turns yellow-brown due to the formation of

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The arrangement of X$$-$$ ions around A+ ion in solid AX is given in the figure (not drawn to scale). If the radius of X

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Upon treatment with ammoniacal H2S, the metal ion that precipitates as a sulphide is

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The pair(s) of coordination complexes/ions exhibiting the same kind of isomerism is(are)

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Among P, Q, R and S, the aromatic compound(s) is(are)

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The total number of carboxylic acid groups is the product P is _________.

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EDTA4$$-$$ is ethylenediaminetetraacetate ion. The total number of N$$-$$Co$$-$$O bond angles in [Co(EDTA)]1$$-$$ comple

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A tetrapeptide has $$-$$COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine (Phe) and alani

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## Mathematics

Let complex numbers $$\alpha \,and\,{1 \over {\overline \alpha }}\,$$ lie on circles $${\left( {x - {x_0}} \right)^2} +

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Let $$f\left( x \right) = x\sin \,\pi x,\,x > 0.$$ Then for all natural numbers $$n,\,f'\left( x \right)$$ vanishes a

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The number of points in $$\left( { - \infty \,\infty } \right),$$ for which $${x^2} - x\sin x - \cos x = 0,$$ is

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The coefficient of three consecutive terms of $${\left( {1 + x} \right)^{n + 5}}$$ are in the ratio $$5:10:14.$$ Then $

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Consider the set of eight vectors $$V = \left\{ {a\,\hat i + b\,\hat j + c\hat k:a,\,b,\,c\, \in \left\{ { - 1,\,1} \rig

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Let $${S_n} = {\sum\limits_{k = 1}^{4n} {\left( { - 1} \right)} ^{{{k\left( {k + 1} \right)} \over 2}}}{k^2}.$$ Then $${

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A pack contains n cards numbered from 1 to n. Two consecutive numbered cards are removed from the pack and the sum of th

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For $$a > b > c > 0,$$ the distance between $$(1, 1)$$ and the point of intersection of the lines $$ax + by + c

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A vertical line passing through the point $$(h,0)$$ intersects the ellipse $${{{x^2}} \over 4} + {{{y^2}} \over 3} = 1$$

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The value of $$\cot \left( {\sum\limits_{n = 1}^{23} {{{\cot }^{ - 1}}} \left( {1 + \sum\limits_{k = 1}^n {2k} } \right)

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A rectangular sheet of fixed perimeter with sides having their lengths in the ratio $$8:15$$ is converted into an open r

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For 3 × 3 matrices M and N, which of the following statement(s)
is(are) NOT correct?

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The area enclosed by the curves $$y = \sin x + {\mathop{\rm cosx}\nolimits} $$ and $$y = \left| {\cos x - \sin x} \right

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Let $$f$$ $$:\,\,\left[ {{1 \over 2},1} \right] \to R$$ (the set of all real number) be a positive,
non-constant and di

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A curve passes through the point $$\left( {1,{\pi \over 6}} \right)$$. Let the slope of
the curve at each point $$(x,y

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Four persons independently solve a certain problem correctly with probabilities $${1 \over 2},{3 \over 4},{1 \over 4},{1

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Of the three independent events $${E_1},{E_2}$$ and $${E_3},$$ the probability that only $${E_1}$$ occurs is $$\alpha ,$

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A line $$l$$ passing through the origin is perpendicular to the lines
$$$\,{l_1}:\left( {3 + t} \right)\widehat i + \le

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Consider the set of eight vectors
$$V = \left\{ {a\widehat i + b\widehat j + c\widehat k:a,b.c \in \left\{ { - 1,1} \ri

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A pack contains $$n$$ cards numbered from $$1$$ to $$n.$$ Two consecutive numbered cards are removed from the pack and t

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## Physics

The diameter of a cylinder is measured using a Vernier callipers with no zero error. It is found that the zero
of the Ve

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The image of an object, formed by a plano-convex lens at a distance of 8 m behind the lens, is real and is
one-third the

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The work done on a particle of mass m by a force
$$$K\left[ {{x \over {{{\left( {{x^2} + {y^2}} \right)}^{3/2}}}}\wideha

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A particle of mass 0.2 kg is moving in one dimension under a force that delivers a constant power 0.5 W to
the particle.

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A particle of mass m is projected from the ground with an initial speed u0 at an angle $$\alpha $$ with the horizontal.

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A bob of mass m, suspended by a string of length l1 is given a minimum velocity required to complete a full circle in th

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A uniform circular disc of mass 50 kg and radius 0.4 m is rotating with an angular velocity of 10 rad s-1
about its own

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One end of a horizontal thick copper wire of length 2L and radius 2R is welded to an end of another
horizontal thin copp

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A solid sphere of radius R and density $$\rho $$ is attached to one end of a mass-less spring of force constant k.
The o

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Two non-reactive monoatomic ideal gases have their atomic masses in the ratio 2 : 3. The ratio of their
partial pressure

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Two non-conducting solid spheres of radii $$R$$ and $$2R,$$ having uniform volume charge densities $${\rho _1}$$ and $${

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In the circuit shown in the figure, there are two parallel plate capacitors each of capacitance $$C.$$ The switch $${S_1

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A ray of light travelling in the direction $${1 \over 2}\left( {\widehat i + \sqrt 3 \widehat j} \right)$$ is incident o

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Two rectangular blocks, having identical dimensions, can be arranged in either configuration-I or configuration-II as sh

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A pulse of light of duration 100 ns is absorbed completely by a small object initially at rest. Power of the pulse is 30

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In the Young's double-slit experiment using a monochromatic light of wavelength $$\lambda$$, the path difference (in ter

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A horizontal stretched string, fixed at two ends, is vibrating in its fifth harmonic according to the equation
y(x, t) =

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A particle of mass M and positive charge Q, moving with a constant velocity $${\overrightarrow u _1} = 4\widehat i$$ ms$

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The work functions of silver and sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the stopping potenti

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A freshly prepared sample of a radioisotope of half-life 1386 s has activity 103 disintegrations per second. Given that

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