JEE Advanced 2013 Paper 2 Question Paper

Question 1

For $a \in \mathbb{R}$ (the set of all real numbers), $a 
eq -1$, $\lim_{n 	o \infty} \frac{\left(1^{a} + 2^{a} + \ldots + n^{a}ight)}{(n+1)^{a-1}\left[(na+1) + (na+2) + \ldots + (na+n)ight]} = \frac{1}{60}$. Then $a =$

Accepted Answer

(B) $7$

Accepted Answer

(D) $\frac{-17}{2}$

Answer

(A) $5$

Answer

(C) $\frac{-15}{2}$

Question 2

Circle(s) touching x-axis at a distance 3 from the origin and having an intercept of length $2\sqrt{7}$ on y-axis is (are)

Accepted Answer

(A) $x^{2} + y^{2} - 6x + 8y + 9 = 0$

Accepted Answer

(C) $x^{2} + y^{2} - 6x - 8y + 9 = 0$

Answer

(B) $x^{2} + y^{2} - 6x + 7y + 9 = 0$

Answer

(D) $x^{2} + y^{2} - 6x - 7y + 9 = 0$

Question 3

Two lines $L_{1} : x = 5, \frac{y}{3 - \alpha} = \frac{z}{-2}$ and $L_{2} : x = \alpha, \frac{y}{-1} = \frac{z}{2 - \alpha}$ are coplanar. Then $\alpha$ can take value(s)

Accepted Answer

(A) $1$

Accepted Answer

(D) $4$

Answer

(B) $2$

Answer

(C) $3$

Question 4

In a triangle PQR, P is the largest angle and $\cos P = \frac{1}{3}$. Further the incircle of the triangle touches the sides PQ, QR and RP at N, L and M respectively, such that the lengths of PN, QL and RM are consecutive even integers. Then possible length(s) of the side(s) of the triangle is (are)

Accepted Answer

(B) $18$

Accepted Answer

(D) $22$

Answer

(A) $16$

Answer

(C) $24$

Question 5

Let $w = \frac{\sqrt{3} + i}{2}$ and $P = \{w^{n} : n = 1, 2, 3, \ldots\}$. Further $H_{1} = \left\{z \in \mathbb{C} : \operatorname{Re} z > \frac{1}{2}\right\}$ and $H_{2} = \left\{z \in \mathbb{C} : \operatorname{Re} z < \frac{-1}{2}\right\}$, where $\mathbb{C}$ is the set of all complex numbers. If $z_{1} \in P \cap H_{1}$, $z_{2} \in P \cap H_{2}$ and O represents the origin, then $\angle z_{1} O z_{2} =$

Accepted Answer

(C) $\frac{2\pi}{3}$

Accepted Answer

(D) $\frac{5\pi}{6}$

Answer

(A) $\frac{\pi}{2}$

Answer

(B) $\frac{\pi}{6}$

Question 6

If $3^{x} = 4^{x-1}$, then $x =$

Accepted Answer

(A) $\frac{2\log_{3} 2}{2\log_{3} 2 - 1}$

Accepted Answer

(B) $\frac{2}{2 - \log_{2} 3}$

Accepted Answer

(C) $\frac{1}{1 - \log_{4} 3}$

Answer

(D) $\frac{2\log_{2} 3}{2\log_{2} 3 - 1}$

Question 7

Let $\omega$ be a complex cube root of unity with $\omega 
eq 1$ and $P = [p_{ij}]$ be a $n 	imes n$ matrix with $p_{ij} = \omega^{i+j}$. Then $P^{2} 
eq 0$, when $n =$

Accepted Answer

(B) $55$

Accepted Answer

(C) $58$

Accepted Answer

(D) $56$

Answer

(A) $57$

Question 8

The function $f(x) = 2|x| + |x + 2| - \left||x + 2| - 2|x|\right|$ has a local minimum or a local maximum at $x =$

Accepted Answer

(A) $-2$

Accepted Answer

(B) $\frac{-2}{3}$

Answer

(C) $2$

Answer

(D) $\frac{2}{3}$

Question 9

Let $f : [0, 1] 	o \mathbb{R}$ (the set of all real numbers) be a function. Suppose the function $f$ is twice differentiable, $f(0) = f(1) = 0$ and satisfies $f''(x) - 2f'(x) + f(x) \geq e^{x}$, $x \in [0, 1]$.

Which of the following is true for $0 < x < 1$ ?

Accepted Answer

(D) $-\infty < f(x) < 0$

Answer

(A) $0 < f(x) < \infty$

Answer

(B) $-\frac{1}{2} < f(x) < \frac{1}{2}$

Answer

(C) $-\frac{1}{4} < f(x) < 1$

Question 10

Let $f : [0, 1] 	o \mathbb{R}$ (the set of all real numbers) be a function. Suppose the function $f$ is twice differentiable, $f(0) = f(1) = 0$ and satisfies $f''(x) - 2f'(x) + f(x) \geq e^{x}$, $x \in [0, 1]$.

If the function $e^{-x} f(x)$ assumes its minimum in the interval $[0, 1]$ at $x = \frac{1}{4}$, which of the following is true ?

Accepted Answer

(C) $f'(x) < f(x), 0 < x < \frac{1}{4}$

Answer

(A) $f'(x) < f(x), \frac{1}{4} < x < \frac{3}{4}$

Answer

(B) $f'(x) > f(x), 0 < x < \frac{1}{4}$

Answer

(D) $f'(x) < f(x), \frac{3}{4} < x < 1$

Question 11

Let PQ be a focal chord of the parabola $y^{2} = 4ax$. The tangents to the parabola at P and Q meet at a point lying on the line $y = 2x + a$, $a > 0$.

Length of chord PQ is

Accepted Answer

(B) $5a$

Answer

(A) $7a$

Answer

(C) $2a$

Answer

(D) $3a$

Question 12

Let PQ be a focal chord of the parabola $y^{2} = 4ax$. The tangents to the parabola at P and Q meet at a point lying on the line $y = 2x + a$, $a > 0$.

If chord PQ subtends an angle $	heta$ at the vertex of $y^{2} = 4ax$, then $	an	heta =$

Accepted Answer

(D) $\frac{-2}{3}\sqrt{5}$

Answer

(A) $\frac{2}{3}\sqrt{7}$

Answer

(B) $\frac{-2}{3}\sqrt{7}$

Answer

(C) $\frac{2}{3}\sqrt{5}$

Question 13

Let $S = S_{1} \cap S_{2} \cap S_{3}$, where
$S_{1} = \{z \in \mathbb{C} : |z| < 4\}$, $S_{2} = \left\{z \in \mathbb{C} : \operatorname{Im}\left[\frac{z - 1 + \sqrt{3}i}{1 - \sqrt{3}i}\right] > 0\right\}$ and $S_{3} = \{z \in \mathbb{C} : \operatorname{Re} z > 0\}$.

Area of $S =$

Accepted Answer

(B) $\frac{20\pi}{3}$

Answer

(A) $\frac{10\pi}{3}$

Answer

(C) $\frac{16\pi}{3}$

Answer

(D) $\frac{32\pi}{3}$

Question 14

Let $S = S_{1} \cap S_{2} \cap S_{3}$, where
$S_{1} = \{z \in \mathbb{C} : |z| < 4\}$, $S_{2} = \left\{z \in \mathbb{C} : \operatorname{Im}\left[\frac{z - 1 + \sqrt{3}i}{1 - \sqrt{3}i}\right] > 0\right\}$ and $S_{3} = \{z \in \mathbb{C} : \operatorname{Re} z > 0\}$.

$\min_{z \in S} |1 - 3i - z| =$

Accepted Answer

(C) $\frac{3 - \sqrt{3}}{2}$

Answer

(A) $\frac{2 - \sqrt{3}}{2}$

Answer

(B) $\frac{2 + \sqrt{3}}{2}$

Answer

(D) $\frac{3 + \sqrt{3}}{2}$

Question 15

A box $B_{1}$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_{2}$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_{3}$ contains 3 white balls, 4 red balls and 5 black balls.

If 1 ball is drawn from each of the boxes $B_{1}$, $B_{2}$ and $B_{3}$, the probability that all 3 drawn balls are of the same colour is

Accepted Answer

(A) $\frac{82}{648}$

Answer

(B) $\frac{90}{648}$

Answer

(C) $\frac{558}{648}$

Answer

(D) $\frac{566}{648}$

Question 16

A box $B_{1}$ contains 1 white ball, 3 red balls and 2 black balls. Another box $B_{2}$ contains 2 white balls, 3 red balls and 4 black balls. A third box $B_{3}$ contains 3 white balls, 4 red balls and 5 black balls.

If 2 balls are drawn (without replacement) from a randomly selected box and one of the balls is white and the other ball is red, the probability that these 2 balls are drawn from box $B_{2}$ is

Accepted Answer

(D) $\frac{55}{181}$

Answer

(A) $\frac{116}{181}$

Answer

(B) $\frac{126}{181}$

Answer

(C) $\frac{65}{181}$

Question 17

Match List I with List II and select the correct answer using the code given below the lists :

Accepted Answer

(B) P-4, Q-3, R-2, S-1

Answer

(A) P-4, Q-3, R-1, S-2

Answer

(C) P-3, Q-4, R-2, S-1

Answer

(D) P-3, Q-4, R-1, S-2

Question 18

A line $L : y = mx + 3$ meets y-axis at $E(0, 3)$ and the arc of the parabola $y^{2} = 16x$, $0 \leq y \leq 6$ at the point $F(x_{0}, y_{0})$. The tangent to the parabola at $F(x_{0}, y_{0})$ intersects the y-axis at $G(0, y_{1})$. The slope $m$ of the line L is chosen such that the area of the triangle EFG has a local maximum.
Match List I with List II and select the correct answer using the code given below the lists :

Accepted Answer

(A) P-4, Q-1, R-2, S-3

Answer

(B) P-3, Q-4, R-1, S-2

Answer

(C) P-1, Q-3, R-2, S-4

Answer

(D) P-1, Q-3, R-4, S-2

Question 19

Match List I with List II and select the correct answer using the code given below the lists :

Accepted Answer

(C) P-3, Q-4, R-1, S-2

Answer

(A) P-4, Q-2, R-3, S-1

Answer

(B) P-2, Q-3, R-1, S-4

Answer

(D) P-1, Q-4, R-3, S-2

Question 20

Consider the lines $L_{1} : \frac{x - 1}{2} = \frac{y}{-1} = \frac{z + 3}{1}$, $L_{2} : \frac{x - 4}{1} = \frac{y + 3}{1} = \frac{z + 3}{2}$ and the planes $P_{1} : 7x + y + 2z = 3$, $P_{2} : 3x + 5y - 6z = 4$. Let $ax + by + cz = d$ be the equation of the plane passing through the point of intersection of lines $L_{1}$ and $L_{2}$, and perpendicular to planes $P_{1}$ and $P_{2}$.
Match List I with List II and select the correct answer using the code given below the lists :

Accepted Answer

(A) P-3, Q-2, R-4, S-1

Answer

(B) P-1, Q-3, R-4, S-2

Answer

(C) P-3, Q-2, R-1, S-4

Answer

(D) P-2, Q-4, R-1, S-3

Question 21

Two bodies, each of mass $M$, are kept fixed with a separation $2L$. A particle of mass $m$ is projected from the midpoint of the line joining their centres, perpendicular to the line. The gravitational constant is $G$. The correct statement(s) is (are)

Accepted Answer

(B) The minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $2\sqrt{\frac{GM}{L}}$.

Answer

(A) The minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $4\sqrt{\frac{GM}{L}}$

Answer

(C) The minimum initial velocity of the mass $m$ to escape the gravitational field of the two bodies is $\sqrt{\frac{2GM}{L}}$

Answer

(D) The energy of the mass $m$ remains constant.

Question 22

A particle of mass $m$ is attached to one end of a mass-less spring of force constant $k$, lying on a frictionless horizontal plane. The other end of the spring is fixed. The particle starts moving horizontally from its equilibrium position at time $t = 0$ with an initial velocity $u_{0}$. When the speed of the particle is $0.5u_{0}$. It collides elastically with a rigid wall. After this collision,

Accepted Answer

(A) the speed of the particle when it returns to its equilibrium position is $u_{0}$.

Accepted Answer

(D) the time at which the particle passes through the equilibrium position for the second time is $t = \frac{5\pi}{3}\sqrt{\frac{m}{k}}$.

Answer

(B) the time at which the particle passes through the equilibrium position for the first time is $t = \pi\sqrt{\frac{m}{k}}$.

Answer

(C) the time at which the maximum compression of the spring occurs is $t = \frac{4\pi}{3}\sqrt{\frac{m}{k}}$.

Question 23

A steady current $I$ flows along an infinitely long hollow cylindrical conductor of radius $R$. This cylinder is placed coaxially inside an infinite solenoid of radius $2R$. The solenoid has $n$ turns per unit length and carries a steady current $I$. Consider a point $P$ at a distance $r$ from the common axis. The correct statement(s) is (are)

Accepted Answer

(A) In the region $0 < r < R$, the magnetic field is non-zero

Accepted Answer

(D) In the region $r > 2R$, the magnetic field is non-zero.

Answer

(B) In the region $R < r < 2R$, the magnetic field is along the common axis.

Answer

(C) In the region $R < r < 2R$, the magnetic field is tangential to the circle of radius $r$, centered on the axis.

Question 24

Two vehicles, each moving with speed $u$ on the same horizontal straight road, are approaching each other. Wind blows along the road with velocity $w$. One of these vehicles blows a whistle of frequency $f_{1}$. An observer in the other vehicle hears the frequency of the whistle to be $f_{2}$. The speed of sound in still air is $V$. The correct statement(s) is (are)

Accepted Answer

(A) If the wind blows from the observer to the source, $f_{2} > f_{1}$.

Accepted Answer

(B) If the wind blows from the source to the observer, $f_{2} > f_{1}$.

Answer

(C) If the wind blows from observer to the source, $f_{2} < f_{1}$.

Answer

(D) If the wind blows from the source to the observer $f_{2} < f_{1}$.

Question 25

Using the expression $2d\sin	heta = \lambda$, one calculates the values of $d$ by measuring the corresponding angles $	heta$ in the range $0$ to $90^{\circ}$. The wavelength $\lambda$ is exactly known and the error in $	heta$ is constant for all values of $	heta$. As $	heta$ increases from $0^{\circ}$,

Accepted Answer

(D) the fractional error in $d$ decreases.

Answer

(A) the absolute error in $d$ remains constant.

Answer

(B) the absolute error in $d$ increases

Answer

(C) the fractional error in $d$ remains constant.

Question 26

Two non-conducting spheres of radii $R_{1}$ and $R_{2}$ and carrying uniform volume charge densities $+\rho$ and $-\rho$, respectively, are placed such that they partially overlap, as shown in the figure. At all points in the overlapping region,

Accepted Answer

(C) the electrostatic field is constant in magnitude

Accepted Answer

(D) the electrostatic field has same direction

Answer

(A) the electrostatic field is zero

Answer

(B) the electrostatic potential is constant

Question 27

The figure shows the variation of specific heat capacity ($C$) of a solid as a function of temperature ($T$). The temperature is increased continuously from $0$ to $500\ \mathrm{K}$ at a constant rate. Ignoring any volume change, the following statement(s) is (are) correct to a reasonable approximation.

Accepted Answer

(A) the rate at which heat is absorbed in the range $0$-$100\ \mathrm{K}$ varies linearly with temperature $T$.

Accepted Answer

(B) heat absorbed in increasing the temperature from $0$-$100\ \mathrm{K}$ is less than the heat required for increasing the temperature from $400$ – $500\ \mathrm{K}$.

Accepted Answer

(C) there is no change in the rate of heat absorption in range $400$ – $500\ \mathrm{K}$.

Accepted Answer

(D) the rate of heat absorption increases in the range $200$ – $300\ \mathrm{K}$.

Question 28

The radius of the orbit of an electron in a Hydrogen-like atom is $4.5a_{0}$ where $a_{0}$ is the Bohr radius. Its orbital angular momentum is $\frac{3h}{2\pi}$. It is given that $h$ is Planck's constant and $R$ is Rydberg constant. The possible wavelength(s), when the atom de-excites, is (are)

Accepted Answer

(A) $\frac{9}{32R}$

Accepted Answer

(C) $\frac{9}{5R}$

Answer

(B) $\frac{9}{16R}$

Answer

(D) $\frac{4}{3R}$

Question 29

A small block of mass $1\ \mathrm{kg}$ is released from rest at the top of a rough track. The track is circular arc of radius $40\ \mathrm{m}$. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is $150\ \mathrm{J}$. (Take the acceleration due to gravity, $g = 10\ \mathrm{m/s^{2}}$).

The speed of the block when it reaches the point Q is

Accepted Answer

(B) $10\ \mathrm{ms^{-1}}$

Answer

(A) $5\ \mathrm{ms^{-1}}$

Answer

(C) $10\sqrt{3}\ \mathrm{ms^{-1}}$

Answer

(D) $20\ \mathrm{ms^{-1}}$

Question 30

A small block of mass $1\ \mathrm{kg}$ is released from rest at the top of a rough track. The track is circular arc of radius $40\ \mathrm{m}$. The block slides along the track without toppling and a frictional force acts on it in the direction opposite to the instantaneous velocity. The work done in overcoming the friction up to the point Q, as shown in the figure, below, is $150\ \mathrm{J}$. (Take the acceleration due to gravity, $g = 10\ \mathrm{m/s^{2}}$).

The magnitude of the normal reaction that acts on the block at the point Q is

Accepted Answer

(A) $7.5\ \mathrm{N}$

Answer

(B) $8.6\ \mathrm{N}$

Answer

(C) $11.5\ \mathrm{N}$

Answer

(D) $22.5\ \mathrm{N}$

Question 31

A thermal power plant produces electric power of $600\ \mathrm{kW}$ at $4000\ \mathrm{V}$, which is to be transported to a place $20\ \mathrm{km}$ away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with the power factor unity. All the currents and voltage mentioned are rms values.

If the direct transmission method with a cable of resistance $0.4\ \Omega\ \mathrm{km^{-1}}$ is used, the power dissipation (in %) during transmission is

Accepted Answer

(B) 30

Answer

(A) 20

Answer

(C) 40

Answer

(D) 50

Question 32

A thermal power plant produces electric power of $600\ \mathrm{kW}$ at $4000\ \mathrm{V}$, which is to be transported to a place $20\ \mathrm{km}$ away from the power plant for consumers' usage. It can be transported either directly with a cable of large current carrying capacity or by using a combination of step-up and step-down transformers at the two ends. The drawback of the direct transmission is the large energy dissipation. In the method using transformers, the dissipation is much smaller. In this method, a step-up transformer is used at the plant side so that the current is reduced to a smaller value. At the consumers' end, a step-down transformer is used to supply power to the consumers at the specified lower voltage. It is reasonable to assume that the power cable is purely resistive and the transformers are ideal with the power factor unity. All the currents and voltage mentioned are rms values.

In the method using the transformers, assume that the ratio of the number of turns in the primary to that in the secondary in the step-up transformer is $1 : 10$. If the power to the consumers has to be supplied at $200\ \mathrm{V}$, the ratio of the number of turns in the primary to that in the secondary in the step-down transformer is

Accepted Answer

(A) $200 : 1$

Answer

(B) $150 : 1$

Answer

(C) $100 : 1$

Answer

(D) $50 : 1$

Question 33

A point Q is moving in a circular orbit of radius $R$ in the x-y plane with an angular velocity $\omega$. This can be considered as equivalent to a loop carrying a steady current $\frac{Q\omega}{2\pi}$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from $0$ to $B$ in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $\gamma$.

The magnitude of the induced electric field in the orbit at any instant of time during the time interval of the magnetic field change, is

Accepted Answer

(B) $\frac{BR}{2}$

Answer

(A) $\frac{BR}{4}$

Answer

(C) $BR$

Answer

(D) $2BR$

Question 34

A point Q is moving in a circular orbit of radius $R$ in the x-y plane with an angular velocity $\omega$. This can be considered as equivalent to a loop carrying a steady current $\frac{Q\omega}{2\pi}$. A uniform magnetic field along the positive z-axis is now switched on, which increases at a constant rate from $0$ to $B$ in one second. Assume that the radius of the orbit remains constant. The application of the magnetic field induces an emf in the orbit. The induced emf is defined as the work done by an induced electric field in moving a unit positive charge around closed loop. It is known that, for an orbiting charge, the magnetic dipole moment is proportional to the angular momentum with a proportionality constant $\gamma$.

The change in the magnetic dipole moment associated with the orbit, at the end of time interval of the magnetic field change, is

Accepted Answer

(B) $-\gamma\frac{BQR^{2}}{2}$

Answer

(A) $-\gamma BQR^{2}$

Answer

(C) $\gamma\frac{BQR^{2}}{2}$

Answer

(D) $\gamma BQR^{2}$

Question 35

The mass of nucleus $^{A}_{Z}\mathrm{X}$ is less than the sum of the masses of $(A-Z)$ number of neutrons and $Z$ number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass $M$ can break into two light nuclei of mass $m_{1}$ and $m_{2}$ only if $(m_{1} + m_{2}) < M$. Also two light nuclei of masses $m_{3}$ and $m_{4}$ can undergo complete fusion and form a heavy nucleus of mass $M'$ only if $(m_{3} + m_{4}) > M'$. The masses of some neutral atoms are given in the table below:

The correct statement is

Accepted Answer

(C) Deuteron and alpha particle can undergo complete fusion.

Answer

(A) The nucleus $^{6}_{3}\mathrm{Li}$ can emit an alpha particle

Answer

(B) The nucleus $^{210}_{84}\mathrm{Po}$ can emit a proton.

Answer

(D) The nuclei $^{70}_{30}\mathrm{Zn}$ and $^{82}_{34}\mathrm{Se}$ can undergo complete fusion.

Question 36

The mass of nucleus $^{A}_{Z}\mathrm{X}$ is less than the sum of the masses of $(A-Z)$ number of neutrons and $Z$ number of protons in the nucleus. The energy equivalent to the corresponding mass difference is known as the binding energy of the nucleus. A heavy nucleus of mass $M$ can break into two light nuclei of mass $m_{1}$ and $m_{2}$ only if $(m_{1} + m_{2}) < M$. Also two light nuclei of masses $m_{3}$ and $m_{4}$ can undergo complete fusion and form a heavy nucleus of mass $M'$ only if $(m_{3} + m_{4}) > M'$. The masses of some neutral atoms are given in the table below:

The kinetic energy (in keV) of the alpha particle, when the nucleus $^{210}_{84}\mathrm{Po}$ at rest undergoes alpha decay, is

Accepted Answer

(A) 5319

Answer

(B) 5422

Answer

(C) 5707

Answer

(D) 5818

Question 37

A right angled prism of refractive index $\mu_{1}$ is placed in a rectangular block of refractive index $\mu_{2}$, which is surrounded by a medium of refractive index $\mu_{3}$, as shown in the figure. A ray of light 'e' enters the rectangular block at normal incidence. Depending upon the relationships between $\mu_{1}$, $\mu_{2}$ and $\mu_{3}$, it takes one of the four possible paths 'ef', 'eg', 'eh', or 'ei'.

Match the paths in List I with conditions of refractive indices in List II and select the correct answer using the codes given below the lists:

Accepted Answer

(D) P-2, Q-3, R-4, S-1

Answer

(A) P-2, Q-3, R-1, S-4

Answer

(B) P-1, Q-2, R-4, S-3

Answer

(C) P-4, Q-1, R-2, S-3

Question 38

Match List I with List II and select the correct answer using the codes given below the lists:

Accepted Answer

(C) P-4, Q-2, R-1, S-3

Answer

(A) P-3, Q-1, R-2, S-4

Answer

(B) P-3, Q-2, R-1, S-4

Answer

(D) P-4, Q-1, R-2, S-3

Question 39

One mole of mono-atomic ideal gas is taken along two cyclic processes $E 	o F 	o G 	o E$ and $E 	o F 	o H 	o E$ as shown in the PV diagram. The processes involved are purely isochoric, isobaric, isothermal or adiabatic.

Match the paths in List I with the magnitudes of the work done in List II and select the correct answer using the codes given below the lists.

Accepted Answer

(A) P-4, Q-3, R-2, S-1

Answer

(B) P-4, Q-3, R-1, S-2

Answer

(C) P-3, Q-1, R-2, S-4

Answer

(D) P-1, Q-3, R-2, S-4

Question 40

Match List I of the nuclear processes with List II containing parent nucleus and one of the end products of each process and then select the correct answer using the codes given below the lists:

Accepted Answer

(C) P-2, Q-1, R-4, S-3

Answer

(A) P-4, Q-2, R-1, S-3

Answer

(B) P-1, Q-3, R-2, S-4

Answer

(D) P-4, Q-3, R-2, S-1

Question 41

The $K_{sp}$ of $\mathrm{Ag_2CrO_4}$ is $1.1 	imes 10^{-12}$ at 298K. The solubility (in mol/L) of $\mathrm{Ag_2CrO_4}$ in a 0.1M $\mathrm{AgNO_3}$ solution is

Accepted Answer

(B) $1.1 	imes 10^{-10}$

Answer

(A) $1.1 	imes 10^{-11}$

Answer

(C) $1.1 	imes 10^{-12}$

Answer

(D) $1.1 	imes 10^{-9}$

Question 42

In the following reaction, the product(s) formed is(are)

Accepted Answer

(B) Q(minor)

Accepted Answer

(D) S(major)

Answer

(A) P(major)

Answer

(C) R(minor)

Question 43

The major product(s) of the following reaction is (are)

Accepted Answer

(B) Q

Answer

(A) P

Answer

(C) R

Answer

(D) S

Question 44

After completion of the reactions (I and II), the organic compound(s) in the reaction mixtures is(are)

Accepted Answer

(C) Reaction I : T, U, acetone and Reaction II : P

Answer

(A) Reaction I : P and Reaction II : P

Answer

(B) Reaction I : U, acetone and Reaction II : Q, acetone

Answer

(D) Reaction I : R, acetone and Reaction II : S, acetone

Question 45

The correct statement(s) about $\mathrm{O_3}$ is(are)

Accepted Answer

(A) O–O bond lengths are equal.

Accepted Answer

(C) $\mathrm{O_3}$ is diamagnetic in nature.

Accepted Answer

(D) $\mathrm{O_3}$ has a bent structure.

Answer

(B) Thermal decomposition of $\mathrm{O_3}$ is endothermic.

Question 46

In the nuclear transmutation
$^{9}_{4}\mathrm{Be} + X \longrightarrow {}^{8}_{4}\mathrm{Be} + Y$
(X, Y) is (are)

Accepted Answer

(A) $(\gamma, \mathrm{n})$

Accepted Answer

(B) $(\mathrm{p}, \mathrm{D})$

Answer

(C) $(\mathrm{n}, \mathrm{D})$

Answer

(D) $(\gamma, \mathrm{p})$

Question 47

The carbon–based reduction method is NOT used for the extraction of

Accepted Answer

(C) aluminium from $\mathrm{Al_2O_3}$

Accepted Answer

(D) magnesium from $\mathrm{MgCO_3.CaCO_3}$

Answer

(A) tin from $\mathrm{SnO_2}$

Answer

(B) iron from $\mathrm{Fe_2O_3}$

Question 48

The thermal dissociation equilibrium of $\mathrm{CaCO_3(s)}$ is studied under different conditions.
$\mathrm{CaCO_3(s)} \rightleftharpoons \mathrm{CaO(s)} + \mathrm{CO_2(g)}$
For this equilibrium, the correct statement(s) is(are)

Accepted Answer

(A) $\Delta H$ is dependent on T

Accepted Answer

(B) K is independent of the initial amount of $\mathrm{CaCO_3}$

Accepted Answer

(D) $\Delta H$ is independent of the catalyst, if any

Answer

(C) K is dependent on the pressure of $\mathrm{CO_2}$ at a given T

Question 49

An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl, gave a precipitate (P) and a filtrate (Q). The precipitate P was found to dissolve in hot water. The filtrate (Q) remained unchanged, when treated with $\mathrm{H_2S}$ in a dilute mineral acid medium. However, it gave a precipitate (R) with $\mathrm{H_2S}$ in an ammoniacal medium. The precipitate R gave a coloured solution (S), when treated with $\mathrm{H_2O_2}$ in an aqueous NaOH medium.

The precipitate P contains

Accepted Answer

(A) $\mathrm{Pb^{2+}}$

Answer

(B) $\mathrm{Hg_2^{2+}}$

Answer

(C) $\mathrm{Ag^{+}}$

Answer

(D) $\mathrm{Hg^{2+}}$

Question 50

An aqueous solution of a mixture of two inorganic salts, when treated with dilute HCl, gave a precipitate (P) and a filtrate (Q). The precipitate P was found to dissolve in hot water. The filtrate (Q) remained unchanged, when treated with $\mathrm{H_2S}$ in a dilute mineral acid medium. However, it gave a precipitate (R) with $\mathrm{H_2S}$ in an ammoniacal medium. The precipitate R gave a coloured solution (S), when treated with $\mathrm{H_2O_2}$ in an aqueous NaOH medium.

The coloured solution S contains

Accepted Answer

(D) $\mathrm{Na_2CrO_4}$

Answer

(A) $\mathrm{Fe_2(SO_4)_3}$

Answer

(B) $\mathrm{CuSO_4}$

Answer

(C) $\mathrm{ZnSO_4}$

Question 51

P and Q are isomers of dicarboxylic acid $\mathrm{C_4H_4O_4}$. Both decolorize $\mathrm{Br_2/H_2O}$. On heating, P forms the cyclic anhydride.
Upon treatment with dilute alkaline $\mathrm{KMnO_4}$, P as well as Q could produce one or more than one from S, T and U.

Compounds formed from P and Q are, respectively

Accepted Answer

(B) Optically inactive S and optically inactive pair (T, U)

Answer

(A) Optically active S and optically active pair (T, U)

Answer

(C) Optically active pair (T, U) and optically active S

Answer

(D) Optically inactive pair (T, U) and optically inactive S

Question 52

P and Q are isomers of dicarboxylic acid $\mathrm{C_4H_4O_4}$. Both decolorize $\mathrm{Br_2/H_2O}$. On heating, P forms the cyclic anhydride.
Upon treatment with dilute alkaline $\mathrm{KMnO_4}$, P as well as Q could produce one or more than one from S, T and U.

In the following reaction sequences V and W are, respectively

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 53

A fixed mass ‘m’ of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure

The succeeding operations that enable this transformation of states are

Accepted Answer

(C) Heating, cooling, cooling, heating

Answer

(A) Heating, cooling, heating, cooling

Answer

(B) Cooling, heating, cooling, heating

Answer

(D) Cooling, heating, heating, cooling

Question 54

A fixed mass ‘m’ of a gas is subjected to transformation of states from K to L to M to N and back to K as shown in the figure

The pair of isochoric processes among the transformation of states is

Accepted Answer

(B) L to M and N to K

Answer

(A) K to L and L to M

Answer

(C) L to M and M to N

Answer

(D) M to N and N to K

Question 55

The reactions of $\mathrm{Cl_2}$ gas with cold-dilute and hot-concentrated NaOH in water give sodium salts of two (different) oxoacids of chlorine, P and Q, respectively. The $\mathrm{Cl_2}$ gas reacts with $\mathrm{SO_2}$ gas, in presence of charcoal, to give a product R. R reacts with white phosphorus to give a compound S. On hydrolysis, S gives an oxoacid of phosphorus, T.

P and Q, respectively, are the sodium salts of

Accepted Answer

(A) hypochlorus and chloric acids

Answer

(B) hypochlorus and chlorus acids

Answer

(C) chloric and perchloric acids

Answer

(D) chloric and hypochlorus acids

Question 56

The reactions of $\mathrm{Cl_2}$ gas with cold-dilute and hot-concentrated NaOH in water give sodium salts of two (different) oxoacids of chlorine, P and Q, respectively. The $\mathrm{Cl_2}$ gas reacts with $\mathrm{SO_2}$ gas, in presence of charcoal, to give a product R. R reacts with white phosphorus to give a compound S. On hydrolysis, S gives an oxoacid of phosphorus, T.

R, S and T, respectively, are

Accepted Answer

(A) $\mathrm{SO_2Cl_2}$, $\mathrm{PCl_5}$ and $\mathrm{H_3PO_4}$

Answer

(B) $\mathrm{SO_2Cl_2}$, $\mathrm{PCl_3}$ and $\mathrm{H_3PO_3}$

Answer

(C) $\mathrm{SOCl_2}$, $\mathrm{PCl_3}$ and $\mathrm{H_3PO_2}$

Answer

(D) $\mathrm{SOCl_2}$, $\mathrm{PCl_5}$ and $\mathrm{H_3PO_4}$

Question 57

The unbalanced chemical reactions given in List – I show missing reagent or condition (?) which are provided in List – II. Match List – I with List – II and select the correct answer using the code given below the lists:

Accepted Answer

(D) P-3, Q-4, R-2, S-1

Answer

(A) P-4, Q-2, R-3, S-1

Answer

(B) P-3, Q-2, R-1, S-4

Answer

(C) P-1, Q-4, R-2, S-3

Question 58

Match the chemical conversions in List – I with appropriate reagents in List – II and select the correct answer using the code given below the lists:

Accepted Answer

(A) P-2, Q-3, R-1, S-4

Answer

(B) P-3, Q-2, R-1, S-4

Answer

(C) P-2, Q-3, R-4, S-1

Answer

(D) P-3, Q-2, R-4, S-1

Question 59

An aqueous solution of X is added slowly to an aqueous solution of Y as shown in List – I. The variation in conductivity of these reactions in List – II. Match List – I with List – II and select the correct answer using the code given below the lists:

Accepted Answer

(A) P-3, Q-4, R-2, S-1

Answer

(B) P-4, Q-3, R-2, S-1

Answer

(C) P-2, Q-3, R-4, S-1

Answer

(D) P-1, Q-4, R-3, S-2

Question 60

The standard reduction potential data at 25°C is given below:
$E^{\circ}(\mathrm{Fe^{3+}}, \mathrm{Fe^{2+}}) = +0.77\ \mathrm{V};$
$E^{\circ}(\mathrm{Fe^{2+}}, \mathrm{Fe}) = -0.44\ \mathrm{V}$
$E^{\circ}(\mathrm{Cu^{2+}}, \mathrm{Cu}) = +0.34\ \mathrm{V};$
$E^{\circ}(\mathrm{Cu^{+}}, \mathrm{Cu}) = +0.52\ \mathrm{V}$
$E^{\circ}[\mathrm{O_2(g)} + 4\mathrm{H^{+}} + 4e^{-} \rightarrow 2\mathrm{H_2O}] = +1.23\ \mathrm{V};$
$E^{\circ}[\mathrm{O_2(g)} + 2\mathrm{H_2O} + 4e^{-} \rightarrow 4\mathrm{OH^{-}}] = +0.40\ \mathrm{V}$
$E^{\circ}(\mathrm{Cr^{3+}}, \mathrm{Cr}) = -0.74\ \mathrm{V};$
$E^{\circ}(\mathrm{Cr^{2+}}, \mathrm{Cr}) = -0.91\ \mathrm{V}$
Match $E^{0}$ of the redox pair in List – I with the values given in List – II and select the correct answer using the code given below the lists:

Accepted Answer

(D) P-3, Q-4, R-1, S-2

Answer

(A) P-4, Q-1, R-2, S-3

Answer

(B) P-2, Q-3, R-4, S-1

Answer

(C) P-1, Q-2, R-3, S-4

Nuclide	Mass
$^{1}_{1}\mathrm{H}$	1.007825 u
$^{2}_{1}\mathrm{H}$	2.014102 u
$^{3}_{1}\mathrm{H}$	3.016050 u
$^{4}_{2}\mathrm{He}$	4.002603 u
$^{6}_{3}\mathrm{Li}$	6.015123 u
$^{7}_{3}\mathrm{Li}$	7.016004 u
$^{70}_{30}\mathrm{Zn}$	69.925325 u
$^{82}_{34}\mathrm{Se}$	81.916709 u
$^{152}_{64}\mathrm{Gd}$	151.919803 u
$^{206}_{82}\mathrm{Pb}$	205.974455 u
$^{209}_{83}\mathrm{Bi}$	208.980388 u
$^{210}_{84}\mathrm{Po}$	209.982876 u

Nuclide	Mass
$^{1}_{1}\mathrm{H}$	1.007825 u
$^{2}_{1}\mathrm{H}$	2.014102 u
$^{3}_{1}\mathrm{H}$	3.016050 u
$^{4}_{2}\mathrm{He}$	4.002603 u
$^{6}_{3}\mathrm{Li}$	6.015123 u
$^{7}_{3}\mathrm{Li}$	7.016004 u
$^{70}_{30}\mathrm{Zn}$	69.925325 u
$^{82}_{34}\mathrm{Se}$	81.916709 u
$^{152}_{64}\mathrm{Gd}$	151.919803 u
$^{206}_{82}\mathrm{Pb}$	205.974455 u
$^{209}_{83}\mathrm{Bi}$	208.980388 u
$^{210}_{84}\mathrm{Po}$	209.982876 u

List I	List II
P. $e \to f$	1. $\mu_{1} > \sqrt{2}\,\mu_{2}$
Q. $e \to g$	2. $\mu_{2} > \mu_{1}$ and $\mu_{2} > \mu_{3}$
R. $e \to h$	3. $\mu_{1} = \mu_{2}$
S. $e \to i$	4. $\mu_{2} < \mu_{1} < \sqrt{2}\,\mu_{2}$ and $\mu_{2} > \mu_{3}$

List I	List II
P.Boltzmann Constant	1. $[\mathrm{ML^{2}T^{-1}}]$
Q.Coefficient of viscosity	2. $[\mathrm{ML^{-1}T^{-1}}]$
R.Plank Constant	3. $[\mathrm{MLT^{-3}K^{-1}}]$
S.Thermal conductivity	4. $[\mathrm{ML^{2}T^{-2}K^{-1}}]$

List I	List II
P. $G \to E$	1. $160\,P_{0}V_{0}\ln 2$
Q. $G \to H$	2. $36\,P_{0}V_{0}$
R. $F \to H$	3. $24\,P_{0}V_{0}$
S. $F \to G$	4. $31\,P_{0}V_{0}$

JEE Advanced 2013 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2013 Paper 2

Chemistry — JEE Advanced 2013 Paper 2

Mathematics — JEE Advanced 2013 Paper 2

Chapters tested in this paper

Attempt JEE Advanced 2013 Paper 2 under exam timing.

List I	List II
P.Alpha decay	1. $^{15}_{8}\mathrm{O} \to {}^{15}_{7}\mathrm{N} + .....$
Q. $\beta^{+}$ decay	2. $^{238}_{92}\mathrm{U} \to {}^{234}_{90}\mathrm{Th} + .....$
R.Fission	3. $^{185}_{83}\mathrm{Bi} \to {}^{184}_{82}\mathrm{Pb} + .....$
S.Proton emission	4. $^{239}_{94}\mathrm{Pu} \to {}^{140}_{57}\mathrm{La} + .....$

List – I	List – II
P. $\mathrm{PbO_2} + \mathrm{H_2SO_4} \xrightarrow{?} \mathrm{PbSO_4} + \mathrm{O_2} + \text{other product}$	1. $\mathrm{NO}$
Q. $\mathrm{Na_2S_2O_3} + \mathrm{H_2O} \xrightarrow{?} \mathrm{NaHSO_4} + \text{other product}$	2. $\mathrm{I_2}$
R. $\mathrm{N_2H_4} \xrightarrow{?} \mathrm{N_2} + \text{other product}$	3.Warm
S. $\mathrm{XeF_2} \xrightarrow{?} \mathrm{Xe} + \text{other product}$	4. $\mathrm{Cl_2}$

List – I	List – II
P.see figure	1.(i) $\mathrm{Hg(OAc)_2}$ ; (ii) $\mathrm{NaBH_4}$
Q.see figure	2.NaOEt
R.see figure	3.Et-Br
S.see figure	4.(i) $\mathrm{BH_3}$ ; (ii) $\mathrm{H_2O_2/NaOH}$

List – I	List – II
P. $(C_2H_5)_3N$ (X) + $CH_3COOH$ (Y)	1.Conductivity decreases and then increases
Q. $\mathrm{KI(0.1M)}$ (X) + $\mathrm{AgNO_3(0.01M)}$ (Y)	2.Conductivity decreases and then does not change much
R. $CH_3COOH$ (X) + $KOH$ (Y)	3.Conductivity increases and then does not change much
S. $NaOH$ (X) + $HI$ (Y)	4.Conductivity does not change much and then increases

List – I	List – II
P. $E^{\circ}(\mathrm{Fe^{3+}}, \mathrm{Fe})$	1. $-0.18\ \mathrm{V}$
Q. $E^{\circ}(4\mathrm{H_2O} \rightleftharpoons 4\mathrm{H^{+}} + 4\mathrm{OH^{-}})$	2. $-0.4\ \mathrm{V}$
R. $E^{\circ}(\mathrm{Cu^{2+}} + \mathrm{Cu} \longrightarrow 2\mathrm{Cu^{+}})$	3. $-0.04\ \mathrm{V}$
S. $E^{\circ}(\mathrm{Cr^{3+}}, \mathrm{Cr^{2+}})$	4. $-0.83\ \mathrm{V}$

List-I	List-II
P. $\left(\frac{1}{y^{2}}\left(\frac{\cos\left(\tan^{-1} y\right) + y\sin\left(\tan^{-1} y\right)}{\cot\left(\sin^{-1} y\right) + \tan\left(\sin^{-1} y\right)}\right)^{2} + y^{4}\right)^{1/2}$ takes value	1. $\frac{1}{2}\sqrt{\frac{5}{3}}$
Q.If $\cos x + \cos y + \cos z = 0 = \sin x + \sin y + \sin z$ then possible value of $\cos\frac{x - y}{2}$ is	2. $\sqrt{2}$
R.If $\cos\left(\frac{\pi}{4} - x\right)\cos 2x + \sin x \sin 2x \sec x = \cos x \sin 2x \sec x + \cos\left(\frac{\pi}{4} + x\right)\cos 2x$ then possible value of $\sec x$ is	3. $\frac{1}{2}$
S.If $\cot\left(\sin^{-1}\sqrt{1 - x^{2}}\right) = \sin\left(\tan^{-1}\left(x\sqrt{6}\right)\right)$ , $x \neq 0$ , then possible value of $x$ is	4. $1$

List-I	List-II
P. $m =$	1. $\frac{1}{2}$
Q.Maximum area of $\Delta EFG$ is	2. $4$
R. $y_{0} =$	3. $2$
S. $y_{1} =$	4. $1$

List-I	List-II
P.Volume of parallelepiped determined by vectors $\vec{a}, \vec{b}$ and $\vec{c}$ is 2. Then the volume of the parallelepiped determined by vectors $2\left(\vec{a} \times \vec{b}\right), 3\left(\vec{b} \times \vec{c}\right)$ and $\left(\vec{c} \times \vec{a}\right)$ is	1. $100$
Q.Volume of parallelepiped determined by vectors $\vec{a}, \vec{b}$ and $\vec{c}$ is 5. Then the volume of the parallelepiped determined by vectors $3\left(\vec{a} + \vec{b}\right), \left(\vec{b} + \vec{c}\right)$ and $2\left(\vec{c} + \vec{a}\right)$ is	2. $30$
R.Area of a triangle with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is 20. Then the area of the triangle with adjacent sides determined by vectors $\left(2\vec{a} + 3\vec{b}\right)$ and $\left(\vec{a} - \vec{b}\right)$ is	3. $24$
S.Area of a parallelogram with adjacent sides determined by vectors $\vec{a}$ and $\vec{b}$ is 30. Then the area of the parallelogram with adjacent sides determined by vectors $\left(\vec{a} + \vec{b}\right)$ and $\vec{a}$ is	4. $60$