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QUESTION: 1

**SECTION – 1: (Only one option correct Type)**

**This section contains 10 multiple choice questions. Each question has four choice (A), (B), (C) and (D) out of which ONLY ONE is correct.**

**Q. 1 - 10 carry 2 marks each.**

**Q.**

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

horizontal thin copper wire of length L and radius R. When the arrangement is stretched by applying forces

at two ends, the ratio of the elongation in the thin wire to that in the thick wire is

Solution:

QUESTION: 2

The work done on a particle of mass m by a force (K being a constant of appropriate dimensions, when the particle is taken from the point (a, 0) to the point (0, a) along a circular

path of radius a about the origin in the x-y plane is

Solution:

QUESTION: 3

Two rectangular blocks, having identical dimensions, can be arranged either in configuration I or in configuration II as shown in the figure. One of the blocks has thermal conductivity k and the other 2k . The temperature difference between the ends along the x-axis is the same in both the configurations. It takes 9 s to transport a certain amount of heat from the hot end to the cold end in the configuration I. The time to transport the same amount of heat in the configuration II is

Solution:

QUESTION: 4

A ray of light travelling in the direction is incident on a plane mirror. After reflection, it travels

along the direction The angle of incidence is

Solution:

Let angle between the directions of incident ray and reflected ray be θ

QUESTION: 5

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

of the Vernier scale lies between 5.10 cm and 5.15 cm of the main scale. The Vernier scale has 50 divisions

equivalent to 2.45 cm. The 24th division of the Vernier scale exactly coincides with one of the main scale

divisions. The diameter of the cylinder is

Solution:

QUESTION: 6

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

partial pressures, when enclosed in a vessel kept at a constant temperature, is 4 : 3. The ratio of their

densities is

Solution:

Here ρ1 and ρ2 are the densities of gases in the vessel containing the mixture

QUESTION: 7

In the Young’s double slit experiment using a monochromatic light of wavelength λ, the path difference (in

terms of an integer n) corresponding to any point having half the peak intensity is

Solution:

QUESTION: 8

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 size of the object. The wavelength of light inside the lens is 2/3 times the wavelength in free

space. The radius of the curved surface of the lens is

Solution:

QUESTION: 9

A particle of mass m is projected from the ground with an initial speed u_{0} at an angle α with the horizontal.

At the highest point of its trajectory, it makes a completely inelastic collision with another identical

particle, which was thrown vertically upward from the ground with the same initial speed u_{0}. The angle that

the composite system makes with the horizontal immediately after the collision is

Solution:

Velocity of particle performing projectile motion at highest point

= v_{1} = v_{0}cos α

Velocity of particle thrown vertically upwards at the position of collision

QUESTION: 10

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

pulse is 30 mW and the speed of light is 3 x 10^{8} m/s. The final momentum of the object is

Solution:

*Multiple options can be correct

QUESTION: 11

**SECTION – 2 : (One or more options correct Type)**

**This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.**

**Q. No. 11 -15 carry 4 marks each and 1 mark is deducted for incorrect answer**

**Q.**

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

S_{1} is pressed first to fully charge the capacitor C_{1} and then released. The switch S_{2} is then pressed to charge

the capacitor C_{2}. After some time, S_{2} is released and then S_{3} is pressed. After some time,

Solution:

After switch S_{1} is closed, C_{1} is charged by 2CV_{0}, when switch S_{2} is closed, C_{1} and C_{2} both have upper plate

charge CV_{0}.

When S_{3} is closed, then upper plate of C_{2} becomes charged by -CV_{0} and lower plate by +CV_{0}

*Multiple options can be correct

QUESTION: 12

A particle of mass M and positive charge Q, moving with a constant velocity enters a region

of uniform static magnetic field normal to the x-y plane. The region of the magnetic field extends from x =

0 to x = L for all values of y. After passing through this region, the particle emerges on the other side after

10 milliseconds with a velocity The correct statement(s) is (are)

Solution:

*Multiple options can be correct

QUESTION: 13

A horizontal stretched string fixed at two ends, is vibrating in its fifth harmonic according to the equation y(x, t) = 0.01m sin [(62.8m^{-1})x] cos[(628s^{-1})t]. Assuming π = 3.14, the correct statement(s) is (are)

Solution:

*Multiple options can be correct

QUESTION: 14

A solid sphere of radius R and density ρ is attached to one end of a mass-less spring of force constant k.

The other end of the spring is connected to another solid sphere of radius R and density 3ρ. The complete

arrangement is placed in a liquid of density 2ρ and is allowed to reach equilibrium. The correct

statement(s) is (are)

Solution:

For equilibrium of the complete system, net force of buoyancy must be equal to

the total weight of the sphere which holds true in the given problem. So both

the spheres are completely submerged

*Multiple options can be correct

QUESTION: 15

Two non-conducting solid spheres of radii R and 2R, having uniform volume charge densities ρ_{1} and ρ_{2}

respectively, touch each other. The net electric field at a distance 2R from the centre of the smaller sphere,

along the line joining the centre of the spheres is zero. The ratio ρ_{1}/ρ_{2} can be

Solution:

*Answer can only contain numeric values

QUESTION: 16

**SECTION – 3 : (Integer value correct Type)**

**This section contains 5 questions. The answer to each question is a single digit integer, ranging from 0 to 9 (both inclusive).**

**Q. No. 16-20 carry 4 marks each and 1 mark is deducted for every incorrect answer**

**Q.**

A bob of mass m , suspended by a string of length l_{1} is given a minimum velocity required to complete a

full circle in the vertical plane. At the highest point, it collides elastically with another bob of mass m

suspended by a string of length l_{2}, which is initially at rest. Both the strings are mass-less and inextensible.

If the second bob, after collision acquires the minimum speed required to complete a full circle in the

vertical plane, the ratio l_{1}/l_{2} is

Solution:

*Answer can only contain numeric values

QUESTION: 17

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. If the initial speed (in m/s) of the particle is zero, the speed (in m/s) after 5 s is

Solution:

*Answer can only contain numeric values

QUESTION: 18

The work functions of Silver and Sodium are 4.6 and 2.3 eV, respectively. The ratio of the slope of the

stopping potential versus frequency plot for Silver to that of Sodium is

Solution:

Slope of graph is h/e = constant

1

*Answer can only contain numeric values

QUESTION: 19

A freshly prepared sample of a radioisotope of half-life 1386 s has activity 10^{3} disintegrations per second.

Given that ln 2 = 0.693, the fraction of the initial number of nuclei (expressed in nearest integer percentage)

that will decay in the first 80 s after preparation of the sample is

Solution:

*Answer can only contain numeric values

QUESTION: 20

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 axis, which is vertical. Two uniform circular rings, each of mass 6.25 kg and radius 0.2 m,

are gently placed symmetrically on the disc in such a manner that they are touching each other along the

axis of the disc and are horizontal. Assume that the friction is large enough such that the rings are at rest

relative to the disc and the system rotates about the original axis. The new angular velocity (in rad s^{-1}) of

the system is

Solution:

QUESTION: 21

**SECTION – 1**

**Q. No. 21- 40 carry 2 marks each**

**This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.**

**Q.**

In the reaction,

P+Q →R+S

the time taken for 75% reaction of P is twice the time taken for 50% reaction of P. The concentration of Q

varies with reaction time as shown in the figure. The overall order of the reaction is

Solution:

Overall order of reaction can be decided by the data given t_{75%} = 2t_{50%}

It is a first order reaction with respect to P.

From graph [Q] is linearly decreasing with time, i.e. order of reaction with respect to Q is zero and the rate

expression is r = k [P]1[Q]0.

Hence (D) is correct.

QUESTION: 22

Consider the following complex ions, P, Q and R

The correct order of the complex ions, according to their spin–only magnetic moment values (in B.M.) is

Solution:

P = Fe^{+3} (no. of unpaired e^{-} = 5)

Q = V^{+2} (no. of unpaired e^{-} = 3)

R = Fe^{+2} (no. of unpaired e^{-} = 4)

As all ligands are weak field, hence the no. of unpaired electrons remains same in the complex ion.

Hence (B) is correct.

QUESTION: 23

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^{–} is 250 pm, the radius of A^{+} is

Solution:

According to the given figure, A^{+} is present in the octahedral void of X^{-}. The limiting radius in octahedral void is related to the radius of sphere as

QUESTION: 24

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

Solution:

NO_{2} remains dissolved in nitric acid colouring it yellow or even red at higher temperature

QUESTION: 25

The compound that does NOT liberate CO_{2}, on treatment with aqueous sodium bicarbonate solution, is

Solution:

pK_{a} of PhOH (carbolic acid) is 9.98 and that of carbonic acid (H_{2}CO_{3}) is 6.63 thus phenol does not give

effervescence with HCO_{3}^{-} ion.

QUESTION: 26

Sulfide ores are common for the metals

Solution:

Sulfide ore of Ag → Argentite (Ag_{2}S), Pb → Galena (PbS), Cu → Copper glance (Cu_{2}S)

Hence (A) is correct.

QUESTION: 27

Methylene blue, from its aqueous solution, is adsorbed on activated charcoal at 250C. For this process, the

correct statement is

Solution:

Adsorption of methylene blue on activated charcoal is physical adsorption hence it is characterised by decrease in enthalpy. Hence (B) is correct

QUESTION: 28

KI in acetone, undergoes S_{N}2 reaction with each of P, Q, R and S. The rates of the reaction vary as

Solution:

Relative reactivity for S_{N}2 reaction in the given structures is

QUESTION: 29

The standard enthalpies of formation of CO_{2}(g), H_{2}O(l) and glucose(s) at 25^{0}C are –40^{0} kJ/mol,

–300 kJ/mol and –1300 kJ/mol, respectively. The standard enthalpy of combustion per gram of glucose at

25^{0}C is

Solution:

QUESTION: 30

Upon treatment with ammoniacal H_{2}S, the metal ion that precipitates as a sulfide is

Solution:

Among Fe^{3+}, Al^{3+}, Mg^{2+}, Zn^{2+} only Zn^{2+} is precipitated with ammonical H_{2}S as ZnS.

*Multiple options can be correct

QUESTION: 31

**SECTION – 2**

**Q.No 31 - 35 carry 4 marks each 1 mark is deducted for every incorrect answer.**

**This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.**

**Q.**

**The initial rate of hydrolysis of methyl acetate (1 M) by a weak acid (HA, 1M) is 1/100 ^{th} of that of a strong acid (HX, 1M), at 25^{o}C. The K_{a} of HA is**

Solution:

*Multiple options can be correct

QUESTION: 32

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

Solution:

*Multiple options can be correct

QUESTION: 33

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

Solution:

(an octahedral complex) and (a square planar complex) will show geometrical isomerism.

will show ionization isomerism

*Multiple options can be correct

QUESTION: 34

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

Solution:

*Multiple options can be correct

QUESTION: 35

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

is(are)

Solution:

*Answer can only contain numeric values

QUESTION: 36

**SECTION-3 (Integer value correct Type)**

**Q. No 36 -40 carry 4 marks each and 1 mark is deducted for every incorrect answer**

**This section contains 5 questions. The answer to each of the questions is a single digit integer, ranging from 0 to 9. (both inclusive).**

**Q.**

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 – 73^{o}C is “M” times that of the de Broglie wavelength of Ne at 727^{o} C. M is

Solution:

*Answer can only contain numeric values

QUESTION: 37

EDTA^{4-} is ethylenediaminetetraacetate ion. The total number of N – Co – O bond angles in [Co(EDTA)]^{1-}

complex ion is

Solution:

*Answer can only contain numeric values

QUESTION: 38

The total number of carboxylic acid groups in the product P is

Solution:

*Answer can only contain numeric values

QUESTION: 39

A tetrapeptide has – COOH group on alanine. This produces glycine (Gly), valine (Val), phenyl alanine

(Phe) and alanine (Ala), on complete hydrolysis. For this tetrapeptide, the number of possible sequences

(primary structures) with – NH_{2} group attached to a chiral center is

Solution:

Because –COOH group of tetrapeptide is intact on alanine, its NH_{2} must be participating in condensation.

Alanine is at one terminus, – – – A.

To fill the 3 blanks, possible options are:

(i) When NH_{2} group attached to non chiral carbon

(ii) When NH2 group attached to chiral carbon

where, Glycine (G)

Valine (V)

Phenyl alanine (P)

Alanine (A)

So the number of possible sequence are 4.

*Answer can only contain numeric values

QUESTION: 40

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

Solution:

lone pairs

QUESTION: 41

SECTION - 1

**Q. No. 41-50 carry 2 marks each**

**This section contains 10 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONLY ONE is correct.**

Q.

**Perpendiculars are drawn from points on the line ** to the plane x + y + z = 3. The feet **of perpendiculars lie on the line**

Solution:

The foot of the perpendicular from point (– 2, – 1, 0) on the plane is the point A (0, 1, 2)

QUESTION: 42

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

bx + ay + c = 0 is less than 2√2 , then

Solution:

QUESTION: 43

The area enclosed by the curves y = sinx + cosx and y = |cosx - sinx| over the interval is

Solution:

=

QUESTION: 44

Four persons independently solve a certain problem correctly with probabilities then the

probability that the problem is solved correctly by at least one of them is

Solution:

P(at least one of them solves correctly) = 1 – P(none of them solves correctly)

QUESTION: 45

Let complex numbers lie on circles

respectively. If z_{0} = x_{0} + iy_{0} satisfies the equation 2|z_{0}|^{2} = r^{2} + 2, then |α| =

Solution:

QUESTION: 46

The number of points in (-∞, ∞), for which x^{2} - xsinx - cosx = 0, is

Solution:

QUESTION: 47

Let (the set of all real numbers) be a positive, non-constant and differentiable function such that f'(x) < 2f(x) and f(1/2) =1 Then the value of lies in the interval

Solution:

QUESTION: 48

Let determine diagonals of a parallelogram PQRS and

be another vector. Then the volume of the parallelepiped determined by the vectors

Solution:

QUESTION: 49

The value of

Solution:

QUESTION: 50

A curve passes through the point Let the slope of the curve at each point (x, y) be Then the equation of the curve is

Solution:

*Multiple options can be correct

QUESTION: 51

**SECTION - 2**

**Q. No 51 -55 carry 4 marks each and 1 mark is deducted for every incorrect answer**

**This section contains 5 multiple choice questions. Each question has four choices (A), (B), (C) and (D) out of which ONE or MORE are correct.**

**Q.**

**A line l passing through the origin is perpendicular to the lines**

Then, the coordinate(s) of the point(s) on l_{2} at a distance of from the point of intersection of l and l_{1} is

(are)

Solution:

The common perpendicular is along

*Multiple options can be correct

QUESTION: 52

Let f(x) = xsin πx, x > 0. Then for all natural numbers n, f'(x) vanishes at

Solution:

*Multiple options can be correct

QUESTION: 53

Let Then S_{n} can take value(s)

Solution:

*Multiple options can be correct

QUESTION: 54

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

Solution:

(A) (N^{T}MN)^{T} = N^{T}M^{T}N = N^{T}MN if M is symmetric and is – N^{T}MN if M is skew symmetric

(B) (MN - NM)^{T} = N^{T}M^{T} - M^{T}N^{T} = NM - MN = –(MN – NM). So, (MN – NM) is skew symmetric

(C) (MN)^{T} = N^{T}M^{T} = NM MN if M and N are symmetric. So, MN is not symmetric

(D) (adj. M) (adj. N) = adj(NM) adj (MN).

*Multiple options can be correct

QUESTION: 55

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

open rectangular box by folding after removing squares of equal area from all four corners. If the total area

of removed squares is 100, the resulting box has maximum volume. Then the lengths of the sides of the

rectangular sheet are

Solution:

Let the sides of rectangle be 15k and 8k and side of square be x then (15k – 2x)(8k – 2x)x is volume

*Answer can only contain numeric values

QUESTION: 56

**SECTION - 3 **

**Q. No 56-60 carry 4 marks each and 1 mark is deducted for every incorrect answer**

**This section contains 5 questions. The answer to each question is single digit integer, ranging from 0 to 9 (both inclusive).**

**Q.**

Consider the set of eight vectors Three non-coplanar vectors can be

chosen from V in 2^{p }ways. Then p is ________

Solution:

Let (1, 1, 1), (–1, 1, 1), (1, –1, 1), (–1, –1, 1) be vectors rest of the vectors are and let us find the number of ways of selecting co–planar vectors.

Observe that out of any 3 coplanar vectors two will be collinear (anti parallel)

Number of ways of selecting the anti parallel pair = 4

Number of ways of selecting the third vector = 6

Total = 24

Number of non co–planar selections =

*Answer can only contain numeric values

QUESTION: 57

Of the three independent events E_{1}, E_{2}, and E_{3}, the probability that only E_{1} occurs is α, only E_{2} occurs is β

and only E_{3} occurs is γ. Let the probability p that none of events E_{1}, E_{2} or E_{3} occurs satisfy the equations

(α - 2β) p = αβ and (β - 3γ) p = 2βγ. All the given probabilities are assumed to lie in the interval (0, 1).

Solution:

*Answer can only contain numeric values

QUESTION: 58

The coefficients of three consecutive terms of (1 + x)^{n+5} are in the ratio 5 : 10 : 14. Then n = _______

Solution:

*Answer can only contain numeric values

QUESTION: 59

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

pack and the sum of the numbers on the remaining cards is 1224. If the smaller of the numbers on the

removed cards is k, then k ? 20 = ________

Solution:

*Answer can only contain numeric values

QUESTION: 60

A vertical line passing through the point (h, 0) intersects the ellipse at the points P and Q. Let

the tangents to the ellipse at P and Q meet at the point R. If Δ(h) = area of the triangle PQR, Δ_{1} =

Solution:

### IIT-JEE 2013 Paper Advanced-1 (solved)

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### IIT-JEE 2013 Paper Advanced-2 (solved)

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### IIT-JEE 2013 Paper Advanced-2 (solved)

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