JEE Advanced 2018 Paper 2 Question Paper

Question 1

Let T be the line passing through the points P($-2$, 7) and Q(2, $-5$). Let $F_{1}$ be the set of all pairs of circles ($S_{1}$, $S_{2}$) such that T is tangent to $S_{1}$ at P and tangent to $S_{2}$ at Q, and also such that $S_{1}$ and $S_{2}$ touch each other at a point, say, M. Let $E_{1}$ be the set representing the locus of M as the pair ($S_{1}$, $S_{2}$) varies in $F_{1}$. Let the set of all straight line segments joining a pair of distinct points of $E_{1}$ and passing through the point R(1, 1) be $F_{2}$. Let $E_{2}$ be the set of the mid-points of the line segments in the set $F_{2}$. Then, which of the following statement(s) is (are) TRUE ?

Accepted Answer

(B) The point $\left(\frac{4}{5}, \frac{7}{5}\right)$ does NOT lie in $E_{2}$

Accepted Answer

(D) The point $\left(0, \frac{3}{2}\right)$ does NOT lie in $E_{1}$

Answer

(A) The point $(-2, 7)$ lies in $E_{1}$

Answer

(C) The point $\left(\frac{1}{2}, 1\right)$ lies in $E_{2}$

Question 2

Let S be the set of all column matrices $\begin{bmatrix} b_{1} \ b_{2} \ b_{3} \end{bmatrix}$ such that $b_{1}$, $b_{2}$, $b_{3} \in R$ and the system of equations (in real variables)
$-x + 2y + 5z = b_{1}$
$2x - 4y + 3z = b_{2}$
$x - 2y + 2z = b_{3}$
has at least one solution. Then, which of the following system(s) (in real variables) has (have) at least one solution for each $\begin{bmatrix} b_{1} \ b_{2} \ b_{3} \end{bmatrix} \in S$ ?

Accepted Answer

(A) $x + 2y + 3z = b_{1}$, $4y + 5z = b_{2}$ and $x + 2y + 6z = b_{3}$

Accepted Answer

(D) $x + 2y + 5z = b_{1}$, $2x + 3z = b_{2}$ and $x + 4y - 5z = b_{3}$

Answer

(B) $x + y + 3z = b_{1}$, $5x + 2y + 6z = b_{2}$ and $-2x - y - 3z = b_{3}$

Answer

(C) $-x + 2y - 5z = b_{1}$, $2x - 4y + 10z = b_{2}$ and $x - 2y + 5z = b_{3}$

Question 3

Consider two straight lines, each of which is tangent to both the circle $x^{2} + y^{2} = \frac{1}{2}$ and the parabola $y^{2} = 4x$. Let these lines intersect at the point Q. Consider the ellipse whose center is at the origin O(0, 0) and whose semi-major axis is OQ. If the length of the minor axis of this ellipse is $\sqrt{2}$, then which of the following statement(s) is (are) TRUE ?

Accepted Answer

(A) For the ellipse, the eccentricity is $\frac{1}{\sqrt{2}}$ and the length of the latus rectum is 1

Accepted Answer

(C) The area of the region bounded by the ellipse between the lines $x = \frac{1}{\sqrt{2}}$ and $x = 1$ is $\frac{1}{4\sqrt{2}}(\pi - 2)$

Answer

(B) For the ellipse, the eccentricity is $\frac{1}{2}$ and the length of the latus rectum is $\frac{1}{2}$

Answer

(D) The area of the region bounded by the ellipse between the lines $x = \frac{1}{\sqrt{2}}$ and $x = 1$ is $\frac{1}{16}(\pi - 2)$

Question 4

Let $s$, $t$, $r$ be non-zero complex numbers and L be the set of solutions $z = x + iy$ ($x$, $y \in R$, $i = \sqrt{-1}$) of the equation $sz + t\bar{z} + r = 0$, where $\bar{z} = x - iy$. Then, which of the following statement(s) is (are) TRUE ?

Accepted Answer

(A) If L has exactly one element, then $|s| 
eq |t|$

Accepted Answer

(C) The number of elements in $L \cap \{z : |z - 1 + i| = 5\}$ is at most 2

Accepted Answer

(D) If L has more than one element, then L has infinitely many elements

Answer

(B) If $|s| = |t|$, then L has infinitely many elements

Question 5

Let $f : (0, \pi) 	o R$ be a twice differentiable function such that
$\lim_{t 	o x} \frac{f(x)\sin t - f(t)\sin x}{t - x} = \sin^{2} x$ for all $x \in (0, \pi)$
If $f\left(\frac{\pi}{6}ight) = -\frac{\pi}{12}$, then which of the following statement(s) is (are) TRUE ?

Accepted Answer

(B) $f(x) < \frac{x^{4}}{6} - x^{2}$ for all $x \in (0, \pi)$

Accepted Answer

(C) There exists $\alpha \in (0, \pi)$ such that $f'(\alpha) = 0$

Accepted Answer

(D) $f''\left(\frac{\pi}{2}\right) + f\left(\frac{\pi}{2}\right) = 0$

Answer

(A) $f\left(\frac{\pi}{4}\right) = \frac{\pi}{4\sqrt{2}}$

Question 6

The value of the integral $\int_{0}^{1/2} \frac{1+\sqrt{3}}{\left((x+1)^{2}(1-x)^{6}\right)^{1/4}}\, dx$ is ______ .

Accepted Answer

2

Question 7

Let P be a matrix of order $3 	imes 3$ such that all the entries in P are from the set $\{-1, 0, 1\}$. Then, the maximum possible value of the determinant of P is ______ .

Accepted Answer

4

Question 8

Let X be a set with exactly 5 elements and Y be a set with exactly 7 elements. If $\alpha$ is the number of one-one functions from X to Y and $\beta$ is the number of onto functions from Y to X, then the value of $\frac{1}{5!}(\beta - \alpha)$ is ______ .

Accepted Answer

119

Question 9

Let $f : R 	o R$ be a differentiable function with $f(0) = 0$. If $y = f(x)$ satisfies the differential equation
$\frac{dy}{dx} = (2+5y)(5y-2)$,
then the value of $\lim_{x 	o -\infty} f(x)$ is ______ .

Accepted Answer

0.4

Question 10

Let $f : R 	o R$ be a differentiable function with $f(0) = 1$ and satisfying the equation
$f(x + y) = f(x)f'(y) + f'(x)f(y)$ for all $x$, $y \in R$.
Then, the value of $\log_{e}(f(4))$ is ______ .

Accepted Answer

2

Question 11

Let P be a point in the first octant, whose image Q in the plane $x + y = 3$ (that is, the line segment PQ is perpendicular to the plane $x + y = 3$ and the mid-point of PQ lies in the plane $x + y = 3$) lies on the z-axis. Let the distance of P from the x-axis be 5. If R is the image of P in the xy-plane, then the length of PR is ______ .

Accepted Answer

8

Question 12

Consider the cube in the first octant with sides OP, OQ and OR of length 1, along the x-axis, y-axis and z-axis, respectively, where O(0, 0, 0) is the origin. Let $S\left(\frac{1}{2}, \frac{1}{2}, \frac{1}{2}ight)$ be the centre of the cube and T be the vertex of the cube opposite to the origin O such that S lies on the diagonal OT. If $\vec{p} = \overrightarrow{SP}$, $\vec{q} = \overrightarrow{SQ}$, $\vec{r} = \overrightarrow{SR}$ and $\vec{t} = \overrightarrow{ST}$, then the value of $\left|(\vec{p} 	imes \vec{q}) 	imes (\vec{r} 	imes \vec{t})ight|$ is ______ .

Accepted Answer

0.5

Question 13

Let
$X = ({}^{10}C_{1})^{2} + 2({}^{10}C_{2})^{2} + 3({}^{10}C_{3})^{2} + .... + 10({}^{10}C_{10})^{2}$,
where ${}^{10}C_{r}$, $r \in \{1, 2, ....., 10\}$ denote binomial coefficients. Then the value of $\frac{1}{1430}X$ is ______ .

Accepted Answer

646

Question 14

Let $E_{1} = \left\{x \in R : x 
eq 1 	ext{ and } \frac{x}{x-1} > 0ight\}$ and $E_{2} = \left\{x \in E_{1} : \sin^{-1}\left(\log_{e}\left(\frac{x}{x-1}ight)ight) 	ext{ is a real number}ight\}$
$\left(	ext{Here, the inverse trigonometric function } \sin^{-1}x 	ext{ assumes values in } \left[-\frac{\pi}{2}, \frac{\pi}{2}ight].ight)$
Let $f : E_{1} 	o R$ be the function defined by $f(x) = \log_{e}\left(\frac{x}{x-1}ight)$
and $g : E_{2} 	o R$ be the function defined by $g(x) = \sin^{-1}\left(\log_{e}\left(\frac{x}{x-1}ight)ight)$.
The correct option is :

Accepted Answer

(A) P $	o$ 4; Q $	o$ 2; R $	o$ 1; S $	o$ 1

Answer

(B) P $	o$ 3; Q $	o$ 3; R $	o$ 6; S $	o$ 5

Answer

(C) P $	o$ 4; Q $	o$ 2; R $	o$ 1; S $	o$ 6

Answer

(D) P $	o$ 4; Q $	o$ 3; R $	o$ 6; S $	o$ 5

Question 15

In a high school, a committee has to be formed from a group of 6 boys $M_{1}$, $M_{2}$, $M_{3}$, $M_{4}$, $M_{5}$, $M_{6}$ and 5 girls $G_{1}$, $G_{2}$, $G_{3}$, $G_{4}$, $G_{5}$.
(i) Let $\alpha_{1}$ be the total number of ways in which the committee can be formed such that the committee has 5 members, having exactly 3 boys and 2 girls.
(ii) Let $\alpha_{2}$ be the total number of ways in which the committee can be formed such that the committee has at least 2 members, and having an equal number of boys and girls.
(iii) Let $\alpha_{3}$ be the total number of ways in which the committee can be formed such that the committee has 5 members, at least 2 of them being girls.
(iv) Let $\alpha_{4}$ be the total number of ways in which the committee can be formed such that the committee has 4 members, having atleast 2 girls and such that both $M_{1}$ and $G_{1}$ are NOT in the committee together.
The correct option is :

Accepted Answer

(C) P $	o$ 4; Q $	o$ 6; R $	o$ 5; S $	o$ 2

Answer

(A) P $	o$ 4; Q $	o$ 6; R $	o$ 2; S $	o$ 1

Answer

(B) P $	o$ 1; Q $	o$ 4; R $	o$ 2; S $	o$ 3

Answer

(D) P $	o$ 4; Q $	o$ 2; R $	o$ 3; S $	o$ 1

Question 16

Let H : $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$, where $a > b > 0$, be a hyperbola in the xy-plane whose conjugate axis LM subtends an angle of $60^{\circ}$ at one of its vertices N. Let the area of the triangle LMN be $4\sqrt{3}$.
The correct option is :

Accepted Answer

(B) P $	o$ 4; Q $	o$ 3; R $	o$ 1; S $	o$ 2

Answer

(A) P $	o$ 4; Q $	o$ 2; R $	o$ 1; S $	o$ 3

Answer

(C) P $	o$ 4; Q $	o$ 1; R $	o$ 3; S $	o$ 2

Answer

(D) P $	o$ 3; Q $	o$ 4; R $	o$ 2; S $	o$ 1

Question 17

Let $f_{1} : R 	o R$, $f_{2} : \left(-\frac{\pi}{2}, \frac{\pi}{2}ight) 	o R$, $f_{3} : (-1, e^{\pi/2} - 2) 	o R$ and $f_{4} : R 	o R$ be functions defined by
(i) $f_{1}(x) = \sin\left(\sqrt{1 - e^{-x^{2}}}ight)$,
(ii) $f_{2}(x) = \begin{cases} \frac{|\sin x|}{	an^{-1} x} & 	ext{if } x 
eq 0 \\ 1 & 	ext{if } x = 0 \end{cases}$, where the inverse trigonometric function $	an^{-1}x$ assumes values in $\left(-\frac{\pi}{2}, \frac{\pi}{2}ight)$,
(iii) $f_{3}(x) = [\sin(\log_{e}(x + 2))]$, where, for $t \in R$, $[t]$ denotes the greatest integer less than or equal to $t$,
(iv) $f_{4}(x) = \begin{cases} x^{2}\sin\left(\frac{1}{x}ight) & 	ext{if } x 
eq 0 \\ 0 & 	ext{if } x = 0 \end{cases}$.
The correct option is :

Accepted Answer

(D) P $	o$ 2; Q $	o$ 1; R $	o$ 4; S $	o$ 3

Answer

(A) P $	o$ 2; Q $	o$ 3; R $	o$ 1; S $	o$ 4

Answer

(B) P $	o$ 4; Q $	o$ 1; R $	o$ 2; S $	o$ 3

Answer

(C) P $	o$ 4; Q $	o$ 2; R $	o$ 1; S $	o$ 3

Question 18

A particle of mass m is initially at rest at the origin. It is subjected to a force and starts moving along the x-axis. Its kinetic energy K changes with time as $dK/dt = \gamma t$, where $\gamma$ is a positive constant of appropriate dimensions. Which of the following statements is (are) true?

Accepted Answer

(A) The force applied on the particle is constant

Accepted Answer

(B) The speed of the particle is proportional to time

Accepted Answer

(D) The force is conservative

Answer

(C) The distance of the particle from the origin increases linearly with time

Question 19

Consider a thin square plate floating on a viscous liquid in a large tank. The height $h$ of the liquid in the tank is much less than the width of the tank. The floating plate is pulled horizontally with a constant velocity $u_{0}$. Which of the following statements is (are) true?

Accepted Answer

(A) The resistive force of liquid on the plate is inversely proportional to $h$

Accepted Answer

(C) The tangential (shear) stress on the floor of the tank increases with $u_{0}$

Accepted Answer

(D) The tangential (shear) stress on the plate varies linearly with the viscosity $\eta$ of the liquid

Answer

(B) The resistive force of liquid on the plate is independent of the area of the plate

Question 20

An infinitely long thin non-conducting wire is parallel to the z-axis and carries a uniform line charge density $\lambda$. It pierces a thin non-conducting spherical shell of radius $R$ in such a way that the arc $PQ$ subtends an angle $120^{\circ}$ at the centre $O$ of the spherical shell, as shown in the figure. The permittivity of free space is $\varepsilon_{0}$. Which of the following statements is (are) true?

Accepted Answer

(A) The electric flux through the shell is $\sqrt{3}R\lambda/\varepsilon_{0}$

Accepted Answer

(B) The z-component of the electric field is zero at all the points on the surface of the shell

Answer

(C) The electric flux through the shell is $\sqrt{2}R\lambda/\varepsilon_{0}$

Answer

(D) The electric field is normal to the surface of the shell at all points

Question 21

A wire is bent in the shape of a right angled triangle and is placed in front of a concave mirror of focal length $f$, as shown in the figure. Which of the figures shown in the four options qualitatively represent(s) the shape of the image of the bent wire? (These figures are not to scale.)

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 22

In a radioactive decay chain, $^{232}_{90}$Th nucleus decays to $^{212}_{82}$Pb nucleus. Let $N_{\alpha}$ and $N_{\beta}$ be the number of $\alpha$ and $\beta^{-}$ particles, respectively, emitted in this decay process. Which of the following statements is (are) true?

Accepted Answer

(A) $N_{\alpha} = 5$

Accepted Answer

(C) $N_{\beta} = 2$

Answer

(B) $N_{\alpha} = 6$

Answer

(D) $N_{\beta} = 4$

Question 23

In an experiment to measure the speed of sound by a resonating air column, a tuning fork of frequency 500 Hz is used. The length of the air column is varied by changing the level of water in the resonance tube. Two successive resonances are heard at air columns of length 50.7 cm and 83.9 cm. Which of the following statements is (are) true?

Accepted Answer

(A) The speed of sound determined from this experiment is 332 ms$^{-1}$

Accepted Answer

(C) The wavelength of the sound wave is 66.4 cm

Answer

(B) The end correction in this experiment is 0.9 cm

Answer

(D) The resonance at 50.7 cm corresponds to the fundamental harmonic

Question 24

A solid horizontal surface is covered with a thin layer of oil. A rectangular block of mass $m = 0.4$ kg is at rest on this surface. An impulse of 1.0 Ns is applied to the block at time t = 0 so that it starts moving along the x-axis with a velocity $v(t) = v_{0}e^{-t/	au}$, where $v_{0}$ is a constant and $	au$ = 4 s. The displacement of the block, in meters, at t = $	au$ is __________. Take $e^{-1}$ = 0.37.

Accepted Answer

6.30

Question 25

A ball is projected from the ground at an angle of $45^{\circ}$ with the horizontal surface. It reaches a maximum height of 120 $m$ and returns to the ground. Upon hitting the ground for the first time, it loses half of its kinetic energy. Immediately after the bounce, the velocity of the ball makes an angle of $30^{\circ}$ with the horizontal surface. The maximum height it reaches after the bounce, in metres, is ____________.

Accepted Answer

30.00

Question 26

A particle, of mass $10^{-3}$ kg and charge 1.0 C, is initially at rest. At time t = 0, the particle comes under the influence of an electric field $\vec{E}(t) = E_{0}\sin\omega t\,\hat{i}$, where $E_{0} = 1.0$ NC$^{-1}$ and $\omega = 10^{3}$ rad s$^{-1}$. Consider the effect of only the electrical force on the particle. Then the maximum speed, in m s$^{-1}$, attained by the particle at subsequent times is ____________.

Accepted Answer

2.00

Question 27

A moving coil galvanometer has 50 turns and each turn has an area $2 	imes 10^{-4}$ m$^{2}$. The magnetic field produced by the magnet inside the galvanometer is 0.02 T. The torsional constant of the suspension wire is $10^{-4}$ N m rad$^{-1}$. When a current flows through the galvanometer, a full scale deflection occurs if the coil rotates by 0.2 rad. The resistance of the coil of the galvanometer is 50 $\Omega$. This galvanometer is to be converted into an ammeter capable of measuring current in the range $0 - 1.0$ A. For this purpose, a shunt resistance is to be added in parallel to the galvanometer. The value of this shunt resistance, in ohms, is ___________.

Accepted Answer

5.56

Question 28

A steel wire of diameter 0.5 mm and Young's modulus $2 	imes 10^{11}$ Nm$^{-2}$ carries a load of mass M. The length of the wire with the load is 1.0 m. A vernier scale with 10 divisions is attached to the end of this wire. Next to the steel wire is a reference wire to which a main scale, of least count 1.0 mm, is attached. The 10 divisions of the vernier scale correspond to 9 divisions of the main scale. Initially, the zero of vernier scale coincides with the zero of main scale. If the load on the steel wire is increased by 1.2 kg, the vernier scale division which coincides with a main scale division is ___________. Take g = 10 ms$^{-2}$ and is $\pi$ = 3.2.

Accepted Answer

3.00

Question 29

One mole of a monatomic ideal gas undergoes an adiabatic expansion in which its volume becomes eight times its initial value. If the initial temperature of the gas is 100 K and the universal gas constant R = 8.0 J mol$^{-1}$K$^{-1}$, the decrease in its internal energy, in Joule, is___________.

Accepted Answer

900.00

Question 30

In a photoelectric experiment a parallel beam of monochromatic light with power of 200 W is incident on a perfectly absorbing cathode of work function 6.25 eV. The frequency of light is just above the threshold frequency so that the photoelectrons are emitted with negligible kinetic energy. Assume that the photoelectron emission efficiency is 100%. A potential difference of 500 V is applied between the cathode and the anode. All the emitted electrons are incident normally on the anode and are absorbed. The anode experiences a force $F = n 	imes 10^{-4}$ N due to the impact of the electrons. The value of n is ___________. Mass of the electron $m_{e} = 9 	imes 10^{-31}$ kg and 1.0 eV $= 1.6 	imes 10^{-19}$ J.

Accepted Answer

24.00

Question 31

Consider a hydrogen-like ionized atom with atomic number Z with a single electron. In the emission spectrum of this atom, the photon emitted in the n = 2 to n = 1 transition has energy 74.8 eV higher than the photon emitted in the n = 3 to n = 2 transition. The ionization energy of the hydrogen atom is 13.6 eV. The value of Z is ___________.

Accepted Answer

3.00

Question 32

The electric field E is measured at a point P(0, 0, d) generated due to various charge distributions and the dependence of E on d is found to be different for different charge distributions. List-I contains different relations between $E$ and d. List-II describes different electric charge distributions, along with their locations. Match the functions in List-I with the related charge distributions in List-II.

Accepted Answer

(B) P $\rightarrow$ 5; Q $\rightarrow$ 3; R $\rightarrow$ 1, 4; S $\rightarrow$ 2

Answer

(A) P $\rightarrow$ 5; Q $\rightarrow$ 3, 4; R $\rightarrow$ 1; S $\rightarrow$ 2

Answer

(C) P $\rightarrow$ 5; Q $\rightarrow$ 3; R $\rightarrow$ 1, 2; S $\rightarrow$ 4

Answer

(D) P $\rightarrow$ 4; Q $\rightarrow$ 2, 3; R $\rightarrow$ 1; S $\rightarrow$ 5

Question 33

A planet of mass M, has two natural satellites with masses $m_{1}$ and $m_{2}$. The radii of their circular orbits are $R_{1}$ and $R_{2}$ respectively. Ignore the gravitational force between the satellites. Define $v_{1}$, $L_{1}$, $K_{1}$ and $T_{1}$ to be, respectively, the orbital speed, angular momentum, kinetic energy and time period of revolution of satellite 1; and $v_{2}$, $L_{2}$, $K_{2}$ and $T_{2}$ to be the corresponding quantities of satellite 2. Given $m_{1}/m_{2} = 2$ and $R_{1}/R_{2} = 1/4$, match the ratios in List-I to the numbers in List-II.

Accepted Answer

(B) P $\rightarrow$ 3; Q $\rightarrow$ 2; R $\rightarrow$ 4; S $\rightarrow$ 1

Answer

(A) P $\rightarrow$ 4; Q $\rightarrow$ 2; R $\rightarrow$ 1; S $\rightarrow$ 3

Answer

(C) P $\rightarrow$ 2; Q $\rightarrow$ 3; R $\rightarrow$ 1; S $\rightarrow$ 4

Answer

(D) P $\rightarrow$ 2; Q $\rightarrow$ 3; R $\rightarrow$ 4; S $\rightarrow$ 1

Question 34

One mole of a monatomic ideal gas undergoes four thermodynamic processes as shown schematically in the PV-diagram below. Among these four processes, one is isobaric, one is isochoric, one is isothermal and one is adiabatic. Match the processes mentioned in List-1 with the corresponding statements in List-II.

Accepted Answer

(C) P $\rightarrow$ 3; Q $\rightarrow$ 4; R $\rightarrow$ 1; S $\rightarrow$ 2

Answer

(A) P $\rightarrow$ 4; Q $\rightarrow$ 3; R $\rightarrow$ 1; S $\rightarrow$ 2

Answer

(B) P $\rightarrow$ 1; Q $\rightarrow$ 3; R $\rightarrow$ 2; S $\rightarrow$ 4

Answer

(D) P $\rightarrow$ 3; Q $\rightarrow$ 4; R $\rightarrow$ 2; S $\rightarrow$ 1

Question 35

In the List-I below, four different paths of a particle are given as functions of time. In these functions, $\alpha$ and $\beta$ are positive constants of appropriate dimensions and $\alpha 
eq \beta$. In each case, the force acting on the particle is either zero or conservative. In List-II, five physical quantities of the particle are mentioned: $\vec{p}$ is the linear momentum, $\vec{L}$ is the angular momentum about the origin, K is the kinetic energy, U is the potential energy and E is the total energy. Match each path in List-I with those quantities in List-II, which are conserved for that path.

Accepted Answer

(A) P $\rightarrow$ 1, 2, 3, 4, 5; Q $\rightarrow$ 2, 5; R $\rightarrow$ 2, 3, 4, 5; S $\rightarrow$ 5

Answer

(B) P $\rightarrow$ 1, 2, 3, 4, 5; Q $\rightarrow$ 3, 5; R $\rightarrow$ 2, 3, 4, 5; S $\rightarrow$ 2, 5

Answer

(C) P $\rightarrow$ 2, 3, 4; Q $\rightarrow$ 5; R $\rightarrow$ 1, 2, 4; S $\rightarrow$ 2, 5

Answer

(D) P $\rightarrow$ 1, 2, 3, 5; Q $\rightarrow$ 2, 5; R $\rightarrow$ 2, 3, 4, 5; S $\rightarrow$ 2, 5

Question 36

The correct option(s) regarding the complex $\left[Co(en)(NH_{3})_{3}(H_{2}O)\right]^{3+}$ (en = $H_{2}NCH_{2}CH_{2}NH_{2}$) is (are)

Accepted Answer

(A) It has two geometrical isomers

Accepted Answer

(B) It will have three geometrical isomers if bidentate 'en' is replaced by two cyanide ligands

Accepted Answer

(D) It absorbs light at longer wavelength as compared to $[Co(en)(NH_{3})_{4}]^{3+}$

Answer

(C) It is paramagnetic

Question 37

The correct option(s) to distinguish nitrate salts of $Mn^{2+}$ and $Cu^{2+}$ taken separately is (are)

Accepted Answer

(B) Only $Cu^{2+}$ shows the formation of precipitate by passing $H_{2}S$ in acidic medium

Accepted Answer

(D) $Cu^{2+}/Cu$ has higher reduction potential than $Mn^{2+}/Mn$ (measured under similar conditions)

Answer

(A) $Mn^{2+}$ shows the characteristic green colour in the flame test

Answer

(C) Only $Mn^{2+}$ shows the formation of precipitate by passing $H_{2}S$ in faintly basic medium

Question 38

Aniline reacts with mixed acid (conc. $HNO_{3}$ and conc. $H_{2}SO_{4}$) at 288 K to give P (51%), Q (47%) and R(2%). The major product(s) of the following reaction sequence is (are)
R $\xrightarrow{	ext{(1) Ac}_{2}	ext{O, pyridine; (2) Br}_{2}	ext{, CH}_{3}	ext{CO}_{2}	ext{H; (3) H}_{3}	ext{O}^{+}	ext{; (4) NaNO}_{2}	ext{, HCl/273--278 K; (5) EtOH, }\Delta}$ S $\xrightarrow{	ext{(1) Sn/HCl; (2) Br}_{2}	ext{/H}_{2}	ext{O (excess); (3) NaNO}_{2}	ext{, HCl/273--278 K; (4) H}_{3}	ext{PO}_{2}}$ major product(s)

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 39

The Fischer presentation of D-glucose is given below

The correct structures(s) of $\beta$-L-glucopyranose is(are)

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 40

For a first order reaction $A(g) \rightarrow 2B(g) + C(g)$ at constant volume and 300 K, the total pressure at the beginning (t = 0) and at time t are $P_{0}$ and $P_{t}$, respectively. Initially, only A is present with concentration $[A]_{0}$, and $t_{1/3}$ is the time required for the partial pressure of A to reach $1/3^{rd}$ of its initial value. The correct option(s) is (are) (Assume that all these gases behave as ideal gases)

Accepted Answer

(A) (A)

Accepted Answer

(D) (D)

Answer

(B) (B)

Answer

(C) (C)

Question 41

For a reaction, $A \rightleftharpoons P$, the plots of [A] and [P] with time at temperatures $T_{1}$ and $T_{2}$ are given below.

If $T_{2} > T_{1}$, the correct statement(s) is (are) (Assume $\Delta H^{\ominus}$ and $\Delta S^{\ominus}$ are independent of temperature and ratio of $\ln K$ at $T_{1}$ to $\ln K$ at $T_{2}$ is greater than $T_{2}/T_{1}$. Here $H$, $S$, $G$ and $K$ are enthalpy, entropy, Gibbs energy and equilibrium constant, respectively.)

Accepted Answer

(A) $\Delta H^{\ominus} < 0, \Delta S^{\ominus} < 0$

Accepted Answer

(C) $\Delta G^{\ominus} < 0, \Delta S^{\ominus} < 0$

Answer

(B) $\Delta G^{\ominus} < 0, \Delta H^{\ominus} > 0$

Answer

(D) $\Delta G^{\ominus} < 0, \Delta S^{\ominus} > 0$

Question 42

The total number of compounds having at least one bridging oxo group among the molecules given below is ____.
$N_{2}O_{3}$, $N_{2}O_{5}$, $P_{4}O_{6}$, $P_{4}O_{7}$, $H_{4}P_{2}O_{5}$, $H_{5}P_{3}O_{10}$, $H_{2}S_{2}O_{3}$, $H_{2}S_{2}O_{5}$

Accepted Answer

6

Question 43

Galena (an ore) is partially oxidized by passing air through it at high temperature. After some time, the passage of air is stopped, but the heating is continued in a closed furnace such that the contents undergo self-reduction. The weight (in kg) of Pb produced per kg of $O_{2}$ consumed is ____.
(Atomic weights in g $mol^{-1}$: O = 16, S = 32, Pb = 207)

Accepted Answer

6.47

Question 44

To measure the quantity of $MnCl_{2}$ dissolved in an aqueous solution, it was completely converted to $KMnO_{4}$ using the reaction, $MnCl_{2} + K_{2}S_{2}O_{8} + H_{2}O \rightarrow KMnO_{4} + H_{2}SO_{4} + HCl$ (equation not balanced). Few drops of concentrated HCl were added to this solution and gently warmed. Further, oxalic acid (225 mg) was added in portions till the colour of the permanganate ion disappeared. The quantity of $MnCl_{2}$ (in mg) present in the initial solution is ____.
(Atomic weights in g $mol^{-1}$: Mn = 55, Cl = 35.5)

Accepted Answer

126

Question 45

For the given compound X, the total number of optically active stereoisomers is ____

This type of bond indicates that the configuration at the specific carbon and geometry of the double bond is fixed

This type of bond indicates that the configuration at the specific carbon and the geometry of the double bond is NOT fixed

Accepted Answer

7

Question 46

In the following reaction sequence, the amount of D (in g) formed from 10 moles of acetophenone is ____.
(Atomic weights in g $mol^{-1}$: H = 1, C = 12, N = 14, O = 16, Br = 80. The yield (%) corresponding to the product in each step is given in the parenthesis)

Accepted Answer

495

Question 47

The surface of copper gets tarnished by the formation of copper oxide. $N_{2}$ gas was passed to prevent the oxide formation during heating of copper at 1250 K. However, the $N_{2}$ gas contains 1 mole % of water vapour as impurity. The water vapour oxidises copper as per the reaction given below:
$2Cu(s) + H_{2}O(g) \rightarrow Cu_{2}O(s) + H_{2}(g)$
$p_{H_{2}}$ is the minimum partial pressure of $H_{2}$ (in bar) needed to prevent the oxidation at 1250 K. The value of $\ln\left(p_{H_{2}}\right)$ is ____.
(Given: total pressure = 1 bar, $R$ (universal gas constant) = 8 J $K^{-1}$ $mol^{-1}$, $\ln(10)$ = 2.3. Cu(s) and $Cu_{2}O(s)$ are mutually immiscible.
At 1250 K: $2Cu(s) + \frac{1}{2} O_{2}(g) \rightarrow Cu_{2}O(s)$; $\Delta G^{\ominus} = -78,000$ J $mol^{-1}$
$H_{2}(g) + \frac{1}{2} O_{2}(g) \rightarrow H_{2}O(g)$; $\Delta G^{\ominus} = -1,78,000$ J $mol^{-1}$; $G$ is the Gibbs energy)

Accepted Answer

-14.6

Question 48

Consider the following reversible reaction,
$A(g) + B(g) \rightleftharpoons AB(g)$
The activation energy of the backward reaction exceeds that of the forward reaction by 2RT (in J $mol^{-1}$). If the pre-exponential factor of the forward reaction is 4 times that of the reverse reaction, the absolute value of $\Delta G^{\ominus}$ (in J $mol^{-1}$) for the reaction at 300 K is ____.
(Given; $\ln(2) = 0.7$, RT = 2500 J $mol^{-1}$ at 300 K and $G$ is the Gibbs energy)

Accepted Answer

8500

Question 49

Consider an electrochemical cell: $A(s) | A^{n+} (aq, 2 M) || B^{2n+} (aq, 1 M) | B(s)$. The value of $\Delta H^{\ominus}$ for the cell reaction is twice that of $\Delta G^{\ominus}$ at 300 K. If the emf of the cell is zero, the $\Delta S^{\ominus}$ (in J $K^{-1}$ $mol^{-1}$) of the cell reaction per mole of B formed at 300 K is ____.
(Given: $\ln(2) = 0.7$, R (universal gas constant) = 8.3 J $K^{-1}$ $mol^{-1}$. $H$, $S$ and $G$ are enthalpy, entropy and Gibbs energy, respectively.)

Accepted Answer

-11.62

Question 50

Match each set of hybrid orbitals from LIST-I with complex(es) given in LIST-II.
The correct option is

Accepted Answer

(C) P $\rightarrow$ 6; Q $\rightarrow$ 4,5; R $\rightarrow$ 1; S $\rightarrow$ 2,3

Answer

(A) P $\rightarrow$ 5; Q $\rightarrow$ 4,6; R $\rightarrow$ 2,3; S $\rightarrow$ 1

Answer

(B) P $\rightarrow$ 5,6; Q $\rightarrow$ 4; R $\rightarrow$ 3; S $\rightarrow$ 1,2

Answer

(D) P $\rightarrow$ 4,6; Q $\rightarrow$ 5,6; R $\rightarrow$ 1,2; S $\rightarrow$ 3

Question 51

The desired product X can be prepared by reacting the major product of the reactions in LIST-I with one or more appropriate reagents in LIST-II.
(Given, order of migratory aptitude: aryl > alkyl > hydrogen)
The correct option is

Accepted Answer

(D) P $\rightarrow$ 1,5; Q $\rightarrow$ 2,3; R $\rightarrow$ 1,5; S $\rightarrow$ 2,3

Answer

(A) P $\rightarrow$ 1; Q $\rightarrow$ 2,3; R $\rightarrow$ 1,4; S $\rightarrow$ 2,4

Answer

(B) P $\rightarrow$ 1,5; Q $\rightarrow$ 3,4; R $\rightarrow$ 4,5; S $\rightarrow$ 3

Answer

(C) P $\rightarrow$ 1,5; Q $\rightarrow$ 3,4; R $\rightarrow$ 5; S $\rightarrow$ 2,4

Question 52

LIST-I contains reactions and LIST-II contains major products.
Match each reaction in LIST-I with one or more products in LIST-II and choose the correct option.

Accepted Answer

(B) P $\rightarrow$ 1,4; Q $\rightarrow$ 2; R $\rightarrow$ 4; S $\rightarrow$ 3

Answer

(A) P $\rightarrow$ 1,5; Q $\rightarrow$ 2; R $\rightarrow$ 3; S $\rightarrow$ 4

Answer

(C) P $\rightarrow$ 1,4; Q $\rightarrow$ 1,2; R $\rightarrow$ 3,4; S $\rightarrow$ 4

Answer

(D) P $\rightarrow$ 4,5; Q $\rightarrow$ 4; R $\rightarrow$ 4; S $\rightarrow$ 3,4

Question 53

Dilution processes of different aqueous solutions, with water, are given in LIST-I. The effects of dilution of the solutions on $[H^{+}]$ are given in LIST-II.
(Note: Degree of dissociation ($\alpha$) of weak acid and weak base is << 1; degree of hydrolysis of salt <<1; $[H^{+}]$ represents the concentration of $H^{+}$ ions)
Match each process given in LIST-I with one or more effect(s) in LIST-II. The correct option is

Accepted Answer

(D) P $\rightarrow$ 1; Q $\rightarrow$ 5; R $\rightarrow$ 4; S $\rightarrow$ 1

Answer

(A) P $\rightarrow$ 4; Q $\rightarrow$ 2; R $\rightarrow$ 3; S $\rightarrow$ 1

Answer

(B) P $\rightarrow$ 4; Q $\rightarrow$ 3; R $\rightarrow$ 2; S $\rightarrow$ 3

Answer

(C) P $\rightarrow$ 1; Q $\rightarrow$ 4; R $\rightarrow$ 5; S $\rightarrow$ 3

LIST-I	LIST-II
P.E is independent of d	1.A point charge Q at the origin
Q. $E \propto \dfrac{1}{d}$	2.A small dipole with point charges Q at $(0, 0, \ell)$ and $-Q$ at $(0, 0, -\ell)$ . Take $2\ell \ll d$
R. $E \propto \dfrac{1}{d^{2}}$	3.An infinite line charge coincident with the x-axis, with uniform linear charge density $\lambda$
S. $E \propto \dfrac{1}{d^{3}}$	4.Two infinite wires carrying uniform linear charge density parallel to the x- axis. The one along $(y = 0, z = \ell)$ has a charge density $+\lambda$ and the one along $(y = 0, z = -\ell)$ has a charge density $-\lambda$ . Take $2\ell << d$
	5.Infinite plane charge coincident with the xy-plane with uniform surface charge density

LIST-I	LIST-II
P. $\dfrac{v_{1}}{v_{2}}$	1. $\dfrac{1}{8}$
Q. $\dfrac{L_{1}}{L_{2}}$	2.1
R. $\dfrac{K_{1}}{K_{2}}$	3.2
S. $\dfrac{T_{1}}{T_{2}}$	4.8

LIST-I	LIST-II
P.In process I	1.Work done by the gas is zero
Q.In process II	2.Temperature of the gas remains unchanged
R.In process III	3.No heat is exchanged between the gas and its surroundings
S.In process IV	4.Work done by the gas is $6P_{0}V_{0}$

LIST-I	LIST-II
P. $\vec{r}(t) = \alpha t\,\hat{i} + \beta t\,\hat{j}$	1. $\vec{p}$
Q. $\vec{r}(t) = \alpha \cos \omega t\,\hat{i} + \beta \sin \omega t\,\hat{j}$	2. $\vec{L}$
R. $\vec{r}(t) = \alpha(\cos \omega t\,\hat{i} + \sin \omega t\,\hat{j})$	3.K
S. $\vec{r}(t) = \alpha t\,\hat{i} + \dfrac{\beta}{2}t^{2}\,\hat{j}$	4.U
	5.E

LIST-I	LIST-II
P. $dsp^{2}$	1. $[FeF_{6}]^{4-}$
Q. $sp^{3}$	2. $[Ti(H_{2}O)_{3}Cl_{3}]$
R. $sp^{3}d^{2}$	3. $[Cr(NH_{3})_{6}]^{3+}$
S. $d^{2}sp^{3}$	4. $[FeCl_{4}]^{2-}$
	5. $Ni(CO)_{4}$
	6. $[Ni(CN)_{4}]^{2-}$

JEE Advanced 2018 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2018 Paper 2

Chemistry — JEE Advanced 2018 Paper 2

Mathematics — JEE Advanced 2018 Paper 2

Chapters tested in this paper

Attempt JEE Advanced 2018 Paper 2 under exam timing.

LIST-I	LIST-II
P.see figure	1. $I_{2}$ , NaOH
Q.see figure	2. $[Ag(NH_{3})_{2}]OH$
R.see figure	3.Fehling solution
S.see figure	4.HCHO, NaOH
	5.NaOBr

LIST-I	LIST-II
P.see figure	1.see figure
Q.see figure	2.see figure
R.see figure	3.see figure
S.see figure	4.see figure
	5.see figure

LIST-I	LIST-II
P.(10 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 60 mL	1.the value of $[H^{+}]$ does not change on dilution
Q.(20 mL of 0.1 M NaOH + 20 mL of 0.1 M acetic acid) diluted to 80 mL	2.the value of $[H^{+}]$ changes to half of its initial value on dilution
R.(20 mL of 0.1 M HCl + 20 mL of 0.1 M ammonia solution) diluted to 80 mL	3.the value of $[H^{+}]$ changes to two times of its initial value on dilution
S.10 mL saturated solution of $Ni(OH)_{2}$ in equilibrium with excess solid $Ni(OH)_{2}$ is diluted to 20 mL (solid $Ni(OH)_{2}$ is still present after dilution).	4.the value of $[H^{+}]$ changes to $\frac{1}{\sqrt{2}}$ times of its initial value on dilution
	5.the value of $[H^{+}]$ changes to $\sqrt{2}$ times of its initial value on dilution

LIST-I	LIST-II
P.The range of $f$ is	1. $\left(-\infty, \frac{1}{1-e}\right] \cup \left[\frac{e}{e-1}, \infty\right)$
Q.The range of $g$ contains	2. $(0, 1)$
R.The domain of $f$ contains	3. $\left[-\frac{1}{2}, \frac{1}{2}\right]$
S.The domain of $g$ is	4. $(-\infty, 0) \cup (0, \infty)$
	5. $\left(-\infty, \frac{e}{e-1}\right]$
	6. $(-\infty, 0) \cup \left(\frac{1}{2}, \frac{e}{e-1}\right]$

LIST-I	LIST-II
P.The value of $\alpha_{1}$ is	1.136
Q.The value of $\alpha_{2}$ is	2.189
R.The value of $\alpha_{3}$ is	3.192
S.The value of $\alpha_{4}$ is	4.200
	5.381
	6.461

LIST-I	LIST-II
P.The length of the conjugate axis of H is	1.8
Q.The eccentricity of H is	2. $\frac{4}{\sqrt{3}}$
R.The distance between the foci of H is	3. $\frac{2}{\sqrt{3}}$
S.The length of the latus rectum of H is	4.4

LIST-I	LIST-II
P.The function $f_{1}$ is	1.NOT continuous at $x = 0$
Q.The function $f_{2}$ is	2.continuous at $x = 0$ and NOT differentiable at $x = 0$
R.The function $f_{3}$ is	3.differentiable at $x = 0$ and its derivative is NOT continuous at $x = 0$
S.The function $f_{4}$ is	4.differentiable at $x = 0$ and its derivative is continuous at $x = 0$