JEE Advanced 2020 · 27 Sep 2020 · Paper 1

Q1.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 θ from the horizontal as shown in the figure below. The maximum value of θ so that the football does not start r …

Q2.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 …

Q3.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 slo …

Q4.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 …

Q5.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)-

Q6.An open-ended U-tube of uniform cross-sectional area contains water (density $10^3\mathrm{kg}{\mathrm{m}}^{-3}$). Initially the water level stands at 0.29 m from the bottom in each arm. Kerosene oil (a water-immiscible liquid) of density $800\mathrm{kg}{\mathrm{m}}^{-3}$ is …

Q7.A particle of mass m moves in circular orbits with potential energy $\mathrm{V}(\mathrm{r})=Fr$, 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 …

Q8.The filament of a light bulb has surface area $64{\mathrm{mm}}^2$. 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 …

Q9.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] $=\left[X^{\alpha }\right]$; [ …

Q10.A uniform electric field, $\overrightarrow{\mathrm{E}}=-400\sqrt{3}\hat{y}{\mathrm{NC}}^{-1}$ 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 $2\sqrt{10}\times 10^6{\mathrm{ms}}^{-1}$. This …

Q11.Shown in the figure is a semicircular metallic strip that has thickness t and resistivity $\rho$. Its inner radius is ${\mathrm{R}}_1$ and outer radius is ${\mathrm{R}}_2$. If a voltage ${\mathrm{V}}_0$ is applied between its two ends, a current I flows in it. In addition, it is …

Q12.As shown schematically in the figure, two vessels contain water solutions (at temperature T) of potassium permanganate $\left({\mathrm{KMnO}}_4\right)$ of different concentrations $n_1$ and $n_2\left(n_1>n_2\right)$ molecules per unit volume with …

Q13.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 fing …

Q14.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 edge …

Q15.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 …

Q16.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 adiabat …

Q17.A stationary tuning fork is in resonance with an air column in a pipe. If the tuning fork is moved with a speed of $2{\mathrm{ms}}^{-1}$ 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 tu …

Q18.A circular disc of radius $R$ carries surface charge density $\sigma (r)={\sigma }_0\left(1-\frac{\mathrm{r}}{\mathrm{R}}\right)$, 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 …

Q1.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

Q2.Which of the following liberates $\mathrm{O}{}_2$ upon hydrolysis?

Q3.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 …

Q4.Newman projections P, Q, R and S are shown below:

Which one of the following options represents identical molecules?

Q5.Which one of the following structures has the IUPAC name 3-ethynyl-2-hydroxy-4-methylhex-3-en-5-ynoic acid?

Q6.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.
| Q. | (see structure …

Q7.In thermodynamics the P-V work done is given by

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

Q8.With respect to the compounds I-V, choose the correct statement(s).

Q9.In the reaction scheme shown below Q, R and S are the major products.

The correct structure of

Q11.With respect to hypochlorite, chlorate and perchlorate ions, choose the correct statement(s).

Q12.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).

Q13.5.00 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 …

Q14.Consider the reaction $\mathbf{A}\rightleftharpoons \mathbf{B}$ at 1000 K. At time ${\mathrm{t}}^{\prime }$, 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. …

Q15.Consider a 70% efficient hydrogen-oxygen fuel cell working under standard conditions at 1 bar and 298 K. Its cell reaction is

The work derived from the cell on the …

Q16.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 alumin …

Q17.${}_{92}^{238}\mathrm{U}$ is known to undergo radioactive decay to form ${}_{82}^{206}\mathrm{Pb}$ by emitting alpha and beta particles. A rock initially contained $68\times 10^{-6}\mathrm{g}$ of ${}_{92}^{238}\mathrm{U}$. If the number of alpha particles that it would emi …

Q18.In the following reaction, compound Q is obtained from compound P via an ionic intermediate

What is the degree of unsaturation of Q?

Q1.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

is

Q2.If the function $f:\mathbb{R}\to \mathbb{R}$ is defined by $f(x)=|x|(x-\sin x)$, then which of the following statements is TRUE?

Q3.Let the functions $f:\mathbb{R}\to \mathbb{R}$ and $g:\mathbb{R}\to \mathbb{R}$ be defined by

Then the area of the region in the first quadrant bounded by the curves …

Q4.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 th …

Q5.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 …

Q6.Consider all rectangles lying in the region

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

Q7.Let the function $f:\mathbb{R}\to \mathbb{R}$ be defined by $f(x)=x^3-x^2+(x-1)\sin x$ and let $g:\mathbb{R}\to \mathbb{R}$ be an arbitrary function. Let $fg:\mathbb{R}\to \mathbb{R}$ be the product function defined by $(fg)(x)=f(x)g(x)$. Then …

Q8.Let M be a $3\times 3$ invertible matrix with real entries and let I denote the $3\times 3$ identity matrix. If $M^{-1}=\text{adj}(\text{adj }M)$, then which of the following statement is/are ALWAYS TRUE?

Q9.Let S be the set of all complex numbers z satisfying $\left|z^2+z+1\right|=1$. Then which of the following statements is/are TRUE?

Q10.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

then which of the following statements is/are TRUE?

Q11.Let $L_1$ and $L_2$ be the following straight lines.
$L_1:\frac{x-1}{1}=\frac{y}{-1}=\frac{z-1}{3}$ 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 …

Q12.Which of the following inequalities is/are TRUE?

Q13.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 n …

Q14.Let $a_1,a_2,a_3,\dots$ be a sequence of positive integers in arithmetic progression with common difference 2. Also, let $b_1,b_2,b_3,\dots$ 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 va …

Q15.Let $f:[0,2]\to \mathbb{R}$ be the function defined by

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

Q16.In a triangle PQR, let $\vec{a}=\overrightarrow{QR}$, $\vec{b}=\overrightarrow{RP}$ and $\vec{c}=\overrightarrow{PQ}$. If

then the …

Q17.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 …

Q18.Let e denote the base of the natural logarithm. The value of the real number a for which the right hand limit

is equal to a nonzero real number, is ____.