JEE Advanced 2017 Paper 2 Question Paper

Question 1

The equation of the plane passing through the point $(1, 1, 1)$ and perpendicular to the planes $2x + y - 2z = 5$ and $3x - 6y - 2z = 7$, is

Accepted Answer

(C) $14x + 2y + 15z = 31$

Answer

(A) $14x + 2y - 15z = 1$

Answer

(B) $14x - 2y + 15z = 27$

Answer

(D) $-14x + 2y + 15z = 3$

Question 2

Let $O$ be the origin and let $PQR$ be an arbitrary triangle. The point $S$ is such that

$\overrightarrow{OP}\cdot\overrightarrow{OQ} + \overrightarrow{OR}\cdot\overrightarrow{OS} = \overrightarrow{OR}\cdot\overrightarrow{OP} + \overrightarrow{OQ}\cdot\overrightarrow{OS} = \overrightarrow{OQ}\cdot\overrightarrow{OR} + \overrightarrow{OP}\cdot\overrightarrow{OS}$

Then the triangle $PQR$ has $S$ as its

Accepted Answer

(D) orthocenter

Answer

(A) centroid

Answer

(B) circumcentre

Answer

(C) incentre

Question 3

If $y = y(x)$ satisfies the differential equation

$8\sqrt{x}\left(\sqrt{9+\sqrt{x}}\right)dy = \left(\sqrt{4+\sqrt{9+\sqrt{x}}}\right)^{-1}dx$, $\quad x > 0$

and $y(0) = \sqrt{7}$, then $y(256) =$

Accepted Answer

(A) $3$

Answer

(B) $9$

Answer

(C) $16$

Answer

(D) $80$

Question 4

If $f : \mathbb{R} 	o \mathbb{R}$ is a twice differentiable function such that $f''(x) > 0$ for all $x \in \mathbb{R}$, and $f\left(\dfrac{1}{2}ight) = \dfrac{1}{2}$, $f(1) = 1$, then

Accepted Answer

(D) $f'(1) > 1$

Answer

(A) $f'(1) \le 0$

Answer

(B) $0 < f'(1) \le \dfrac{1}{2}$

Answer

(C) $\dfrac{1}{2} < f'(1) \le 1$

Question 5

How many $3 	imes 3$ matrices $M$ with entries from $\{0, 1, 2\}$ are there, for which the sum of the diagonal entries of $M^{T}M$ is $5$ ?

Accepted Answer

(B) $198$

Answer

(A) $126$

Answer

(C) $162$

Answer

(D) $135$

Question 6

Let $S = \{1, 2, 3, \dots, 9\}$. For $k = 1, 2, \dots, 5$, let $N_{k}$ be the number of subsets of $S$, each containing five elements out of which exactly $k$ are odd. Then $N_{1} + N_{2} + N_{3} + N_{4} + N_{5} =$

Accepted Answer

(D) $126$

Answer

(A) $210$

Answer

(B) $252$

Answer

(C) $125$

Question 7

Three randomly chosen nonnegative integers $x$, $y$ and $z$ are found to satisfy the equation $x + y + z = 10$. Then the probability that $z$ is even, is

Accepted Answer

(B) $\dfrac{6}{11}$

Answer

(A) $\dfrac{36}{55}$

Answer

(C) $\dfrac{1}{2}$

Answer

(D) $\dfrac{5}{11}$

Question 8

Let $\alpha$ and $\beta$ be nonzero real numbers such that $2(\cos\beta - \cos\alpha) + \cos\alpha\cos\beta = 1$. Then which of the following is/are true ?

Accepted Answer

(A) $	an\left(\dfrac{\alpha}{2}ight) + \sqrt{3}	an\left(\dfrac{\beta}{2}ight) = 0$

Accepted Answer

(C) $	an\left(\dfrac{\alpha}{2}ight) - \sqrt{3}	an\left(\dfrac{\beta}{2}ight) = 0$

Answer

(B) $\sqrt{3}	an\left(\dfrac{\alpha}{2}ight) + 	an\left(\dfrac{\beta}{2}ight) = 0$

Answer

(D) $\sqrt{3}	an\left(\dfrac{\alpha}{2}ight) - 	an\left(\dfrac{\beta}{2}ight) = 0$

Question 9

If $f : \mathbb{R} 	o \mathbb{R}$ is a differentiable function such that $f'(x) > 2f(x)$ for all $x \in \mathbb{R}$, and $f(0) = 1$, then

Accepted Answer

(A) $f(x)$ is increasing in $(0, \infty)$

Accepted Answer

(C) $f(x) > e^{2x}$ in $(0, \infty)$

Answer

(B) $f(x)$ is decreasing in $(0, \infty)$

Answer

(D) $f'(x) < e^{2x}$ in $(0, \infty)$

Question 10

Let $f(x) = \dfrac{1 - x\left(1 + |1-x|ight)}{|1-x|}\cos\left(\dfrac{1}{1-x}ight)$ for $x 
e 1$. Then

Accepted Answer

(A) $\lim\limits_{x 	o 1^{-}} f(x) = 0$

Accepted Answer

(D) $\lim\limits_{x 	o 1^{+}} f(x)$ does not exist

Answer

(B) $\lim\limits_{x 	o 1^{-}} f(x)$ does not exist

Answer

(C) $\lim\limits_{x 	o 1^{+}} f(x) = 0$

Question 11

If $f(x) = \begin{vmatrix} \cos(2x) & \cos(2x) & \sin(2x) \ -\cos x & \cos x & -\sin x \ \sin x & \sin x & \cos x \end{vmatrix}$, then

Accepted Answer

(B) $f'(x) = 0$ at more than three points in $(-\pi, \pi)$

Accepted Answer

(C) $f(x)$ attains its maximum at $x = 0$

Answer

(A) $f'(x) = 0$ at exactly three points in $(-\pi, \pi)$

Answer

(D) $f(x)$ attains its minimum at $x = 0$

Question 12

If the line $x = \alpha$ divides the area of region $R = \{(x, y) \in \mathbb{R}^{2} : x^{3} \le y \le x,\ 0 \le x \le 1\}$ into two equal parts, then

Accepted Answer

(B) $\dfrac{1}{2} < \alpha < 1$

Accepted Answer

(C) $2\alpha^{4} - 4\alpha^{2} + 1 = 0$

Answer

(A) $0 < \alpha \le \dfrac{1}{2}$

Answer

(D) $\alpha^{4} + 4\alpha^{2} - 1 = 0$

Question 13

If $I = \displaystyle\sum_{k=1}^{98} \int_{k}^{k+1} \dfrac{k+1}{x(x+1)}\,dx$, then

Accepted Answer

(B) $I < \log_{e} 99$

Accepted Answer

(D) $I > \dfrac{49}{50}$

Answer

(A) $I > \log_{e} 99$

Answer

(C) $I < \dfrac{49}{50}$

Question 14

PARAGRAPH 1
Let $O$ be the origin, and $\overrightarrow{OX}$, $\overrightarrow{OY}$, $\overrightarrow{OZ}$ be three unit vectors in the directions of the sides $\overrightarrow{QR}$, $\overrightarrow{RP}$, $\overrightarrow{PQ}$, respectively, of a triangle $PQR$.

$\left|\overrightarrow{OX} 	imes \overrightarrow{OY}ight| =$

Accepted Answer

(A) $\sin(P + Q)$

Answer

(B) $\sin 2R$

Answer

(C) $\sin(P + R)$

Answer

(D) $\sin(Q + R)$

Question 15

PARAGRAPH 1
Let $O$ be the origin, and $\overrightarrow{OX}$, $\overrightarrow{OY}$, $\overrightarrow{OZ}$ be three unit vectors in the directions of the sides $\overrightarrow{QR}$, $\overrightarrow{RP}$, $\overrightarrow{PQ}$, respectively, of a triangle $PQR$.

If the triangle $PQR$ varies, then the minimum value of $\cos(P+Q) + \cos(Q+R) + \cos(R+P)$ is

Accepted Answer

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

Answer

(A) $-\dfrac{5}{3}$

Answer

(C) $\dfrac{3}{2}$

Answer

(D) $\dfrac{5}{3}$

Question 16

PARAGRAPH 2
Let $p$, $q$ be integers and let $\alpha$, $\beta$ be the roots of the equation $x^{2} - x - 1 = 0$, where $\alpha 
e \beta$. For $n = 0, 1, 2, \dots$, let $a_{n} = p\alpha^{n} + q\beta^{n}$.

FACT: If $a$ and $b$ are rational numbers and $a + b\sqrt{5} = 0$, then $a = 0 = b$.

$a_{12} =$

Accepted Answer

(B) $a_{11} + a_{10}$

Answer

(A) $a_{11} - a_{10}$

Answer

(C) $2a_{11} + a_{10}$

Answer

(D) $a_{11} + 2a_{10}$

Question 17

PARAGRAPH 2
Let $p$, $q$ be integers and let $\alpha$, $\beta$ be the roots of the equation $x^{2} - x - 1 = 0$, where $\alpha 
e \beta$. For $n = 0, 1, 2, \dots$, let $a_{n} = p\alpha^{n} + q\beta^{n}$.

FACT: If $a$ and $b$ are rational numbers and $a + b\sqrt{5} = 0$, then $a = 0 = b$.

If $a_{4} = 28$, then $p + 2q =$

Accepted Answer

(D) $12$

Answer

(A) $21$

Answer

(B) $14$

Answer

(C) $7$

Question 18

Consider an expanding sphere of instantaneous radius $R$ whose total mass remains constant. The expansion is such that the instantaneous density $\rho$ remains uniform throughout the volume. The rate of fractional change in density $\left(\dfrac{1}{\rho}\dfrac{d\rho}{dt}\right)$ is constant. The velocity $v$ of any point on the surface of the expanding sphere is proportional to

Accepted Answer

(A) $R$

Answer

(B) $R^{3}$

Answer

(C) $\dfrac{1}{R}$

Answer

(D) $R^{2/3}$

Question 19

Consider regular polygons with number of sides $n = 3, 4, 5, \dots$ as shown in the figure. The center of mass of all the polygons is at height $h$ from the ground. They roll on a horizontal surface about the leading vertex without slipping and sliding as depicted. The maximum increase in height of the locus of the center of mass for each polygon is $\Delta$. Then $\Delta$ depends on $n$ and $h$ as

Accepted Answer

(B) $\Delta = h\left(\dfrac{1}{\cos\left(\frac{\pi}{n}\right)} - 1\right)$

Answer

(A) $\Delta = h\sin^{2}\!\left(\dfrac{\pi}{n}\right)$

Answer

(C) $\Delta = h\sin\!\left(\dfrac{2\pi}{n}\right)$

Answer

(D) $\Delta = h	an^{2}\!\left(\dfrac{\pi}{2n}ight)$

Question 20

A photoelectric material having work-function $\phi_{0}$ is illuminated with light of wavelength $\lambda$ $\left(\lambda < \dfrac{hc}{\phi_{0}}\right)$. The fastest photoelectron has a de Broglie wavelength $\lambda_{d}$. A change in wavelength of the incident light by $\Delta\lambda$ results in change $\Delta\lambda_{d}$ in $\lambda_{d}$. then the ratio $\Delta\lambda_{d}/\Delta\lambda$ is proportional to

Accepted Answer

(D) $\lambda_{d}^{3}/\lambda^{2}$

Answer

(A) $\lambda_{d}/\lambda$

Answer

(B) $\lambda_{d}^{2}/\lambda$

Answer

(C) $\lambda_{d}^{3}/\lambda$

Question 21

A symmetric star conducting wire loop is carrying a steady state current $I$ as shown in figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is

Accepted Answer

(A) $\dfrac{\mu_{0}I}{4\pi a}\,6[\sqrt{3}-1]$

Answer

(B) $\dfrac{\mu_{0}I}{4\pi a}\,6[\sqrt{3}+1]$

Answer

(C) $\dfrac{\mu_{0}I}{4\pi a}\,3[\sqrt{3}-1]$

Answer

(D) $\dfrac{\mu_{0}I}{4\pi a}\,3[2-\sqrt{3}]$

Question 22

Three vectors $\vec{P}$, $\vec{Q}$ and $\vec{R}$ are shown in the figure. Let $S$ be any point on the vector $\vec{R}$. The distance between the point $P$ ad $S$ is $b|\vec{R}|$. The general relation among vectors $\vec{P}$, $\vec{Q}$ and $\vec{S}$ is

Accepted Answer

(A) $\vec{S} = (1-b)\vec{P} + b\vec{Q}$

Answer

(B) $\vec{S} = (b-1)\vec{P} + b\vec{Q}$

Answer

(C) $\vec{S} = (1-b^{2})\vec{P} + b\vec{Q}$

Answer

(D) $\vec{S} = (1-b)\vec{P} + b^{2}\vec{Q}$

Question 23

A rocket is launched normal to the surface of earth, away from the Sun, along the line joining the Sun and the Earth. The Sun is $3	imes10^{5}$ times heavier than the Earth and is at a distance $2.5	imes10^{4}$ times larger than the radius of the Earth. The escape velocity from Earth's gravitational field is $v_{e} = 11.2\ 	ext{km s}^{-1}$. The minimum initial $(v_{s})$ required for the rocket to be able to leave the Sun-earth system is closest to
(Ignore the rotation and revolution of the Earth and the presence of any other planet)

Accepted Answer

(B) $v_{s} = 42\ 	ext{km s}^{-1}$

Answer

(A) $v_{s} = 22\ 	ext{km s}^{-1}$

Answer

(C) $v_{s} = 62\ 	ext{km s}^{-1}$

Answer

(D) $v_{s} = 72\ 	ext{km s}^{-1}$

Question 24

A person measures the depth of a well by measuring the time interval between dropping a stone and receiving the sound of impact with the bottom of the well. The error in his measurement of time is $\delta T = 0.01$ seconds and he measures the depth of the well to be $L = 20$ meters. Take the acceleration due to gravity $g = 10\ 	ext{ms}^{-2}$ and the velocity of sound is $300\ 	ext{ms}^{-1}$. Then the fractional error in the measurement, $\delta L/L$, is closest to

Accepted Answer

(B) $1\ \%$

Answer

(A) $0.2\ \%$

Answer

(C) $3\ \%$

Answer

(D) $5\ \%$

Question 25

A uniform magnetic field $B$ exists in the region between $x = 0$ and $x = \dfrac{3R}{2}$ (region 2 in the figure) pointing normally into the plane of the paper. A particle with charge $+Q$ and momentum $p$ directed along x-axis enters region 2 from region 1 at point $P_{1}$ $(y = -R)$. Which of the following option(s) is/are correct?

Accepted Answer

(A) For $B > \dfrac{2}{3}\dfrac{p}{QR}$, the particle will re-enter region 1

Accepted Answer

(B) For $B = \dfrac{8}{13}\dfrac{p}{QR}$, the particle will enter region 3 through the point $P_{2}$ on x-axis

Answer

(C) When the particle re-enters region 1 through the longest possible path in region 2, the magnitude of the change in its linear momentum between point $P_{1}$ and the farthest point from y-axis is $p/\sqrt{2}$

Answer

(D) For a fixed $B$, particles of same charge $Q$ and same velocity $v$, the distance between the point $P_{1}$ and the point of re-entry into region 1 is inversely proportional to the mass of the particle

Question 26

The instantaneous voltages at three terminals marked X, Y and Z are given by

$V_{X} = V_{0}\sin\omega t$

$V_{Y} = V_{0}\sin\!\left(\omega t + \dfrac{2\pi}{3}\right)$ and

$V_{Z} = V_{0}\sin\!\left(\omega t + \dfrac{4\pi}{3}\right)$.

An ideal voltmeter is configured to read rms value of the potential difference between its terminals. It is connected between points X and Y and then between Y and Z. The reading(s) of the voltmeter will be

Accepted Answer

(A) $V_{XY}^{rms} = V_{0}\sqrt{\dfrac{3}{2}}$

Accepted Answer

(D) independent of the choice of the two terminals

Answer

(B) $V_{YZ}^{rms} = V_{0}\sqrt{\dfrac{1}{2}}$

Answer

(C) $V_{XY}^{rms} = V_{0}$

Question 27

A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius R as shown in the figure. Which of the following statements is/are correct?

Accepted Answer

(A) The electric flux passing through the *curved* surface of the hemisphere is $-\dfrac{Q}{2\varepsilon_{0}}\left(1 - \dfrac{1}{\sqrt{2}}\right)$

Accepted Answer

(D) The circumference of the flat surface is an equipotential

Answer

(B) Total flux through the curved and the flat surfaces is $\dfrac{Q}{\varepsilon_{0}}$

Answer

(C) The component of the electric field normal to the flat surface is constant over the surface

Question 28

Two coherent monochromatic point sources $S_{1}$ and $S_{2}$ of wavelength $\lambda = 600$ nm are placed symmetrically on either side of the centre of the circle as shown. The sources are separated by a distance $d = 1.8$ mm. This arrangement produces interference fringes visible as alternate bright and dark spots on the circumference of the circle. The angular separation between two consecutive bright spots is $\Delta	heta$. Which of the following options is/are correct?

Accepted Answer

(B) At $P_{2}$ the order of the fringe will be maximum

Accepted Answer

(C) The total number of fringes produced between $P_{1}$ and $P_{2}$ in the first quadrant is close to 3000

Answer

(A) A dark spot will be formed at the point $P_{2}$

Answer

(D) The angular separation between two consecutive bright spots decreases as we move from $P_{1}$ to $P_{2}$ along the first quadrant

Question 29

A source of constant voltage V is connected to a resistance R and two ideal inductors $L_{1}$ and $L_{2}$ through a switch S as shown. There is no mutual inductance between the two inductors. The switch S is initially open. At $t = 0$, the switch is closed and current begins to flow. Which of the following options is/are correct?

Accepted Answer

(A) After a long time, the current through $L_{1}$ will be $\dfrac{V}{R}\dfrac{L_{2}}{L_{1}+L_{2}}$

Accepted Answer

(B) After a long time, the current through $L_{2}$ will be $\dfrac{V}{R}\dfrac{L_{1}}{L_{1}+L_{2}}$

Accepted Answer

(C) The ratio of the currents through $L_{1}$ and $L_{2}$ is fixed at all times $(t > 0)$

Answer

(D) At $t = 0$, the current through the resistance R is $\dfrac{V}{R}$

Question 30

A rigid uniform bar AB of length L is slipping from its vertical position on a frictionless floor (as shown in the figure). At some instant of time, the angle made by the bar with the vortical is $	heta$. Which of the following statements about its motion is/are correct?

Accepted Answer

(A) The midpoint of the bar will fall vertically downward

Accepted Answer

(C) Instantaneous torque about the point in contact with the floor is proportional to $\sin	heta$

Accepted Answer

(D) When the bar makes an angle $	heta$ with the vertical, the displacement of its midpoint from the initial position is proportional to $(1-\cos	heta)$

Answer

(B) The trajectory of the point A is a parabola

Question 31

A wheel of radius R and mass M is placed at the bottom of a fixed step of height R as shown in the figure. A constant force is continuously applied on the surface of the wheel so that it just climbs the step without slipping. Consider the torque $	au$ about an axis normal to the plane of the paper passing through the point Q. Which of the following options is/are correct?

Accepted Answer

(A) If the force is applied at point P tangentially then $	au$ decreases continuously as the wheel climbs

Answer

(B) If the force is applied normal to the circumference at point X then $	au$ is constant

Answer

(C) If the force is applied normal to the circumference at point P then $	au$ is zero

Answer

(D) If the force is applied tangentially at point S then $	au 
eq 0$ but the wheel never climbs the step

Question 32

PARAGRAPH 1
Consider a simple RC circuit as shown in Figure 1.

Process 1: In the circuit the switch S is closed at $t = 0$ and the capacitor is fully charged to voltage $V_{0}$ (i.e. charging continues for time $T \gg RC$). In the process some dissipation $(E_{D})$ occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is $E_{C}$.

Process 2: In a different process the voltage is first set to $\dfrac{V_{0}}{3}$ and maintained for a charging time $T \gg RC$. Then the voltage is raised to $\dfrac{2V_{0}}{3}$ without discharging the capacitor and again maintained for time $T \gg RC$. The process is repeated one more time by raising the voltage to $V_{0}$ and the capacitor is charged to the same final voltage $V_{0}$ as in Process 1.
These two processes are depicted in Figure 2.

In Process 1, the energy stored in the capacitor $E_{C}$ and heat dissipated across resistance $E_{D}$ are related by:

Accepted Answer

(A) $E_{C} = E_{D}$

Answer

(B) $E_{C} = E_{D}\ln 2$

Answer

(C) $E_{C} = \dfrac{1}{2}E_{D}$

Answer

(D) $E_{C} = 2E_{D}$

Question 33

PARAGRAPH 1
Consider a simple RC circuit as shown in Figure 1.

Process 1: In the circuit the switch S is closed at $t = 0$ and the capacitor is fully charged to voltage $V_{0}$ (i.e. charging continues for time $T \gg RC$). In the process some dissipation $(E_{D})$ occurs across the resistance R. The amount of energy finally stored in the fully charged capacitor is $E_{C}$.

Process 2: In a different process the voltage is first set to $\dfrac{V_{0}}{3}$ and maintained for a charging time $T \gg RC$. Then the voltage is raised to $\dfrac{2V_{0}}{3}$ without discharging the capacitor and again maintained for time $T \gg RC$. The process is repeated one more time by raising the voltage to $V_{0}$ and the capacitor is charged to the same final voltage $V_{0}$ as in Process 1.
These two processes are depicted in Figure 2.

In Process 2, total energy dissipated across the resistance $E_{D}$ is:

Accepted Answer

(C) $E_{D} = \dfrac{1}{3}\left(\dfrac{1}{2}CV_{0}^{2}\right)$

Answer

(A) $E_{D} = \dfrac{1}{2}CV_{0}^{2}$

Answer

(B) $E_{D} = 3\left(\dfrac{1}{2}CV_{0}^{2}\right)$

Answer

(D) $E_{D} = 3CV_{0}^{2}$

Question 34

PARAGRAPH 2
One twirls a circular ring (of mass M and radius R) near the tip of one's finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is r. The finger rotates with an angular velocity $\omega_{0}$. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is $\mu$ and the acceleration due to gravity is g.

The total kinetic energy of the ring is

Accepted Answer

(C) $M\omega_{0}^{2}(R-r)^{2}$

Answer

(A) $M\omega_{0}^{2}R^{2}$

Answer

(B) $\dfrac{1}{2}M\omega_{0}^{2}(R-r)^{2}$

Answer

(D) $\dfrac{3}{2}M\omega_{0}^{2}(R-r)^{2}$

Question 35

PARAGRAPH 2
One twirls a circular ring (of mass M and radius R) near the tip of one's finger as shown in Figure 1. In the process the finger never loses contact with the inner rim of the ring. The finger traces out the surface of a cone, shown by the dotted line. The radius of the path traced out by the point where the ring and the finger is in contact is r. The finger rotates with an angular velocity $\omega_{0}$. The rotating ring rolls without slipping on the outside of a smaller circle described by the point where the ring and the finger is in contact (Figure 2). The coefficient of friction between the ring and the finger is $\mu$ and the acceleration due to gravity is g.

The minimum value of $\omega_{0}$ below which the ring will drop down is

Accepted Answer

(A) $\sqrt{\dfrac{g}{\mu(R-r)}}$

Answer

(B) $\sqrt{\dfrac{2g}{\mu(R-r)}}$

Answer

(C) $\sqrt{\dfrac{3g}{2\mu(R-r)}}$

Answer

(D) $\sqrt{\dfrac{g}{2\mu(R-r)}}$

Question 36

Pure water freezes at 273 K and 1 bar. The addition of 34.5 g of ethanol to 500 g of water changes the freezing point of the solution. Use the freezing point depression constant of water as 2 K kg mol$^{-1}$. The figures shown below represent plots of vapour pressure (V.P.) versus temperature (T). [molecular weight of ethanol is 46 g mol$^{-1}$]
Among the following, the option representing change the freezing point is

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 37

For the following cell,

$\mathrm{Zn}(s)\,|\,\mathrm{ZnSO_{4}}(aq)\,\|\,\mathrm{CuSO_{4}}(aq)\,|\,\mathrm{Cu}(s)$

When the concentration of $\mathrm{Zn^{2+}}$ is 10 times the concentration of $\mathrm{Cu^{2+}}$, the expression for $\Delta G$ (in J mol$^{-1}$) is
[F is Faraday constant; R is gas constant; T is temperature; $E^{0}(cell)$ = 1.1 V]

Accepted Answer

(B) $2.303\,RT - 2.2\,F$

Answer

(A) $1.1\,F$

Answer

(C) $2.303\,RT + 1.1\,F$

Answer

(D) $-2.2\,F$

Question 38

The standard state Gibbs free energies of formation of C(graphite) and C(diamond) at T = 298 K are

$\Delta_{f}G^{0}\left[\mathrm{C(graphite)}ight] = 0\ \mathrm{kJ\,mol^{-1}}$

$\Delta_{f}G^{0}\left[\mathrm{C(diamond)}ight] = 2.9\ \mathrm{kJ\,mol^{-1}}$

The standard state means that the pressure should be 1 bar, and substance should be pure at a given temperature. The conversion of graphite [C(graphite)] to diamond [C(diamond)] reduces its volume by $2	imes10^{-6}\ \mathrm{m^{3}\,mol^{-1}}$. If C(graphite) is converted to C(diamond) isothermally at T = 298 K, the pressure at which C(graphite) is in equilibrium with C(diamond), is
[Useful information: 1 J = 1 kg m$^{2}$s$^{-2}$; 1 Pa = 1 kg m$^{-1}$s$^{-2}$; 1 bar = $10^{5}$ Pa]

Accepted Answer

(A) 14501 bar

Answer

(B) 58001 bar

Answer

(C) 1450 bar

Answer

(D) 29001 bar

Question 39

Which of the following combination will produce $\mathrm{H_{2}}$ gas?

Accepted Answer

(C) Zn metal and NaOH(aq)

Answer

(A) Fe metal and conc. $\mathrm{HNO_{3}}$

Answer

(B) Cu metal and conc. $\mathrm{HNO_{3}}$

Answer

(D) Au metal and NaCN (aq) in the presence of air

Question 40

The order of the oxidation state of the phosphorus atom in $\mathrm{H_{3}PO_{2}}$, $\mathrm{H_{3}PO_{4}}$, $\mathrm{H_{3}PO_{3}}$, and $\mathrm{H_{4}P_{2}O_{6}}$ is

Accepted Answer

(C) $\mathrm{H_{3}PO_{4}} > \mathrm{H_{4}P_{2}O_{6}} > \mathrm{H_{3}PO_{3}} > \mathrm{H_{3}PO_{2}}$

Answer

(A) $\mathrm{H_{3}PO_{3}} > \mathrm{H_{3}PO_{2}} > \mathrm{H_{3}PO_{4}} > \mathrm{H_{4}P_{2}O_{6}}$

Answer

(B) $\mathrm{H_{3}PO_{4}} > \mathrm{H_{3}PO_{2}} > \mathrm{H_{3}PO_{3}} > \mathrm{H_{4}P_{2}O_{6}}$

Answer

(D) $\mathrm{H_{3}PO_{2}} > \mathrm{H_{3}PO_{3}} > \mathrm{H_{4}P_{2}O_{6}} > \mathrm{H_{3}PO_{4}}$

Question 41

The major product of the following reaction is

Accepted Answer

(C) (C)

Answer

(A) (A)

Answer

(B) (B)

Answer

(D) (D)

Question 42

The order of basicity among the following compound is

Accepted Answer

(C) IV > I > II > III

Answer

(A) II > I > IV > III

Answer

(B) IV > II > III > I

Answer

(D) I > IV > III > II

Question 43

The correct statement(s) about surface properties is(are)

Accepted Answer

(A) Adsorption is accompanied by decrease in enthalpy and decrease in entropy of the system

Accepted Answer

(B) The critical temperatures of ethane and nitrogen are 563 K and 126 K, respectively. The adsorption of ethane will be more than that of nitrogen on same amount of activated charcoal at a given temperature

Answer

(C) Cloud is an emulsion type of colloid in which liquid is dispersed phase and gas is dispersion medium

Answer

(D) Brownian motion of colloidal particles does not depend on the size of the particles but depends on viscosity of the solution

Question 44

For a reaction taking place in a container in equilibrium with its surroundings, the effect of temperature on its equilibrium constant $K$ in terms of change in entropy is described by

Accepted Answer

(B) With increase in temperature, the value of $K$ for endothermic reaction increases because unfavourable change in entropy of the surroundings decreases

Accepted Answer

(D) With increase in temperature, the value of $K$ for exothermic reaction decreases because favourable change in entropy of the surrounding decreases

Answer

(A) With increase in temperature, the value of $K$ for exothermic reaction decreases because entropy change of the system is positive

Answer

(C) With increase in temperature, the value of $K$ for endothermic reaction increases because the entropy change of the system is negative

Question 45

In a bimolecular reaction, the steric factor P was experimentally determined to be 4.5. The correct option(s) among the following is(are)

Accepted Answer

(A) The activation energy of the reaction is unaffected by the value of the steric factor

Accepted Answer

(B) Experimentally determined value of frequency factor is higher than that predicted by Arrhenius equation

Answer

(C) Since P = 4.5, the reaction will not proceed unless an effective catalyst is used

Answer

(D) The value of frequency factor predicted by Arrhenius equation is higher than that determined experimentally

Question 46

For the following compounds, the correct statement(s) with respect to nucleophilic substitution reactions is(are)

Accepted Answer

(A) **I** and **III** follow $\mathrm{S_{N}}1$ mechanism

Accepted Answer

(B) **I** and **II** follow $\mathrm{S_{N}}2$ mechanism

Accepted Answer

(C) Compound **IV** undergoes inversion of configuration

Accepted Answer

(D) The order of reactivity for **I**, **III** and **IV** is: **IV** > **I** > **III**

Question 47

Among the following, the correct statement(s) is(are)

Accepted Answer

(A) $\mathrm{Al(CH_{3})_{3}}$ has the three-centre two-electron bonds in its dimeric structure

Accepted Answer

(B) $\mathrm{BH_{3}}$ has the three-centre two-electron bonds in its dimeric structure

Accepted Answer

(D) The Lewis acidity of $\mathrm{BCl_{3}}$ is greater than that of $\mathrm{AlCl_{3}}$

Answer

(C) $\mathrm{AlCl_{3}}$ has the three-centre two-electron bonds in its dimeric structure

Question 48

The option(s) with only amphoteric oxides is(are)

Accepted Answer

(A) $\mathrm{Cr_{2}O_{3}}$, BeO, SnO, $\mathrm{SnO_{2}}$

Accepted Answer

(D) ZnO, $\mathrm{Al_{2}O_{3}}$, PbO, $\mathrm{PbO_{2}}$

Answer

(B) $\mathrm{Cr_{2}O_{3}}$, CrO, SnO, PbO

Answer

(C) NO, $\mathrm{B_{2}O_{3}}$, PbO, $\mathrm{SnO_{2}}$

Question 49

Compounds **P** and **R** upon ozonolysis produce **Q** and **S**, respectively. The molecular formula of **Q** and **S** is $\mathrm{C_{8}H_{8}O}$. **Q** undergoes Cannizzaro reaction but not haloform reaction, whereas **S** undergoes haloform reaction but not Cannizzaro reaction.

The option(s) with suitable combination of **P** and **R**, respectively, is(are)

Accepted Answer

(A) (A)

Accepted Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 50

PARAGRAPH 1
Upon heating $\mathrm{KClO_{3}}$ in the presence of catalytic amount of $\mathrm{MnO_{2}}$, a gas **W** is formed. Excess amount of **W** reacts with white phosphorus to give **X**. The reaction of **X** with $\mathrm{HNO_{3}}$ gives **Y** and **Z**.

**W** and **X** are, respectively

Accepted Answer

(C) $\mathrm{O_{2}}$ and $\mathrm{P_{4}O_{10}}$

Answer

(A) $\mathrm{O_{3}}$ and $\mathrm{P_{4}O_{6}}$

Answer

(B) $\mathrm{O_{2}}$ and $\mathrm{P_{4}O_{6}}$

Answer

(D) $\mathrm{O_{3}}$ and $\mathrm{P_{4}O_{10}}$

Question 51

PARAGRAPH 1
Upon heating $\mathrm{KClO_{3}}$ in the presence of catalytic amount of $\mathrm{MnO_{2}}$, a gas **W** is formed. Excess amount of **W** reacts with white phosphorus to give **X**. The reaction of **X** with $\mathrm{HNO_{3}}$ gives **Y** and **Z**.

**Y** and **Z** are, respectively

Accepted Answer

(B) $\mathrm{N_{2}O_{5}}$ and $\mathrm{HPO_{3}}$

Answer

(A) $\mathrm{N_{2}O_{3}}$ and $\mathrm{H_{3}PO_{4}}$

Answer

(C) $\mathrm{N_{2}O_{4}}$ and $\mathrm{HPO_{3}}$

Answer

(D) $\mathrm{N_{2}O_{4}}$ and $\mathrm{H_{3}PO_{3}}$

Question 52

PARAGRAPH 2
The reaction of compound **P** with $\mathrm{CH_{3}MgBr}$(excess) in $\mathrm{(C_{2}H_{5})_{2}O}$ followed by addition of $\mathrm{H_{2}O}$ gives **Q**. The compound **Q** on treatment with $\mathrm{H_{2}SO_{4}}$ at 0$^{\circ}$C gives **R**. The reaction of **R** with $\mathrm{CH_{3}COCl}$ in the presence of anhydrous $\mathrm{AlCl_{3}}$ in $\mathrm{CH_{2}Cl_{2}}$ followed by treatment with $\mathrm{H_{2}O}$ produces compound **S** [Et in compound **P** is ethyl group]

The product **S** is

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 53

PARAGRAPH 2
The reaction of compound **P** with $\mathrm{CH_{3}MgBr}$(excess) in $\mathrm{(C_{2}H_{5})_{2}O}$ followed by addition of $\mathrm{H_{2}O}$ gives **Q**. The compound **Q** on treatment with $\mathrm{H_{2}SO_{4}}$ at 0$^{\circ}$C gives **R**. The reaction of **R** with $\mathrm{CH_{3}COCl}$ in the presence of anhydrous $\mathrm{AlCl_{3}}$ in $\mathrm{CH_{2}Cl_{2}}$ followed by treatment with $\mathrm{H_{2}O}$ produces compound **S** [Et in compound **P** is ethyl group]

The reactions, **Q** to **R** and **R** to **S**, are

Accepted Answer

(C) Friedel-Crafts alkylation, dehydration and Friedel-Crafts acylation

Answer

(A) Dehydration and Friedel-Crafts acylation

Answer

(B) Aromatic sulfonation and Friedel-Crafts acylation

Answer

(D) Friedel-Crafts alkylation and Friedel-Crafts acylation

JEE Advanced 2017 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2017 Paper 2

Chemistry — JEE Advanced 2017 Paper 2

Mathematics — JEE Advanced 2017 Paper 2

Chapters tested in this paper

Attempt JEE Advanced 2017 Paper 2 under exam timing.