JEE Main 2020 · 06 Sep 2020 · Shift 1

Q1.A screw gauge has 50 divisions on its circular scale. The circular scale is 4 units ahead of the pitch scale marking, prior to use. Upon one complete rotation of the circular scale, a displacement of 0.5 mm is noticed on the pitch scale. The nature of zero error involved, and the …

Q2.A sound source S is moving along a straight track with speed v, and is emitting sound of frequency $v_0$ (see figure). An observer is standing at a finite distance, at the point O, from the track. The time variation of frequency heard by the observer is best represented by:
( …

Q3.In the figure below, P and Q are two equally intense coherent sources emitting radiation of wavelength 20 m. The separation between P and Q is 5 m and the phase of P is ahead of that of Q by $90^{\circ }$. A, B and C are three distinct points of observation, each equidistant from …

Q4.If the potential energy between two molecules in given by $U=\frac{A}{r^6}+\frac{B}{r^{12}}$, then at equilibrium, separation between molecules, and the potential energy are:

Q5.An AC circuit has $\mathrm{R}=100\Omega ,\mathrm{C}=2\mu \mathrm{F}$ and $\mathrm{L}=80\mathrm{mH}$, connected in series. The quality factor of the circuit is:

Q6.Charge $Q_1$ and $Q_2$ are at point $A$ and $B$ of a right angle triangle OAB (see figure). The resultant electric field at point O is perpendicular to the hypotenuse, then $\frac{{\mathrm{Q}}_1}{{\mathrm{Q}}_2}$ is proportional to:

Q7.Shown in the figure is a hollow icecream cone (it is open at the top). If its mass is M, radius of its top, R and height, H, then its moment of inertia about its axis is:

Q8.Four point masses, each of mass m, are fixed at the corners of a square of side l. The square is rotating with angular frequency $\omega$, about an axis passing through one of the corners of the square and parallel to its diagonal, as shown in the figure. The angular momentum o …

Q9.For the given input voltage waveform ${\mathrm{V}}_{\text{in }}(\mathrm{t})$, the output voltage waveform ${\mathrm{V}}_0(\mathrm{t})$, across the capacitor is correctly depicted by:

Q10.A particle of charge $q$ and mass $m$ is moving with a velocity $-v\hat{i}(v\ne 0)$ towards a large screen placed in the $Y-Z$ plane at a distance $d$. If there is a magnetic field $\vec{B}=B_0\hat{k}$, the maximum value of $v$ for which the particle will not …

Q11.An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height $h$ from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: …

Q12.A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and fa …

Q13.An electron, a doubly ionized helium ion $\left({\mathrm{He}}^{++}\right)$ and a proton are having the same kinetic energy. The relation between their respective de-Broglie wavelength ${\lambda }_{\mathrm{e}},{\lambda }_{\mathrm{He}}++$ and ${\lambda }_{\mathrm{p}}$ is:

Q14.A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ${\mathrm{ms}}^{-2}$) is of the order of:

Q15.You are given that Mass of ${}_3^7\mathrm{Li}=7.0160\mathrm{u}$, Mass of ${}_2^4\mathrm{He}=4.0026\mathrm{u}$ and ${}_1^1\mathrm{H}=1.0079\mathrm{u}$. When 20 g of ${}_3^7\mathrm{Li}$ is converted into ${}_2^4\mathrm{He}$ by proton captu …

Q16.A point like object is placed at a distance of 1 m in front of convex lens of focal length 0.5 m. A plane mirror is placed at a distance of 2 m behind the lens. The position and nature of the final image formed by the system is:

Q17.Molecules of an ideal gas are known to have three translational degrees of freedom and two rotational degrees of freedom. The gas is maintained at a temperature of T.
The total internal energy, $U$ of a mole of this gas, and the value of …

Q18.An object of mass $m$ is suspended at the end of a massless wire of length $L$ and area of cross - selection, A. Young modulus of the material of the wire is Y. If the mass is pulled down slightly its frequency of oscillation along the vertical direction is:

Q19.An electron is moving along $+x$ direction with a velocity of $6\times 10^6{\mathrm{ms}}^{-1}$. It enters a region of uniform electric field of $300\mathrm{V}/\mathrm{cm}$ pointing along +y direction. The magnitude and direction of the magnetic field set up in this r …

Q20.The density of a solid metal sphere is determined by measuring its mass and its diameter. The maximum error in the density of the sphere is $\left(\frac{x}{100}\right)\%$. If the relative errors in measuring the mass and the diameter are $6.0\%$ and $1.5\%$ respectively, …

Q21.Two bodies of the same mass are moving with the same speed, but in different directions in a plane. They have a completely inelastic collision and move together thereafter with a final speed which is half of their initial speed. The angle between the initial velocities of the two …

Q22.Suppose that intensity of a laser is $\left(\frac{315}{\pi }\right)\mathrm{W}/{\mathrm{m}}^2$. The rms electric field, in units of $\mathrm{V}/\mathrm{m}$ associated with this source is close to the nearest integer is ____. …

Q23.Initially a gas of diatomic molecules is contained in a cylinder of volume ${\mathrm{V}}_1$ at a pressure $P_1$ and temperature 250 K . Assuming that $25\%$ of the molecules get dissociated causing a change in number of moles. The pressure of the resulting gas at tempera …

Q24.A part of complete circuit is shown in the figure. At some instant, the value of current I is 1 A and it is decreasing at a rate of $10^2{\mathrm{As}}^{-1}$. The value of the potential difference ${\mathrm{V}}_{\mathrm{P}}-{\mathrm{V}}_{\mathrm{Q}}$, (in volts) at that instant, …

Q1.The correct statement with respect to dinitrogen is:

Q2.Consider the following reactions:

(see reaction scheme)

' A ' is :

Q3.The major product obtained from the following reaction is:

Q4.A solution of two components containing ${\mathrm{n}}_1$ moles of the $1^{\text{st }}$ component and ${\mathrm{n}}^2$ moles of the $2^{\text{nd }}$ component is prepared. $M_1$ and $M_2$ are the molecular weights of component 1 and 2 respectively. If d is the de …

Q5.The INCORRECT statement is:

Q6.Consider the Assertion and Reason given below.

Assertion (A): Ethene polymerized in the presence of Ziegler Natta Catalyst at high temperature and pressure is used to make buckets and dustbins.
Reason (R): High density polymers are closely packed and are chemically inert. Choose …

Q7.Arrange the following solutions in the decreasing order of pOH
(1) 0.01 M HCl
(2) 0.01 M NaOH
(3) $0.01\mathrm{M}{\mathrm{CH}}_3\mathrm{COONa}$
(4) 0.01 M NaCl

Q8.Among the sulphates of alkaline earth metals, the solubilities of ${\mathrm{BeSO}}_4$ and ${\mathrm{MgSO}}_4$ in water, respectively, are:

Q9.The major products of the following reaction are:

Q10.The present of soluble fluoride ion upto 1 ppm concentration in drinking water, is:

Q11.The increasing order of ${\mathrm{pK}}_{\mathrm{b}}$ values of the following compounds is:

I (see structure)
II (see structure)
III (see structure)
IV (see structure)

Q12.Which of the following compounds shows geometrical isomerism?

Q13.The set that contains atomic numbers of only transition elements, is

Q14.The variation of equilibrium constant with temperature is given below:
| ${\mathrm{T}}_2=100^{\circ }\mathrm{C}$ | …

Q15.Kraft temperature is the temperature:

Q16.For the reaction
${\mathrm{Fe}}_2\mathrm{N}(\mathrm{s})+\frac{3}{2}{\mathrm{H}}_2(\mathrm{g})=2\mathrm{Fe}(\mathrm{s})+{\mathrm{NH}}_3(\mathrm{g})$

Q17.The species that has a spin - only magnetic moment of 5.9 BM , is:
( ${\mathrm{T}}_{\mathrm{d}}=$ tetrahedral)

Q18.The lanthanoid that does NOT show +4 oxidation state is:

Q19.Consider the following reactions
$\mathrm{A}\to \mathrm{P}1;\mathrm{B}\to \mathrm{P}2;\mathrm{C}\to \mathrm{P}3;\mathrm{D}\to \mathrm{P}4$,
The order of the above reactions are $\mathrm{a},\mathrm{b},\mathrm{c}$ and d , respecti …

Q20.In an estimation of bromine by Carius method, 1.6 g of an organic compound gave 1.88 g of AgBr . The mass percentage of bromine in the compound is ____
(Atomic mass, $\mathrm{Ag}=108,\mathrm{Br}=80\mathrm{g}{\mathrm{mol}}^{-1}$ )

Q21.Potassium chlorate is prepared by the electrolysis of KCl in basic solution
$6{\mathrm{HO}}^{-}+{\mathrm{Cl}}^{-}\to {\mathrm{ClO}}_3^{-}+3{\mathrm{H}}_2\mathrm{O}+6{\mathrm{e}}^{-}$
If only $60\%$ of the current is utilized in the reaction, the time (rounded to the n …

Q22.The number of $\mathrm{Cl}=\mathrm{O}$ bonds in perchloric acid is," ____".

Q23.The elevation of boiling point of 0.10 m aqueous ${\mathrm{CrCl}}_3\times {\mathrm{NH}}_3$ solution is two times that of 0.05 m aqueous ${\mathrm{CaCl}}_2$ solution. The value of x is ____
[Assume $100\%$ ionisation of the complex and ${\mathrm{CaCl}}_2$, coordinati …

Q24.A spherical balloon of radius 3 cm containing helium gas has a pressure of $48\times 10^{-3}$ bar. At the same temperature, the pressure, of a spherical balloon of radius 12 cm containing the same amount of gas will be $\_\_\_\_$ $\times 10^{-6}$ bar.

Q1.If $\alpha$ and $\beta$ be two roots of the equation $x^2-64x+256=0$. Then the value of ${\left(\frac{{\alpha }^3}{{\beta }^5}\right)}^{1/8}+{\left(\frac{{\beta }^3}{{\alpha }^5}\right)}^{1/8}$ is:

Q2.The area (in sq. units) of the region $\mathrm{A}=\left\{(\mathrm{x},\mathrm{y}):|\mathrm{x}|+|\mathrm{y}|\le 1,2{\mathrm{y}}^2\ge |\mathrm{x}|\right\}$ is:

Q3.The general solution of the differential equation $\sqrt{1+x^2+y^2+x^2{y}^2}+xy\frac{dy}{dx}=0$ is: (where C is a constant of integration)

Q4.Let $L_1$ be a tangent to the parabola $y^2=4(x+1)$ and $L_2$ be a tangent to the parabola $y^2=8(x+2)$ such that $L_1$ and $L_2$ intersect at right angles. Then $L_1$ and $L_2$ meet on the straight line:

Q5.If $f(x+y)=f(x)f(y)$ and ${\sum }_{x=1}^{\infty }f(x)=2,x,y\in N$ where $N$ is the set of all natural numbers, then the value of $\frac{f(4)}{f(2)}$ is:

Q6.If $I_1={\int }_0^1{\left(1-x^{50}\right)}^{100}dx$ and $I_2={\int }_0^1{\left(1-x^{50}\right)}^{101}dx$ such that $I_2=\alpha I_1$ then $\alpha$ equals to:

Q7.Out of 11 consecutive natural numbers if three numbers are selected at random (without repetition), then the probability that they are in A.P. with positive common difference, is:

Q8.A ray of light coming from the point $(2,2\sqrt{3})$ is incident at an angle $30^{\circ }$ on the line $x=1$ at the point $A$. The ray gets reflected on the line $x=1$ and meets $x$-axis at the point $B$. Then, the line $AB$ passes through the point:

Q9.Which of the following points lies on the locus of the foot of perpendicular drawn upon any tangent to the ellipse, $\frac{x^2}{4}+\frac{y^2}{2}=1$ from any of its foci?

Q10.The region represented by $\{z=x+iy\in C:|z|-\mathrm{Re}(z)\le 1\}$ is also given by the inequality:

Q11.The position of a moving car at time $t$ is given by $f(t)=a{t}^2+bt+c,t>0$, where $a,b$ and c are real numbers greater than 1. Then the average speed of the car over the time interval $\left[t_1,t_2\right]$ is attained at the point:

Q12.If ${\sum }_{\mathrm{i}=1}^{\mathrm{n}}\left({\mathrm{x}}_{\mathrm{i}}-\mathrm{a}\right)=\mathrm{n}$ and ${\sum }_{\mathrm{i}=1}^{\mathrm{n}}{\left({\mathrm{x}}_{\mathrm{i}}-\mathrm{a}\right)}^2=\mathrm{na},(\mathrm{n},\mathrm{a}>1)$ then the standard deviation of n observations …

Q13.If $\{\mathrm{p}\}$ denotes the fractional part of the number p , then $\left\{\frac{3^{200}}{8}\right\}$, is equal to

Q14.The shortest distance between the lines $\frac{x-1}{0}=\frac{y+1}{-1}=\frac{z}{1}$ and $x+y+z+1=0,2x-y+z+3=0$ is:

Q15.The negation of the Boolean expression $\mathbf{p}\vee (\sim \mathbf{p}\wedge \mathbf{q})$ is equivalent to:

Q16.Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

Q17.Let $m$ and $M$ be respectively the minimum and maximum values of …

Q18.Let $\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}$ and p be any non zero distinct real numbers such that $\left(a^2+b^2+c^2\right)p^2-2(ab+bc+cd)p+\left(b^2+c^2+d^2\right)=0$. Then:

Q19.The value of $\lambda$ and $\mu$ for which the system of linear equations

has infinitely many solutions are, respectively:

Q20.Set A has m elements and Set B has n elements. If the total number of subsets of A is 112 more than the total number of subsets of $B$, then the value of $m.n$ is ______.

Q21.Let $f:R\to R$ be defined as $f(x)=\{\begin{array}{cc}{x}^5\sin \left(\frac{1}{x}\right)+5x^2,& x<0\\ 0,& x=0\\ x^5\cos \left(\frac{1}{x}\right)+\lambda x^2,& x>0\end{array}$

The value of $\lambda$ for which $f^{\prime \prime }(0)$ exis …

Q22.If $\vec{a}$ and $\vec{b}$ are unit vectors, then the greatest value of $\sqrt{3}|\vec{a}+\vec{b}|+|\vec{a}-\vec{b}|$ is ______.

Q23.Let $AD$ and $BC$ be two vertical poles at $A$ and $b$ respectively on a horizontal ground. If $AD=8\mathrm{m},BC=11\mathrm{m}$ and $AB=10\mathrm{m}$; then the distance (in meters) of a point $M$ on $AB$ from the point $A$ such that …

Q24.The angle of elevation of the top of a hill from a point on the horizontal plane passing through the foot of the hill is found to be $45^{\circ }$. After walking a distance of 80 meters towards the top, up a slope inclined at an angle of $30^{\circ }$ to the horizontal plane, the a …