JEE Advanced 2019 Paper 2 Question Paper

Question 1

Three lines
$L_1 : \vec{r} = \lambda\hat{i},\ \lambda \in \mathbb{R}$
$L_2 : \vec{r} = \hat{k} + \mu\hat{j},\ \mu \in \mathbb{R}$ and
$L_3 : \vec{r} = \hat{i} + \hat{j} + 
u\hat{k},\ 
u \in \mathbb{R}$
are given. For which point(s) Q on $L_2$ can we find a point P on $L_1$ and a point R on $L_3$ so that P, Q and R are collinear?

Accepted Answer

(A) $\hat{k} - \dfrac{1}{2}\hat{j}$

Accepted Answer

(B) $\hat{k} + \dfrac{1}{2}\hat{j}$

Answer

(C) $\hat{k}$

Answer

(D) $\hat{k} + \hat{j}$

Question 2

Let $x \in \mathbb{R}$ and let
$P = \begin{bmatrix} 1 & 1 & 1 \ 0 & 2 & 2 \ 0 & 0 & 3 \end{bmatrix}$, $Q = \begin{bmatrix} 2 & x & x \ 0 & 4 & 0 \ x & x & 6 \end{bmatrix}$ and $R = PQP^{-1}$
Then which of the following options is/are correct?

Accepted Answer

(A) For $x = 0$, if $R\begin{bmatrix} 1 \ a \ b \end{bmatrix} = 6\begin{bmatrix} 1 \ a \ b \end{bmatrix}$, then $a + b = 5$

Accepted Answer

(C) $\det R = \det\begin{bmatrix} 2 & x & x \ 0 & 4 & 0 \ x & x & 5 \end{bmatrix} + 8$, for all $x \in \mathbb{R}$

Answer

(B) For $x = 1$, there exists a unit vector $\alpha\hat{i} + \beta\hat{j} + \gamma\hat{k}$ for which $R\begin{bmatrix} \alpha \ \beta \ \gamma \end{bmatrix} = \begin{bmatrix} 0 \ 0 \ 0 \end{bmatrix}$

Answer

(D) There exists a real number $x$ such that $PQ = QP$

Question 3

For non–negative integers n, let
$f(n) = \dfrac{\displaystyle\sum_{k=0}^{n} \sin\left(\dfrac{k+1}{n+2}\pi\right)\sin\left(\dfrac{k+2}{n+2}\pi\right)}{\displaystyle\sum_{k=0}^{n} \sin^{2}\left(\dfrac{k+1}{n+2}\pi\right)}$
Assuming $\cos^{-1}x$ takes values in $[0, \pi]$, which of the following options is/are correct?

Accepted Answer

(A) $f(4) = \dfrac{\sqrt{3}}{2}$

Accepted Answer

(B) If $\alpha = 	an(\cos^{-1}f(6))$, then $\alpha^{2} + 2\alpha - 1 = 0$

Accepted Answer

(C) $\sin(7\,\cos^{-1}f(5)) = 0$

Answer

(D) $\lim\limits_{n 	o \infty} f(n) = \dfrac{1}{2}$

Question 4

For $a \in \mathbb{R}$ $|a| > 1$, let
$\lim\limits_{n 	o \infty}\left( \dfrac{1 + \sqrt[3]{2} + .... + \sqrt[3]{n}}{n^{7/3}\left( \dfrac{1}{(an+1)^{2}} + \dfrac{1}{(an+2)^{2}} + ... + \dfrac{1}{(an+n)^{2}} ight)} ight) = 54$
Then the possible value(s) of a is/are

Accepted Answer

(A) 8

Accepted Answer

(D) $-9$

Answer

(B) $-6$

Answer

(C) 7

Question 5

Let $f(x) = \dfrac{\sin \pi x}{x^{2}}$, $x > 0$
Let $x_1 < x_2 < x_3 < ... < x_n < ....$ be all the points of local maximum of f and $y_1 < y_2 < y_3 < .... < y_n < ....$ be all the points of local minimum of f.
Then which of the following options is/are correct?

Accepted Answer

(B) $|x_n - y_n| > 1$ for every n

Accepted Answer

(C) $x_n \in \left(2n,\ 2n + \dfrac{1}{2}\right)$ for every n

Accepted Answer

(D) $x_{n+1} - x_n > 2$ for every n

Answer

(A) $x_1 < y_1$

Question 6

Let $f : \mathbb{R} 	o \mathbb{R}$ be given by $f(x) = (x - 1)(x - 2)(x - 5)$. Define
$F(x) = \displaystyle\int_{0}^{x} f(t)\, dt$, $x > 0$
Then which of the following options is/are correct?

Accepted Answer

(A) $F(x) 
eq 0$ for all $x \in (0, 5)$

Accepted Answer

(B) F has a local minimum at $x = 1$

Accepted Answer

(C) F has a local maximum at $x = 2$

Answer

(D) F has two local maxima and one local minimum in $(0, \infty)$

Question 7

Let $P_1 = I = \begin{bmatrix} 1 & 0 & 0 \ 0 & 1 & 0 \ 0 & 0 & 1 \end{bmatrix}$, $P_2 = \begin{bmatrix} 1 & 0 & 0 \ 0 & 0 & 1 \ 0 & 1 & 0 \end{bmatrix}$ $P_3 = \begin{bmatrix} 0 & 1 & 0 \ 1 & 0 & 0 \ 0 & 0 & 1 \end{bmatrix}$
$P_4 = \begin{bmatrix} 0 & 1 & 0 \ 0 & 0 & 1 \ 1 & 0 & 0 \end{bmatrix}$, $P_5 = \begin{bmatrix} 0 & 0 & 1 \ 1 & 0 & 0 \ 0 & 1 & 0 \end{bmatrix}$, $P_6 = \begin{bmatrix} 0 & 0 & 1 \ 0 & 1 & 0 \ 1 & 0 & 0 \end{bmatrix}$
and $X = \displaystyle\sum_{k=1}^{6} P_k \begin{bmatrix} 2 & 1 & 3 \ 1 & 0 & 2 \ 3 & 2 & 1 \end{bmatrix} P_k^{T}$
where $P_k^{T}$ denotes the transpose of the matrix $P_k$. Then which of the following options is/are correct?

Accepted Answer

(B) X is a symmetric matrix

Accepted Answer

(C) The sum of diagonal entries of X is 18

Accepted Answer

(D) If $X\begin{bmatrix} 1 \ 1 \ 1 \end{bmatrix} = \alpha\begin{bmatrix} 1 \ 1 \ 1 \end{bmatrix}$, then $\alpha = 30$

Answer

(A) $X - 30I$ is an invertible matrix

Question 8

Let $f : \mathbb{R} 	o \mathbb{R}$ be a function. We say that f has
PROPERTY 1 if $\lim\limits_{h 	o 0} \dfrac{f(h) - f(0)}{\sqrt{|h|}}$ exists and is finite, and
PROPERTY 2 if $\lim\limits_{h 	o 0} \dfrac{f(h) - f(0)}{h^{2}}$ exists and if finite.
Then which of the following options is/are correct?

Accepted Answer

(C) $f(x) = |x|$ has PROPERTY 1

Accepted Answer

(D) $f(x) = x^{2/3}$ has PROPERTY 1

Answer

(A) $f(x) = x|x|$ has PROPERTY 2

Answer

(B) $f(x) = \sin x$ has PROPERTY 2

Question 9

The value of the integral
$\displaystyle\int_{0}^{\pi/2} \dfrac{3\sqrt{\cos	heta}}{\left(\sqrt{\cos	heta} + \sqrt{\sin	heta}ight)^{5}}\, d	heta$ equals ____

Accepted Answer

0.50

Question 10

Let $\vec{a} = 2\hat{i} + \hat{j} - \hat{k}$ and $\vec{b} = \hat{i} + 2\hat{j} + \hat{k}$ be two vectors. Consider a vector $\vec{c} = \alpha\vec{a} + \beta\vec{b}$, $\alpha,\ \beta \in \mathbb{R}$. If the projection of $\vec{c}$ on the vector $\left(\vec{a} + \vec{b}ight)$ is $3\sqrt{2}$, then the minimum value of $\left(\vec{c} - \left(\vec{a} 	imes \vec{b}ight)ight)\cdot\vec{c}$ equals ____

Accepted Answer

18.00

Question 11

Five persons A, B, C, D and E are seated in a circular arrangement. If each of them is given a hat of one of the three colours red, blue and green, then the number of ways of distributing the hats such that the persons seated in adjacent seats get different coloured hats is ______

Accepted Answer

30.00

Question 12

Suppose $\det \begin{bmatrix} \displaystyle\sum_{k=0}^{n} k & \displaystyle\sum_{k=0}^{n} {}^{n}C_k k^{2} \ \displaystyle\sum_{k=0}^{n} {}^{n}C_k k & \displaystyle\sum_{k=0}^{n} {}^{n}C_k 3^{k} \end{bmatrix} = 0$ holds for some positive integer n. Then $\displaystyle\sum_{k=0}^{n} \dfrac{{}^{n}C_k}{k+1}$ equals. ____

Accepted Answer

6.20

Question 13

Let $|x|$ denote the number of elements in a set X. Let $S = \{1, 2, 3, 4, 5, 6\}$ be a sample space, where each element is equally likely to occur. If A and B are independent events associated with S, then the number of ordered pairs (A, B) such that $1 \le |B| < |A|$, equals ______

Accepted Answer

422.00

Question 14

The value of $\sec^{-1}\left( \dfrac{1}{4}\displaystyle\sum_{k=0}^{10} \sec\left(\dfrac{7\pi}{12} + \dfrac{k\pi}{2}\right)\sec\left(\dfrac{7\pi}{12} + \dfrac{(k+1)\pi}{2}\right) \right)$ in the interval $\left[-\dfrac{\pi}{4},\ \dfrac{3\pi}{4}\right]$ equals ____

Accepted Answer

0.00

Question 15

Answer the following by appropriately matching the lists based on the information given in the paragraph
Let $f(x) = \sin(\pi \cos x)$ and $g(x) = \cos(2\pi \sin x)$ be two functions defined for $x > 0$. Define the following sets whose elements are written in the increasing order:
$X = \{x : f(x) = 0\}$, $Y = \{x : f'(x) = 0\}$,
$Z = \{x : g(x) = 0\}$, $W = \{x : g'(x) = 0\}$
List – I contains the set X, Y, Z and W. List – II contains some information regarding these sets.
Which of the following is the only CORRECT combination?

Accepted Answer

(C) (II), (Q), (T)

Answer

(A) (II), (R), (S)

Answer

(B) (I), (Q), (U)

Answer

(D) (I), (P), (R)

Question 16

Answer the following by appropriately matching the lists based on the information given in the paragraph
Let $f(x) = \sin(\pi \cos x)$ and $g(x) = \cos(2\pi \sin x)$ be two functions defined for $x > 0$. Define the following sets whose elements are written in the increasing order:
$X = \{x : f(x) = 0\}$, $Y = \{x : f'(x) = 0\}$,
$Z = \{x : g(x) = 0\}$, $W = \{x : g'(x) = 0\}$
List – I contains the set X, Y, Z and W. List – II contains some information regarding these sets.
Which of the following is the only CORRECT combination?

Accepted Answer

(A) (IV), (P), (R), (S)

Answer

(B) (III), (P), (Q), (U)

Answer

(C) (IV), (Q), (T)

Answer

(D) (III), (R), (U)

Question 17

Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles $C_1 : x^{2} + y^{2} = 9$ and $C_2 : (x - 3)^{2} + (y - 4)^{2} = 16$, intersect at the points X and Y. Suppose that another circle $C_3 : (x - h)^{2} + (y - k)^{2} = r^{2}$ satisfies and following conditions:
(i) centre of $C_3$ is collinear with the centres of $C_1$ and $C_2$
(ii) $C_1$ and $C_2$ both lie inside $C_3$, and
(iii) $C_3$ touches $C_1$ at M and $C_2$ at N.
Let the line through X and Y intersect $C_3$ at Z and W, and let a common tangent of $C_1$ and $C_3$ be a tangent to the parabola $x^{2} = 8\alpha y$.
There are some expressions given in the List–I whose values are given in List–II below:
Which of the following is the only CORRECT combination?

Accepted Answer

(B) (II), (Q)

Answer

(A) (II), (T)

Answer

(C) (I), (U)

Answer

(D) (I), (S)

Question 18

Answer the following by appropriately matching the lists based on the information given in the paragraph
Let the circles $C_1 : x^{2} + y^{2} = 9$ and $C_2 : (x - 3)^{2} + (y - 4)^{2} = 16$, intersect at the points X and Y. Suppose that another circle $C_3 : (x - h)^{2} + (y - k)^{2} = r^{2}$ satisfies and following conditions:
(i) centre of $C_3$ is collinear with the centres of $C_1$ and $C_2$
(ii) $C_1$ and $C_2$ both lie inside $C_3$, and
(iii) $C_3$ touches $C_1$ at M and $C_2$ at N.
Let the line through X and Y intersect $C_3$ at Z and W, and let a common tangent of $C_1$ and $C_3$ be a tangent to the parabola $x^{2} = 8\alpha y$.
There are some expressions given in the List–I whose values are given in List–II below:
Which of the following is the only INCORRECT combination?

Accepted Answer

(A) (IV), (S)

Answer

(B) (III), (R)

Answer

(C) (IV), (U)

Answer

(D) (I), (P)

Question 19

In a Young's double slit experiment, the slit separation d is 0.3 mm and the screen distance D is 1 m. A parallel beam of light of wavelength 600 nm is incident on the slits at angle $\alpha$ as shown in figure. On the screen, the point O is equidistant from the slits and distance PO is 11.0 mm. Which of the following statements(s) is/are correct ?

Accepted Answer

(C) For $\alpha = \frac{0.36}{\pi}$ degree, there will be destructive interference at point P.

Answer

(A) For $\alpha = \frac{0.36}{\pi}$ degree, there will be destructive interference at point O.

Answer

(B) Fringe spacing depends on $\alpha$.

Answer

(D) For $\alpha = 0$, there will be constructive interference at point P.

Question 20

A block of mass 2M is attached to a massless spring with spring-constant k. This block is connected to two other blocks of masses M and 2M using two massless pulleys and strings. The accelerations of the blocks are $a_1$, $a_2$ and $a_3$ as shown in the figure. the system is released from rest with the spring in its unstretched state. The maximum extension of the spring is $x_0$. Which of the following option(s) is/are correct?
[g is the acceleration due to gravity. neglect friction]

Accepted Answer

(A) $a_2 - a_1 = a_1 - a_3$

Answer

(B) At an extension of $\frac{x_0}{4}$ of the spring, the magnitude of acceleration of the block connected to the spring is $\frac{3g}{10}$

Answer

(C) $x_0 = \frac{4Mg}{k}$

Answer

(D) When spring achieves an extension of $\frac{x_0}{2}$ for the first time, the speed of the block connected to the spring is $3g\sqrt{\frac{M}{5k}}$.

Question 21

A thin and uniform rod of mass M and length L is held vertical on a floor with large friction. The rod is released from rest so that it falls by rotating about its contact-point with the floor without slipping. Which of the following statement(s) is/are correct, when the rod makes an angle $60^\circ$ with vertical ?
[g is the acceleration due to gravity]

Accepted Answer

(A) The radial acceleration of the rod's center of mass will be $\frac{3g}{4}$

Accepted Answer

(B) The angular speed of the rod will be $\sqrt{\frac{3g}{2L}}$

Accepted Answer

(D) The normal reaction force from the floor on the rod will be $\frac{Mg}{16}$

Answer

(C) The angular acceleration of the rod will be $\frac{2g}{L}$

Question 22

A small particle of mass m moving inside a heavy, hollow and straight tube along the tube axis undergoes elastic collision at two ends. The tube has no friction and it is closed at one end by a flat surface while the other end is fitted with a heavy movable flat piston as shown in figure. When the distance of the piston from closed end is $L = L_0$ the particle speed is $v = v_0$. The piston is moved inward at a very low speed V such that $V << \frac{dL}{L}v_0$, where dL is the infinitesimal displacement of the piston. which of the following statement(s) is/are correct ?

Accepted Answer

(A) The particle's kinetic energy increases by a factor of 4 when the piston is moved inward from $L_0$ to $\frac{1}{2}L_0$.

Accepted Answer

(B) After each collision with the piston, the particle speed increases by 2V.

Answer

(C) If the piston moves inward by dL, the particle speed increases by $2v\frac{dL}{L}$

Answer

(D) The rate at which the particle strikes the piston is v/L

Question 23

Three glass cylinders of equal height H = 30 cm and same refractive index n = 1.5 are placed on a horizontal surface as shown in figure. Cylinder I has a flat top, cylinder II has a convex top and cylinder III has a concave top. The radii of curvature of the two curved tops are same (R = 3m). If $H_1$, $H_2$ and $H_3$ are the apparent depths of a point X on the bottom of the three cylinders, respectively, the correct statement(s) is/are:

Accepted Answer

(A) $H_2 > H_1$

Accepted Answer

(B) $H_2 > H_3$

Answer

(C) $H_3 > H_1$

Answer

(D) $0.8$ cm $< (H_2 - H_1) < 0.9$ cm

Question 24

An electric dipole with dipole moment $\frac{p_0}{\sqrt{2}}\left(\hat{i}+\hat{j}\right)$ is held fixed at the origin O in the presence of an uniform electric field of magnitude $E_0$. If the potential is constant on a circle of radius R centered at the origin as shown in figure, then the correct statement(s) is/are :
($\epsilon_0$ is permittivity of free space. R >> dipole size)

Accepted Answer

(B) Total electric field at point B is $\vec{E}_B = 0$

Accepted Answer

(C) $R = \left(\frac{p_0}{4\pi\epsilon_0 E_0}\right)^{1/3}$

Answer

(A) Total electric field at point A is $\vec{E}_A = \sqrt{2}E_0\left(\hat{i}+\hat{j}\right)$

Answer

(D) The magnitude of total electric field on any two points of the circle will be same.

Question 25

A free hydrogen atom after absorbing a photon of wavelength $\lambda_a$ gets excited from the state n = 1 to the state n = 4. Immediately after that the electron jumps to n = m state by emitting a photon of wavelength $\lambda_e$. Let the change in momentum of atom due to the absorption and the emission are $\Delta p_a$ and $\Delta p_e$. respectively. If $\frac{\lambda_a}{\lambda_e} = \frac{1}{5}$, which of the option(s) is /are correct ?
[Use hc = 1242 eV nm; 1 nm = $10^{-9}$m, h and c are Planck's constant and speed of light, respectively]

Accepted Answer

(B) The ratio of kinetic energy of the electron in the state n = m to the state n = 1 is $\frac{1}{4}$

Accepted Answer

(D) m = 2

Answer

(A) $\frac{\Delta p_a}{\Delta p_e} = \frac{1}{2}$

Answer

(C) $\lambda_e = 418$ nm

Question 26

A mixture of ideal gas contains 5 moles of monatomic gas and 1 mole of rigid diatomic gas is initially at pressure $P_0$, volume $V_0$, and temperature $T_0$. If the gas mixture is adiabatically compressed to a volume $\frac{V_0}{4}$, then the correct statement(s) is /are, (Given $2^{1.2} = 2.3$; $2^{3.2} = 9.2$; R is gas constant)

Accepted Answer

(A) Adiabatic constant of the gas mixture is 1.6

Accepted Answer

(B) The final pressure of the gas mixture after compression is in between $9P_0$ and $10P_0$

Accepted Answer

(C) The work $|W|$ done during the process is $13RT_0$

Answer

(D) The average kinetic energy of the gas mixture after compression is in between $18RT_0$ and $19RT_0$.

Question 27

Suppose a $^{226}_{88}\mathrm{Ra}$ nucleus at rest and in ground state undergoes $\alpha$-decay to a $^{222}_{86}\mathrm{Rn}$ nucleus in its excited state. The kinetic energy of the emitted $\alpha$ particle is found to be 4.44 MeV. $^{222}_{86}\mathrm{Rn}$ nucleus then goes to its ground state by $\gamma$-decay. The energy of the emitted $\gamma$ photon is ______keV.
[Given: atomic mass of $^{226}_{88}\mathrm{Ra}$ = 226.005 u, atomic mass of $^{222}_{86}\mathrm{Rn}$ = 222.000 u, atomic mass of $\alpha$ particle = 4.000 u, 1 u = 931 MeV/$c^2$, c is speed of the light]

Accepted Answer

135.00

Question 28

A ball is thrown from ground at an angle $	heta$ with horizontal and with an initial speed $u_0$. For the resulting projectile motion, the magnitude of average velocity of the ball up to the point when it hits the ground for the first time is $V_1$. After hitting the ground, the ball rebounds at the same angle $	heta$ but with a reduced speed of $u_0/\alpha$. Its motion continues for a long time as shown in figure. If the magnitude of average velocity of the ball for entire duration of motion is $0.8 V_1$, the value of $\alpha$ is_________.

Accepted Answer

4.00

Question 29

A 10 cm long perfectly conducting wire PQ is moving with a velocity 1 cm/s on a pair of horizontal rails of zero resistance. One side of the rails is connected to an inductor L = 1 mH and a resistance R = 1 $\Omega$ as shown in the figure. The horizontal rails, L and R lie in the same plane with a uniform magnetic field B = 1 T perpendicular to the plane. If the key S is closed at certain instant, the current in the circuit after 1 millisecond is $x 	imes 10^{-3}$ A, where the value of x is ________.
[Assume the velocity of wire PQ remains constant (1 cm/s) after key S is closed. Given: $e^{-1} = 0.37$, where e is base of the natural logarithm]

Accepted Answer

0.63

Question 30

A perfectly reflecting mirror of mass M mounted on a spring constitutes a spring-mass system of angular frequency $\Omega$ such that $\frac{4\pi M\Omega}{h} = 10^{24}\ \mathrm{m}^{-2}$ with h as Planck's constant. N photons of wavelength $\lambda = 8\pi 	imes 10^{-6}$ m strike the mirror simultaneously at normal incidence such that the mirror gets displaced by 1 $\mu$m. If the value of N is $x 	imes 10^{12}$, then the value of x is __________.
[Consider the spring as massless]

Accepted Answer

1.00

Question 31

A monochromatic light is incident from air on a refracting surface of prism of angle $75^\circ$ and refractive index $n_0 = \sqrt{3}$. The other refracting surface of the prism is coated by a thin film of material of refractive index n as shown in figure. The light suffers total internal reflection at the coated prism surface for an incidence angle of $	heta \le 60^\circ$. The value of $n^2$ is ________.

Accepted Answer

1.50

Question 32

An optical bench has 1.5 m long scale having four equal divisions in each cm. While measuring the focal length of a convex lens, the lens is kept at 75 cm mark of the scale and the object pin is kept at 45 cm mark. The image of the object pin on the other side of the lens overlaps with image pin that is kept at 135 cm mark. In this experiment, the percentage error in the measurement of the focal length of the lens is________.

Accepted Answer

1.39

Question 33

Answer the following by appropriately matching the list based on the information given in the paragraph.
A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $\mu$, $2\mu$, $3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L_0$ and $2L_0$. It is found that in string-1 ($\mu$) at free length $L_0$ and tension $T_0$ the fundamental mode frequency is $f_0$.
List-I gives the above four strings while list-II lists the magnitude of some quantity.
If the tension in each string is $T_0$, the correct match for the highest fundamental frequency in $f_0$ units will be,

Accepted Answer

(A) I $	o$ P, II $	o$ R, III $	o$ S, IV $	o$ Q

Answer

(B) I $	o$ Q, II $	o$ S, III $	o$ R, IV $	o$ P

Answer

(C) I $	o$ P, II $	o$ Q, III $	o$ T, IV $	o$ S

Answer

(D) I $	o$ Q, II $	o$ P, III $	o$ R, IV $	o$ T

Question 34

Answer the following by appropriately matching the list based on the information given in the paragraph.
A musical instrument is made using four different metal strings, 1, 2, 3 and 4 with mass per unit length $\mu$, $2\mu$, $3\mu$ and $4\mu$ respectively. The instrument is played by vibrating the strings by varying the free length in between the range $L_0$ and $2L_0$. It is found that in string-1 ($\mu$) at free length $L_0$ and tension $T_0$ the fundamental mode frequency is $f_0$.
List-I gives the above four strings while list-II lists the magnitude of some quantity.
The length of the string 1, 2, 3 and 4 are kept fixed at $L_0$, $\frac{3L_0}{2}$, $\frac{5L_0}{4}$ and $\frac{7L_0}{4}$, respectively. Strings 1, 2, 3 and 4 are vibrated at their $1^{st}$, $3^{rd}$, $5^{th}$ and $14^{th}$ harmonics, respectively such that all the strings have same frequency. The correct match for the tension in the four strings in the units of $T_0$ will be,

Accepted Answer

(A) I $	o$ P, II $	o$ Q, III $	o$ T, IV $	o$ U

Answer

(B) I $	o$ P, II $	o$ Q, III $	o$ R, IV $	o$ T

Answer

(C) I $	o$ P, II $	o$ R, III $	o$ T, IV $	o$ U

Answer

(D) I $	o$ T, II $	o$ Q, III $	o$ R, IV $	o$ U

Question 35

Answer the following by appropriately matching the list based on the information given in the paragraph.
In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $T\Delta X$, where T is temperature of the system and $\Delta X$ is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas $X = \frac{3}{2}R\ln\left(\frac{T}{T_A}\right) + R\ln\left(\frac{V}{V_A}\right)$. Here, R is gas constant, V is volume of gas. $T_A$ and $V_A$ are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
If the process carried out on one mole of monatomic ideal gas is as shown in figure in the PV-diagram with $P_0V_0 = \frac{1}{3}RT_0$, the correct match is,

Accepted Answer

(A) I $	o$ Q, II $	o$ R, III $	o$ S, IV $	o$ U

Answer

(B) I $	o$ Q, II $	o$ S, III $	o$ R, IV $	o$ U

Answer

(C) I $	o$ Q, II $	o$ R, III $	o$ P, IV $	o$ U

Answer

(D) I $	o$ S, II $	o$ R, III $	o$ Q, IV $	o$ T

Question 36

Answer the following by appropriately matching the list based on the information given in the paragraph.
In a thermodynamic process on an ideal monatomic gas, the infinitesimal heat absorbed by the gas is given by $T\Delta X$, where T is temperature of the system and $\Delta X$ is the infinitesimal change in a thermodynamic quantity X of the system. For a mole of monatomic ideal gas $X = \frac{3}{2}R\ln\left(\frac{T}{T_A}\right) + R\ln\left(\frac{V}{V_A}\right)$. Here, R is gas constant, V is volume of gas. $T_A$ and $V_A$ are constants.
The List-I below gives some quantities involved in a process and List-II gives some possible values of these quantities.
If the process on one mole of monatomic ideal gas is as shown in the TV-diagram with $P_0V_0 = \frac{1}{3}RT_0$, the correct match is,

Accepted Answer

(D) I $	o$ P, II $	o$ R, III $	o$ T, IV $	o$ P

Answer

(A) I $	o$ P, II $	o$ T, III $	o$ Q, IV $	o$ T

Answer

(B) I $	o$ S, II $	o$ T, III $	o$ Q, IV $	o$ U

Answer

(C) I $	o$ P, II $	o$ R, III $	o$ T, IV $	o$ S

Question 37

Choose the correct option(s) that give(s) an aromatic compound as the major product

Accepted Answer

(B) (B)

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(C) (C)

Question 38

Consider the following reactions (unbalanced)
Zn + hot conc. H$_{2}$SO$_{4}$ $\longrightarrow$ G + R + X
Zn + conc.NaOH $\longrightarrow$ T + Q
G + H$_{2}$S + NH$_{4}$OH $\longrightarrow$ Z(a precipitate) + X + Y
Choose the correct option(s)

Accepted Answer

(B) R is a V-shaped molecule

Accepted Answer

(C) Z is dirty white in colour

Accepted Answer

(D) Bond order of Q is 1 in its ground state

Answer

(A) The oxidation state of Zn in T is +1

Question 39

Which of the following reactions produce(s) propane as a major product?

Accepted Answer

(A) (A)

Accepted Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 40

Choose the correct option(s) from the following:

Accepted Answer

(B) Teflon is prepared by heating tetrafluoroethene in presence of a persulphate catalyst at high pressure

Accepted Answer

(D) Nylon-6 has amide linkages

Answer

(A) Cellulose has only $\alpha$-D-glucose units that are joined by glycosidic linkages

Answer

(C) Natural rubber is polyisoprene containing 	extit{trans} alkene units

Question 41

The ground state energy of hydrogen atom is $-$ 13.6 eV. Consider an electronic state $\psi$ of He$^{+}$ whose energy, azumuthal quantum number and magnetic quantum number are -3.4 eV, 2 and 0, respectively. Which of the following statement(s) is(are) true for the state $\psi$ ?

Accepted Answer

(A) It is a 4d state

Accepted Answer

(B) It has 2 angular nodes

Answer

(C) It has 3 radial nodes

Answer

(D) The nuclear charge experienced by the electron in this state is less than 2e, where e is the magnitude of the electronic charge

Question 42

The cyanide process of gold extraction involves leaching out gold from its ore with CN$^{-}$ in the presence of Q in water to form R. Subsequently, R is treated with T to obtain Au and Z. Choose the correct option(s)

Accepted Answer

(A) Z is $\left[\mathrm{Zn(CN)}_{4}\right]^{2-}$

Accepted Answer

(B) T is Zn

Accepted Answer

(D) Q is O$_{2}$

Answer

(C) R is $\left[\mathrm{Au(CN)}_{4}\right]^{-}$

Question 43

With reference to 	extit{aqua regia}, choose the correct option(s)

Accepted Answer

(A) The yellow colour of 	extit{aqua regia} is due to the presence of NOCl and Cl$_{2}$

Accepted Answer

(C) Reaction of gold with 	extit{aqua regia} produces an anion having Au in +3 oxidation state

Answer

(B) 	extit{Aqua regia} is prepared by mixing conc. HCl and conc. HNO$_{3}$ in 3 : 1 (	extit{v/v}) ratio

Answer

(D) Reaction of gold with 	extit{aqua regia} produces NO$_{2}$ in the absence of air

Question 44

Choose the correct option(s) for the following reaction sequence
Consider Q, R and S as major products

Accepted Answer

(A) (A)

Accepted Answer

(D) (D)

Answer

(B) (B)

Answer

(C) (C)

Question 45

Total number of isomers, considering both structural and stereoisomers, of cyclic ethers with the molecular formula C$_{4}$H$_{8}$O is________

Accepted Answer

10.00

Question 46

The mole fraction of urea in an aqueous urea solution containing 900 g of water is 0.05. If the density of the solution is 1.2 g cm$^{-3}$, the molarity of urea solution is_______
(Given data: Molar masses of urea and water are 60 g mol$^{-1}$ and 18 g mol$^{-1}$, respectively)

Accepted Answer

2.98

Question 47

Total number of 	extit{cis} N-Mn-Cl bond angles (that is, Mn $-$ N and Mn $-$ Cl bonds in 	extit{cis} positions) present in a molecule of 	extit{cis}-[Mn(en)$_{2}$Cl$_{2}$] complex is______(en = NH$_{2}$CH$_{2}$CH$_{2}$NH$_{2}$)

Accepted Answer

6.00

Question 48

The amount of water produced (in g) in the oxidation of 1 mole of rhombic sulphur by conc. HNO$_{3}$ to a compound with the highest oxidation state of sulphur is______
(Given data : Molar mass of water = 18 g mol$^{-1}$)

Accepted Answer

288.00

Question 49

The decomposition reaction $2\mathrm{N}_{2}\mathrm{O}_{5}\left(gight) \xrightarrow{\Delta} 2\mathrm{N}_{2}\mathrm{O}_{4}\left(gight) + \mathrm{O}_{2}\left(gight)$ is started in a closed cylinder under isothermal isochoric condition at an initial pressure of 1 atm. After Y $	imes$ 10$^{3}$ s, the pressure inside the cylinder is found to be 1.45 atm. If the rate constant of the reaction is 5 $	imes$ 10$^{-4}$ s$^{-1}$, assuming ideal gas behaviour, the value of 	extbf{Y} is________

Accepted Answer

2.30

Question 50

Total number of hydroxyl groups present in a molecule of the major product 	extbf{P} is__________

Accepted Answer

6.00

Question 51

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following, List-I contains some quantities for the n$^{th}$ orbit of the atom and List-II contains options showing how they depend on n.
Which of the following options has the correct combination considering List-I and List-II?

Accepted Answer

(A) (III), (P)

Answer

(B) (IV), (U)

Answer

(C) (III), (S)

Answer

(D) (IV), (Q)

Question 52

Consider the Bohr's model of a one-electron atom where the electron moves around the nucleus. In the following, List-I contains some quantities for the n$^{th}$ orbit of the atom and List-II contains options showing how they depend on n.
Which of the following options has the correct combination considering List-I and List-II?

Accepted Answer

(A) (I), (T)

Answer

(B) (II), (R)

Answer

(C) (I), (P)

Answer

(D) (II), (Q)

Question 53

Answer the following by appropriately matching the lists based on the information given in the paragraph
List-I includes starting materials and reagents of selected chemical reactions. List-II gives structures of compounds that may be formed as intermediate products and/or final products from the reactions of List-I.
Which of the following options has the correct combination considering List-I and List-II?

Accepted Answer

(B) (II), (P), (S), (U)

Answer

(A) (II), (P), (S), (T)

Answer

(C) (I), (S), (Q), (R)

Answer

(D) (I), (Q), (T), (U)

Question 54

Answer the following by appropriately matching the lists based on the information given in the paragraph
List-I includes starting materials and reagents of selected chemical reactions. List-II gives structures of compounds that may be formed as intermediate products and/or final products from the reactions of List-I.
Which of the following options has the correct combination considering List-I and List-II?

Accepted Answer

(B) (IV), (Q), (R)

Answer

(A) (IV), (Q), (U)

Answer

(C) (III), (S), (R)

Answer

(D) (III), (T), (U)

List-I	List-II
I.String-1 ( $\mu$ )	P. $1$
II.String-2 ( $2\mu$ )	Q. $\frac{1}{2}$
III.String-3 ( $3\mu$ )	R. $\frac{1}{\sqrt{2}}$
IV.String-4 ( $4\mu$ )	S. $\frac{1}{\sqrt{3}}$
	T. $\frac{3}{16}$
	U. $\frac{1}{16}$

List-I	List-II
I.String-1 ( $\mu$ )	P. $1$
II.String-2 ( $2\mu$ )	Q. $\frac{1}{2}$
III.String-3 ( $3\mu$ )	R. $\frac{1}{\sqrt{2}}$
IV.String-4 ( $4\mu$ )	S. $\frac{1}{\sqrt{3}}$
	T. $\frac{3}{16}$
	U. $\frac{1}{16}$

List-I	List-II
I.Work done by the system in process $1 \to 2 \to 3$	P. $\frac{1}{3}RT_0\ln 2$
II.Change in internal energy in process $1 \to 2 \to 3$	Q. $\frac{1}{3}RT_0$
III.Heat absorbed by the system in process $1 \to 2 \to 3$	R. $RT_0$
IV.Heat absorbed by the system in process $1 \to 2$	S. $\frac{4}{3}RT_0$
	T. $\frac{1}{3}RT_0(3+\ln 2)$
	U. $\frac{5}{6}RT_0$

List-I	List-II
I.Work done by the system in process $1 \to 2 \to 3$	P. $\frac{1}{3}RT_0\ln 2$
II.Change in internal energy in process $1 \to 2 \to 3$	Q. $\frac{1}{3}RT_0$
III.Heat absorbed by the system in process $1 \to 2 \to 3$	R. $RT_0$
IV.Heat absorbed by the system in process $1 \to 2$	S. $\frac{4}{3}RT_0$
	T. $\frac{1}{3}RT_0(3+\ln 2)$
	U. $\frac{5}{6}RT_0$

LIST-I	LIST-II
I.Radius of the n $^{th}$ orbit	P. $\propto n^{-2}$
II.Angular momentum of the electron in the n $^{th}$ orbit	Q. $\propto n^{-1}$
III.Kinetic energy of the electron in the n $^{th}$ orbit	R. $\propto n^{0}$
IV.Potential energy of the electron in the n $^{th}$ orbit	S. $\propto n^{1}$
	T. $\propto n^{2}$
	U. $\propto n^{1/2}$

JEE Advanced 2019 Paper 2 Question Paper with Answers

Physics — JEE Advanced 2019 Paper 2

Chemistry — JEE Advanced 2019 Paper 2

Mathematics — JEE Advanced 2019 Paper 2

Chapters tested in this paper

Attempt JEE Advanced 2019 Paper 2 under exam timing.

LIST-I	LIST-II
I.see figure	P.see figure
II.see figure	Q.see figure
III.see figure	R.see figure
IV.see figure	S.see figure
	T.see figure
	U.see figure

List – I	List – II
I.X	P. $\supseteq\left\{\dfrac{\pi}{2},\ \dfrac{3\pi}{2},\ 4\pi,\ 7\pi\right\}$
II.Y	Q.an arithmetic progression
III.Z	R.NOT an arithmetic progression
IV.W	S. $\supseteq\left\{\dfrac{\pi}{6},\ \dfrac{7\pi}{6},\ \dfrac{13\pi}{6}\right\}$
	T. $\supseteq\left\{\dfrac{\pi}{3},\ \dfrac{2\pi}{3},\ \pi\right\}$
	U. $\supseteq\left\{\dfrac{\pi}{6},\ \dfrac{3\pi}{4}\right\}$

List – I	List – II
I. $2h + k$	P.6
II. $\dfrac{\text{Length of ZW}}{\text{Length of XY}}$	Q. $\sqrt{6}$
III. $\dfrac{\text{Area of triangle MZN}}{\text{Area of triaangle ZMW}}$	R. $\dfrac{5}{4}$
IV. $\alpha$	S. $\dfrac{21}{5}$
	T. $2\sqrt{6}$
	U. $\dfrac{10}{3}$