JEE Advanced 2020 Paper 1 Question Paper

Question 1

Suppose a, b denote the distinct real roots of the quadratic polynomial $x^{2} + 20x - 2020$ and suppose c,d denote the distinct complex roots of the quadratic polynomial $x^{2} - 20x + 2020$. Then the value of

$ac(a - c) + ad(a - d) + bc(b - c) + bd(b - d)$

is

Accepted Answer

(D) $16000$

Answer

(A) $0$

Answer

(B) $8000$

Answer

(C) $8080$

Question 2

If the function $f : \mathbb{R} 	o \mathbb{R}$ is defined by $f(x) = |x|(x - \sin x)$, then which of the following statements is TRUE ?

Accepted Answer

(C) $f$ is BOTH one-one and onto

Answer

(A) $f$ is one-one, but NOT onto

Answer

(B) $f$ is onto, but NOT one-one

Answer

(D) $f$ is NEITHER one-one NOR onto

Question 3

Let the functions $f : \mathbb{R} 	o \mathbb{R}$ and $g : \mathbb{R} 	o \mathbb{R}$ be defined by

$f(x) = e^{x-1} - e^{-|x-1|}$ and $g(x) = \frac{1}{2}\left(e^{x-1} + e^{1-x}ight)$.

Then the area of the region in the first quadrant bounded by the curves $y = f(x)$, $y = g(x)$ and $x = 0$ is

Accepted Answer

(A) $\left(2 - \sqrt{3}\right) + \frac{1}{2}\left(e - e^{-1}\right)$

Answer

(B) $\left(2 + \sqrt{3}\right) + \frac{1}{2}\left(e - e^{-1}\right)$

Answer

(C) $\left(2 - \sqrt{3}\right) + \frac{1}{2}\left(e + e^{-1}\right)$

Answer

(D) $\left(2 + \sqrt{3}\right) + \frac{1}{2}\left(e + e^{-1}\right)$

Question 4

Let a, b and $\lambda$ be positive real numbers. Suppose P is an end point of the latus rectum of the parabola $y^{2} = 4\lambda x$, and suppose the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ passes through the point P. If the tangents to the parabola and the ellipse at the point P are perpendicular to each other, then the eccentricity of the ellipse is

Accepted Answer

(A) $\frac{1}{\sqrt{2}}$

Answer

(B) $\frac{1}{2}$

Answer

(C) $\frac{1}{3}$

Answer

(D) $\frac{2}{5}$

Question 5

Let $C_{1}$ and $C_{2}$ be two biased coins such that the probabilities of getting head in a single toss are $\frac{2}{3}$ and $\frac{1}{3}$, respectively. Suppose $\alpha$ is the number of heads that appear when $C_{1}$ is tossed twice, independently, and suppose $\beta$ is the number of heads that appear when $C_{2}$ is tossed twice, independently, Then probability that the roots of the quadratic polynomial $x^{2} - \alpha x + \beta$ are real and equal, is

Accepted Answer

(B) $\frac{20}{81}$

Answer

(A) $\frac{40}{81}$

Answer

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

Answer

(D) $\frac{1}{4}$

Question 6

Consider all rectangles lying in the region

$\left\{(x, y) \in \mathbb{R} 	imes \mathbb{R} : 0 \leq x \leq \frac{\pi}{2} 	ext{ and } 0 \leq y \leq 2\sin(2x)ight\}$

and having one side on the x-axis. The area of the rectangle which has the maximum perimeter among all such rectangles, is

Accepted Answer

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

Answer

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

Answer

(B) $\pi$

Answer

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

Question 7

Let the function $f : \mathbb{R} 	o \mathbb{R}$ be defined by $f(x) = x^{3} - x^{2} + (x - 1)\sin x$ and let $g : \mathbb{R} 	o \mathbb{R}$ be an arbitrary function. Let fg $: \mathbb{R} 	o \mathbb{R}$ be the product function defined by $(f g)(x) = f(x)\, g(x)$. Then which of the following statements is/are TRUE ?

Accepted Answer

(A) If g is continuous at $x = 1$, then fg is differentiable at $x = 1$

Accepted Answer

(C) If g is differentiable at $x = 1$, then fg is differentiable at $x = 1$

Answer

(B) If fg is differentiable at $x = 1$, then g is continuous at $x = 1$

Answer

(D) If fg is differentiable at $x = 1$, then g is differentiable at $x = 1$

Question 8

Let M be a $3 	imes 3$ invertible matrix with real entries and let I denote the $3 	imes 3$ identity matrix. If $M^{-1} = \operatorname{adj}(\operatorname{adj} M)$, then which of the following statement is/are ALWAYS TRUE ?

Accepted Answer

(B) $\det M = 1$

Accepted Answer

(C) $M^{2} = I$

Accepted Answer

(D) $(\operatorname{adj} M)^{2} = I$

Answer

(A) $M = I$

Question 9

Let S be the set of all complex numbers z satisfying $|z^{2} + z + 1| = 1$. Then which of the following statements is/are TRUE ?

Accepted Answer

(B) $|z| \leq 2$ for all $z \in S$

Accepted Answer

(C) $\left|z + \frac{1}{2}\right| \geq \frac{1}{2}$ for all $z \in S$

Answer

(A) $\left|z + \frac{1}{2}\right| \leq \frac{1}{2}$ for all $z \in S$

Answer

(D) The set S has exactly four elements

Question 10

Let x, y and z be positive real numbers. Suppose x, y and z are lengths of the sides of a triangle opposite to its angles X, Y and Z, respectively. If

$	an\frac{X}{2} + 	an\frac{Z}{2} = \frac{2y}{x + y + z}$,

then which of the following statements is/are TRUE?

Accepted Answer

(B) $Y = X + Z$

Accepted Answer

(C) $	an\frac{X}{2} = \frac{x}{y + z}$

Answer

(A) $2Y = X + Z$

Answer

(D) $x^{2} + z^{2} - y^{2} = xz$

Question 11

Let $L_{1}$ and $L_{2}$ be the following straight line.

$L_{1} : \frac{x - 1}{1} = \frac{y}{-1} = \frac{z - 1}{3}$ and $L_{2} : \frac{x - 1}{-3} = \frac{y}{-1} = \frac{z - 1}{1}$

Suppose the straight line

$L : \frac{x - \alpha}{l} = \frac{y - 1}{m} = \frac{z - \gamma}{-2}$

lies in the plane containing $L_{1}$ and $L_{2}$, and passes through the point of intersection of $L_{1}$ and $L_{2}$. If the line L bisects the acute angle between the lines $L_{1}$ and $L_{2}$, then which of the following statements is/are TRUE?

Accepted Answer

(A) $\alpha - \gamma = 3$

Accepted Answer

(B) $l + m = 2$

Answer

(C) $\alpha - \gamma = 1$

Answer

(D) $l + m = 0$

Question 12

Which of the following inequalities is/are TRUE?

Accepted Answer

(A) $\int_{0}^{1} x\cos x\, dx \geq \frac{3}{8}$

Accepted Answer

(B) $\int_{0}^{1} x\sin x\, dx \geq \frac{3}{10}$

Accepted Answer

(D) $\int_{0}^{1} x^{2}\sin x\, dx \geq \frac{2}{9}$

Answer

(C) $\int_{0}^{1} x^{2}\cos x\, dx \geq \frac{1}{2}$

Question 13

Let m be the minimum possible value of $\log_{3}\left(3^{y_{1}} + 3^{y_{2}} + 3^{y_{3}}\right)$, where $y_{1}, y_{2}, y_{3}$ are real numbers for which $y_{1} + y_{2} + y_{3} = 9$. Let M be the maximum possible value of $\left(\log_{3} x_{1} + \log_{3} x_{2} + \log_{3} x_{3}\right)$, where $x_{1}, x_{2}, x_{3}$ are positive real numbers for which $x_{1} + x_{2} + x_{3} = 9$. Then the value of $\log_{2}\left(m^{3}\right) + \log_{3}\left(M^{2}\right)$ is ______.

Accepted Answer

8.00

Question 14

Let $a_{1}$, $a_{2}$, $a_{3}$, ..... be a sequence of positive integers in arithmetic progression with common difference 2. Also, let $b_{1}$, $b_{2}$, $b_{3}$, ..... be a sequence of positive integers in geometric progression with common ratio 2. If $a_{1} = b_{1} = c$, then the number of all possible values of c, for which the equality

$2\left(a_{1} + a_{2} + \ldots + a_{n}\right) = b_{1} + b_{2} + \ldots + b_{n}$

holds for some positive integer n, is ______

Accepted Answer

1.00

Question 15

Let $f : [0, 2] 	o \mathbb{R}$ be the function defined by

$f(x) = (3 - \sin(2\pi x))\sin\left(\pi x - \frac{\pi}{4}ight) - \sin\left(3\pi x + \frac{\pi}{4}ight)$

If $\alpha, \beta \in [0, 2]$ are such that $\{x \in [0, 2] : f(x) \geq 0\} = [\alpha, \beta]$, then the value of $\beta - \alpha$ is ______

Accepted Answer

1.00

Question 16

In a triangle PQR, let $\vec{a} = \overrightarrow{QR}$, $\vec{b} = \overrightarrow{RP}$ and $\vec{c} = \overrightarrow{PQ}$. If $|\vec{a}| = 3$, $|\vec{b}| = 4$ and $\frac{\vec{a}\cdot(\vec{c} - \vec{b})}{\vec{c}\cdot(\vec{a} - \vec{b})} = \frac{|\vec{a}|}{|\vec{a}| + |\vec{b}|}$, then the value of $\left|\vec{a} 	imes \vec{b}ight|^{2}$ is ______

Accepted Answer

108.00

Question 17

For a polynomial g(x) with real coefficient, let $m_{g}$ denote the number of distinct real roots of g(x). Suppose S is the set of polynomials with real coefficient defined by

$S = \left\{\left(x^{2} - 1\right)^{2}\left(a_{0} + a_{1}x + a_{2}x^{2} + a_{3}x^{3}\right) : a_{0}, a_{1}, a_{2}, a_{3} \in \mathbb{R}\right\}$.

For a polynomial f, let $f'$ and $f''$ denote its first and second order derivatives, respectively. Then the minimum possible value of $\left(m_{f'} + m_{f''}\right)$, where $f \in S$, is ______

Accepted Answer

5.00

Question 18

Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit

$\lim_{x 	o 0^{+}} \frac{(1 - x)^{\frac{1}{x}} - e^{-1}}{x^{a}}$

is equal to a nonzero real number, is ______.

Accepted Answer

1.00

Question 19

A football of radius R is kept on a hole of radius r $(r < R)$ made on a plank kept horizontally. One end of the plank is now lifted so that it gets tilted making an angle $	heta$ from the horizontal as shown in the figure below. The maximum value of $	heta$ so that the football does not start rolling down the plank satisfies (figure is schematic and not drawn to scale) -

Accepted Answer

(A) $\sin	heta = \frac{r}{R}$

Answer

(B) $	an	heta = \frac{r}{R}$

Answer

(C) $\sin	heta = \frac{r}{2R}$

Answer

(D) $\cos	heta = \frac{r}{2R}$

Question 20

A light disc made of aluminium (a nonmagnetic material) is kept horizontally and is free to rotate about its axis as shown in the figure. A strong magnet is held vertically at a point above the disc away from its axis. On revolving the magnet about the axis of the disc, the disc will (figure is schematic and not drawn to scale)-

Accepted Answer

(B) rotate in the same direction as the direction of magnet's motion

Answer

(A) rotate in the direction opposite to the direction of magnet's motion

Answer

(C) not rotate and its temperature will remain unchanged

Answer

(D) not rotate but its temperature will slowly rise

Question 21

A small roller of diameter 20 cm has an axle of diameter 10 cm (see figure below on the left). It is on a horizontal floor and a meter scale is positioned horizontally on its axle with one edge of the scale on top of the axle (see figure on the right). The scale is now pushed slowly on the axle so that it moves without slipping on the axle, and the roller starts rolling without slipping. After the roller has moved 50 cm, the position of the scale will look like (figures are schematic and not drawn to scale)-

Accepted Answer

(B) (B)

Answer

(A) (A)

Answer

(C) (C)

Answer

(D) (D)

Question 22

A circular coil of radius R and N turns has negligible resistance. As shown in the schematic figure, its two ends are connected to two wires and it is hanging by those wires with its plane being vertical. The wires are connected to a capacitor with charge Q through a switch. The coil is in a horizontal uniform magnetic field $B_o$ parallel to the plane of the coil. When the switch is closed, the capacitor gets discharged through the coil in a very short time. By the time the capacitor is discharged fully, magnitude of the angular momentum gained by the coil will be (assume that the discharge time is so short that the coil has hardly rotated during this time)-

Accepted Answer

(B) $\pi NQB_oR^2$

Answer

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

Answer

(C) $2\pi NQB_oR^2$

Answer

(D) $4\pi NQB_oR^2$

Question 23

A parallel beam of light strikes a piece of transparent glass having cross section as shown in the figure below. Correct shape of the emergent wavefront will be (figures are schematic and not drawn to scale)-

Accepted Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Answer

(D) (D)

Question 24

An open-ended U-tube of uniform cross-sectional area contains water (density $10^{3}$ kg $m^{-3}$). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density 800 kg $m^{-3}$ is added to the left arm until its length is 0.1 m, as shown in the schematic figure below. The ratio $\left(\frac{h_1}{h_2}\right)$ of the heights of the liquid in the two arms is-

Accepted Answer

(B) $\frac{35}{33}$

Answer

(A) $\frac{15}{14}$

Answer

(C) $\frac{7}{6}$

Answer

(D) $\frac{5}{4}$

Question 25

A particle of mass m moves in circular orbits with potential energy $V(r) = Fr$, where F is a positive constant and r is its distance from the origin. Its energies are calculated using the Bohr model. If the radius of the particle's orbit is denoted by R and its speed and energy are denoted by v and E, respectively, then for the $n^{th}$ orbit (here h is the Planck's constant)-

Accepted Answer

(B) $R \propto n^{2/3}$ and $v \propto n^{1/3}$

Accepted Answer

(C) $E = \frac{3}{2}\left(\frac{n^2h^2F^2}{4\pi^2m}\right)^{1/3}$

Answer

(A) $R \propto n^{1/3}$ and $v \propto n^{2/3}$

Answer

(D) $E = 2\left(\frac{n^2h^2F^2}{4\pi^2m}\right)^{1/3}$

Question 26

The filament of a light bulb has surface area 64 $mm^2$. The filament can be considered as a black body at temperature 2500 K emitting radiation like a point source when viewed from far. At night the light bulb is observed from a distance of 100 m. Assume the pupil of the eyes of the observer to be circular with radius 3 mm. Then (Take Stefan-Boltzmann constant = 5.67 × $10^{-8}$ $Wm^{-2}K^{-4}$, Wien's displacement constant = 2.90 × $10^{-3}$ m-K, Planck's constant = 6.63 × $10^{-34}$ Js, speed of light in vacuum= 3.00 × $10^{8}$ $ms^{-1}$)-

Accepted Answer

(B) radiated power entering into one eye of the observer is in the range 3.15 × $10^{-8}$ W to 3.25 × $10^{-8}$ W

Accepted Answer

(C) the wavelength corresponding to the maximum intensity of light is 1160 nm

Accepted Answer

(D) taking the average wavelength of emitted radiation to be 1740 nm, the total number of photons entering per second into one eye of the observer is in the range 2.75 × $10^{11}$ to 2.85 × $10^{11}$

Answer

(A) power radiated by the filament is in the range 642 W to 645 W

Question 27

Sometimes it is convenient to construct a system of units so that all quantities can be expressed in terms of only one physical quantity. In one such system, dimensions of different quantities are given in terms of a quantity X as follows: [position] = $[X^{\alpha}]$; [speed] = $[X^{\beta}]$; [acceleration] = $[X^{p}]$; [linear momentum] = $[X^{q}]$; [force] = $[X^{r}]$. Then -

Accepted Answer

(A) $\alpha + p = 2\beta$

Accepted Answer

(B) $p + q - r = \beta$

Answer

(C) $p - q + r = \alpha$

Answer

(D) $p + q + r = \beta$

Question 28

A uniform electric field, $\vec{E} = -400\sqrt{3}\hat{y}$ $NC^{-1}$ is applied in a region. A charged particle of mass m carrying positive charge q is projected in this region with an initial speed of $2\sqrt{10} 	imes 10^{6}$ $ms^{-1}$. This particle is aimed to hit a target T, which is 5 m away from its entry point into the field as shown schematically in the figure. Take $\frac{q}{m} = 10^{10}$ $Ckg^{-1}$. Then-

Accepted Answer

(B) the particle will hit T if projected either at an angle 30º or 60º from the horizontal

Accepted Answer

(C) time taken by the particle to hit T could be $\sqrt{\frac{5}{6}}$ μs as well as $\sqrt{\frac{5}{2}}$ μs

Answer

(A) the particle will hit T if projected at an angle 45º from the horizontal

Answer

(D) time taken by the particle to hit T is $\sqrt{\frac{5}{3}}$ μs

Question 29

Shown in the figure is a semicircular metallic strip that has thickness t and resistivity ρ. Its inner radius is $R_1$ and outer radius is $R_2$. If a voltage $V_0$ is applied between its two ends, a current I flows in it. In addition, it is observed that a transverse voltage $\Delta V$ develops between its inner and outer surfaces due to purely kinetic effects of moving electrons (ignore any role of the magnetic field due to the current). Then (figure is schematic and not drawn to scale)-

Accepted Answer

(A) $I = \frac{V_0t}{\pi\rho}\ln\left(\frac{R_2}{R_1}\right)$

Accepted Answer

(C) the outer surface is at a lower voltage than the inner surface

Accepted Answer

(D) $\Delta V \propto I^2$

Answer

(B) the outer surface is at a higher voltage than the inner surface

Question 30

As shown schematically in the figure, two vessels contain water solutions (at temperature $T$) of potassium permanganate ($KMnO_4$) of different concentrations $n_1$ and $n_2$ ($n_1 > n_2$) molecules per unit volume with $\Delta n = (n_1 - n_2) \ll n_1$. When they are connected by a tube of small length $\ell$ and cross-sectional area S, $KMnO_4$ starts to diffuse from the left to the right vessel through the tube. Consider the collection of molecules to behave as dilute ideal gases and the difference in their partial pressure in the two vessels causing the diffusion. The speed v of the molecules is limited by the viscous force $-\beta v$ on each molecule, where β is a constant. Neglecting all terms of the order $(\Delta n)^2$, which of the following is/are correct? ($k_B$ is the Boltzmann constant)-

Accepted Answer

(A) the force causing the molecules to move across the tube is $\Delta nk_BTS$

Accepted Answer

(B) force balance implies $n_1\beta v\ell = \Delta nk_BT$

Accepted Answer

(C) total number of molecules going across the tube per sec is $\left(\frac{\Delta n}{\ell}\right)\left(\frac{k_BT}{\beta}\right)S$

Answer

(D) rate of molecules getting transferred through the tube does not change with time

Question 31

Put a uniform meter scale horizontally on your extended index fingers with the left one at 0.00 cm and the right one at 90.00 cm. When you attempt to move both the fingers slowly towards the center, initially only the left finger slips with respect to the scale and the right finger does not. After some distance, the left finger stops and the right one starts slipping. Then the right finger stops at a distance $x_R$ from the center (50.00 cm) of the scale and the left one starts slipping again. This happens because of the difference in the frictional forces on the two fingers. If the coefficients of static and dynamic friction between the fingers and the scale are 0.40 and 0.32, respectively, the value of $x_R$ (in cm) is ______.

Accepted Answer

25.60

Question 32

When water is filled carefully in a glass, one can fill it to a height h above the rim of the glass due to the surface tension of water. To calculate h just before water starts flowing, model the shape of the water above the rim as a disc of thickness h having semicircular edges, as shown schematically in the figure. When the pressure of water at the bottom of this disc exceeds what can be withstood due to the surface tension, the water surface breaks near the rim and water starts flowing from there. If the density of water, its surface tension and the acceleration due to gravity are $10^{3}$ kg $m^{-3}$, 0.07 $Nm^{-1}$ and 10 $ms^{-2}$, respectively, the value of h (in mm) is _________.

Accepted Answer

3.65 to 3.85

Question 33

One end of a spring of negligible unstretched length and spring constant k is fixed at the origin (0,0). A point particle of mass m carrying a positive charge q is attached at its other end. The entire system is kept on a smooth horizontal surface. When a point dipole $\vec{p}$ pointing towards the charge q is fixed at the origin, the spring gets stretched to a length $\ell$ and attains a new equilibrium position (see figure below). If the point mass is now displaced slightly by $\Delta\ell \ll \ell$ from its equilibrium position and released, it is found to oscillate at frequency $\frac{1}{\delta}\sqrt{\frac{k}{m}}$. The value of δ is ______.

Accepted Answer

0.50 OR 3.13 TO 3.15

Question 34

Consider one mole of helium gas enclosed in a container at initial pressure $P_1$ and volume $V_1$. It expands isothermally to volume $4V_1$. After this, the gas expands adiabatically and its volume becomes $32V_1$. The work done by the gas during isothermal and adiabatic expansion processes are $W_{iso}$ and $W_{adia}$, respectively. If the ratio $\frac{W_{iso}}{W_{adia}} = f\ln2$, then $f$ is _________.

Accepted Answer

1.77 to 1.79

Question 35

A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of 2 $ms^{-1}$ in front of the open end of the pipe and parallel to it, the length of the pipe should be changed for the resonance to occur with the moving tuning fork. If the speed of sound in air is 320 $ms^{-1}$, the smallest value of the percentage change required in the length of the pipe is ____________.

Accepted Answer

0.62 to 0.64

Question 36

A circular disc of radius $R$ carries surface charge density $\sigma(r) = \sigma_0\left(1 - \frac{r}{R}\right)$, where $\sigma_0$ is a constant and $r$ is the distance from the center of the disc. Electric flux through a large spherical surface that encloses the charged disc completely is $\phi_0$. Electric flux through another spherical surface of radius $\frac{R}{4}$ and concentric with the disc is $\phi$. Then the ratio $\frac{\phi_0}{\phi}$ is_________.

Accepted Answer

6.40

Question 37

If the distribution of molecular speeds of a gas is as per the figure shown below, then the ratio of the most probable, the average and the roots mean square speeds, respectively, is

Accepted Answer

(B) 1 : 1 : 1.224

Answer

(A) 1 : 1 : 1

Answer

(C) 1 : 1.128 : 1.224

Answer

(D) 1 : 1.128 : 1

Question 38

Which of the following liberates $O_2$ upon hydrolysis?

Accepted Answer

(B) $KO_2$

Answer

(A) $Pb_3O_4$

Answer

(C) $Na_2O_2$

Answer

(D) $Li_2O_2$

Question 39

A colorless aqueous solution contains nitrates of two metals, X and Y. When it was added to an aqueous solution of NaCl, a white precipitate was formed. This precipitate was found to be partly soluble in hot water to give a residue P and a solution Q. The residue P was soluble in aq. $NH_3$ and also in excess sodium thiosulfate. The hot solution Q gave a yellow precipitate with KI. The metals X and Y, respectively, are

Accepted Answer

(A) Ag and Pb

Answer

(B) Ag and Cd

Answer

(C) Cd and Pb

Answer

(D) Cd and Zn

Question 40

Newman projections P, Q, R and S are shown below :

Which one of the following options represents identical molecules ?

Accepted Answer

(C) Q and R

Answer

(A) P and Q

Answer

(B) Q and S

Answer

(D) R and S

Question 41

Which one of the following structures has the IUPAC name 3-ethynyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid ?

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(B) (B)

Answer

(C) (C)

Question 42

The Fischer projection of D-erythrose is shown below.

D-Erythrose and its isomers are listed as P, Q, R, and S in Column-I. Choose the correct relationship of P, Q, R, and S with D-erythrose from Column II.

Accepted Answer

(C) P → 2, Q → 1, R → 1, S → 3

Answer

(A) P → 2, Q → 3, R → 2, S → 2

Answer

(B) P → 3, Q → 1, R → 1, S → 2

Answer

(D) P → 2, Q → 3, R → 3, S → 1

Question 43

In thermodynamics the P-V work done is given by

$w = -\int dV\, P_{ext}$ .

For a system undergoing a particular process, the work done is ,

$w = -\int dV \left( \frac{RT}{V-b} - \frac{a}{V^2} \right)$.

This equation is applicable to a

Accepted Answer

(A) System that satisfies the van der Waals equation of state.

Accepted Answer

(B) Process that is reversible and isothermal.

Accepted Answer

(C) Process that is reversible and adiabatic.

Answer

(D) Process that is irreversible and at constant pressure.

Question 44

With respect to the compounds I-V, choose the correct statement(s).

Accepted Answer

(A) The acidity of compound I is due to delocalization in the conjugate base.

Accepted Answer

(B) The conjugate base of compound IV is aromatic.

Accepted Answer

(C) Compound II becomes more acidic, when it has a $-NO_2$ substituent.

Answer

(D) The acidity of compounds follows the order I > IV > V > II > III.

Question 45

In the reaction scheme shown below Q, R and S are the major products.

The correct structure of

Accepted Answer

(B) (B)

Accepted Answer

(D) (D)

Answer

(A) (A)

Answer

(C) (C)

Question 46

Choose the correct statement(s) among the following :

Accepted Answer

(A) $[FeCl_4]^-$ has tetrahedral geometry.

Accepted Answer

(C) $[FeCl_4]^-$ has higher spin-only magnetic moment than $[Co(en)(NH_3)_2Cl_2]^+$.

Answer

(B) $[Co(en)(NH_3)_2Cl_2]^+$ has 2 geometrical isomers.

Answer

(D) The cobalt ion in $[Co(en)(NH_3)_2Cl_2]^+$ has $sp^3d^2$ hybridization.

Question 47

With respect to hypochlorite, chlorate and perchlorate ions, choose the correct statement(s).

Accepted Answer

(A) The hypochlorite ion is the strongest conjugate base.

Accepted Answer

(B) The molecular shape of only chlorate ion is influenced by the lone pair of electrons of Cl.

Accepted Answer

(D) The hypochlorite ion oxidizes the sulfite ion.

Answer

(C) The hypochlorite and chlorate ions disproportionate to give rise to identical set of ions.

Question 48

The cubic unit cell structure of a compound containing cation M and anion X is shown below. When compared to the anion, the cation has smaller ionic radius. Choose the correct statement(s).

Accepted Answer

(A) The empirical formula of the compound is MX.

Accepted Answer

(C) The ratio of M-X bond length to the cubic unit cell edge length is 0.866.

Answer

(B) The cation M and anion X have different coordination geometries.

Answer

(D) The ratio of the ionic radii of cation M to anion X is 0.414.

Question 49

5.00 mL of 0.10 M oxalic acid solution taken in a conical flask is titrated against NaOH from a burette using phenolphthalein indicator. The volume of NaOH required for the appearance of permanent faint pink color is tabulated below for five experiments. What is the concentration, in molarity, of the NaOH solution ?

Accepted Answer

0.11

Question 50

Consider the reaction A ⇌ B at 1000 K. At time t', the temperature of the system was increased to 2000 K and the system was allowed to reach equilibrium. Throughout this experiment the partial pressure of A was maintained at 1 bar. Given below is the plot of the partial pressure of B with time. What is the ratio of the standard Gibbs energy of the reaction at 1000 K to that at 2000 K?

Accepted Answer

0.25

Question 51

Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is

$H_2 (g) + \frac{1}{2} O_2(g) ightarrow H_2O(\ell)$.

The work derived from the cell on the consumption of $1.0 	imes 10^{-3}$ mol of $H_2(g)$ is used to compress 1.00 mol of a monoatomic ideal gas in a thermally insulted container. What is the change in the temperature (in K) of the ideal gas ?

The standard reduction potentials for the two half-cells are given below.

$O_2(g) + 4\,H^+ (aq.) + 4e^- ightarrow 2H_2O\,(\ell)$ , $E^\circ = 1.23$ V,

$2H^+ (aq.) + 2e^- ightarrow H_2(g)$, $E^\circ = 0.00$ V.

Use $F = 96500$ C $mol^{-1}$, $R = 8.314$ J $mol^{-1}K^{-1}$

Accepted Answer

13.00 - 13.60

Question 52

Aluminium reacts with sulfuric acid to form aluminium sulfate and hydrogen. What is the volume of hydrogen gas in liters (L) produced at 300 K and 1.0 atm pressure, when 5.4 g of aluminium and 50.0 mL of 5.0 M sulfuric acid are combined for the reaction ?
(Use molar mass of aluminium as 27.0 g $mol^{-1}$ , $R = 0.082$ atm L $mol^{-1}\,K^{-1}$)

Accepted Answer

6.00 - 6.20

Question 53

$^{238}_{92}U$ is known to undergo radioactive decay to form $^{206}_{82}Pb$ by emitting alpha and beta particles. A rock initially contained $68 	imes 10^{-6}$ g of $^{238}_{92}U$. If the number of alpha particles that it would emit during its radioactive decay of $^{238}_{92}U$ to $^{206}_{82}Pb$ in three half-lives is $Z 	imes 10^{18}$ , then what is the value of Z ?

Accepted Answer

1.19 - 1.21

Question 54

In the following reaction, compound Q is obtained from compound P via an ionic intermediate

What is the degree of unsaturation of Q ?

Accepted Answer

18.00

Column-I	Column-II
P.see figure	1.Diastereomer
Q.see figure	2.Identical
R.see figure	3.Enantiomer
S.see figure

Exp. No.	Vol. of NaOH (mL)
1	12.5
2	10.5
3	9.0
4	9.0
5	9.0

JEE Advanced 2020 Paper 1 Question Paper with Answers

Physics — JEE Advanced 2020 Paper 1

Chemistry — JEE Advanced 2020 Paper 1

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