JEE Main 2020 · 05 Sep 2020 · Shift 1

Q1.A hollow spherical shell at outer radius R floats just submerged under the water surface. The inner radius of the shell is $r$. If the specific gravity of the shell material is $\frac{27}{8}$ w.r.t water, the value of $r$ is.

Q2.A balloon is moving up in air vertically above a point A on the ground. When it is at a height ${\mathrm{h}}_1$, a girl standing at a distance d (point B) from A (see figure) sees it at the angle $45^0$ with respect to the vertical. When the balloon climbs up a future heigh …

Q3.A physical quantity $z$ depends on four observables $a,c,c$ and $d$, as $z=\frac{a^2{b}^{\frac{2}{3}}}{\sqrt{c}{d}^3}$. The percentages of error in the measurement of $\mathrm{a},\mathrm{b},\mathrm{c}$ and d are $2\%,1.5\%,4\%$ and $2.5\%$ respectively. …

Q4.A wheel is rotating freely with an angular speed $\omega$ on a shaft. The moment of inertia of the wheel is I and the moment of inertia of the shaft is negligible. Another wheel of moment of inertia 3 I initially at rest is suddenly coupled to the same shaft. The resultant frac …

Q5.In a resonance tube experiment when the tube is filled with water up to a height of 17.0 cm from bottom, it resonates with a given tuning fork. When the water level is raised the next resonance with the same tuning fork occurs at a height of 24.5 cm . If the velocity of sound in …

Q6.An electron is constrained to move along the y - axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is …

Q7.With increasing biasing voltage of a photodiode, the photocurrent magnitude:

Q8.A bullet of mass 5 g , traveling with a speed of $210\mathrm{m}/\mathrm{s}$, strikes a fixed wooden target. One half of its kinetic energy is converted into heat in the bullet while the other half is converted into heat in the wood. The rise of temperature of the bullet if th …

Q9.The value of the acceleration due to gravity is $g_1$ at a height $h=\frac{R}{2}$ ( $R=$ radius of the earth) from the surface of the earth. It is again equal to $g_1$ at a depth d below the surface of the earth. The ratio $\left(\frac{d}{R}\right)$ equals:

Q10.For a concave lens of focal length $f$, the relation between object and image distances $u$ and is $v$, respectively, from its pole can best be represented by ( $u-v$ is the reference line):

Q11.A solid sphere of radius R carries a charge $\mathrm{Q}+\mathrm{q}$ distributed uniformly over its volume. A very small point like piece of it of mass m gets detached from the bottom of the sphere and falls down vertically under gravity. This piece carries charge q. If it acquire …

Q12.A galvanometer of resistance G is converted into a voltmeter of range $0-$ IV by connecting a resistance ${\mathrm{R}}_1$ in series with it. The additional resistance that should be connected in series with ${\mathrm{R}}_1$ to increase the range of the voltmeter to …

Q13.Number of molecules in a volume of $4{\mathrm{cm}}^3$ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to? (Given, mean kinetic energy of a molecule (at T ) is …

Q14.A square loop of side 2a, and carrying current I , is kept in XZ plane with its centre at origin. A long wire carrying the same current I is placed parallel to the z -axis and passing through the point $(0,b,0),(b\gg a)$. The magnitude of the torque on the loop about z - axis …

Q15.Assume that the displacement (s) of air is proportional to the pressure difference ( $\Lambda \mathrm{p}$ ) created by a sound wave. Displacement (s) further depends on the speed of sound (v), density of air ( $\rho$ ) and the frequency (f). If …

Q16.A helicopter rises from rest on the ground vertically upwards with a constant acceleration g . A food packet is dropped from the helicopter when it is at a height h . The time taken by the packet to reach the ground is close to [ $g$ is the acceleration due to gravity]:

Q17.Activities of three radioactive substances A, B and C are represented by the curves A, B and C in the figure. Then their half lives $T_{\frac{1}{2}}(A):T_{\frac{1}{2}}(B):T_{\frac{1}{2}}(C)$ are in the ratio:

Q18.An electrical power line, having a total resistance of $2\Omega$, delivers 1 kW at 220 V. The efficiency of the transmission line is approximately:

Q19.Two capacitors of capacitances C and 2C are charged to potential differences V and 2V, respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration …

Q20.A force $\vec{F}=(\hat{i}+2\hat{j}+3\hat{k})$ N acts at a point $(4\hat{i}+3\hat{j}-\hat{k})$ m. Then the magnitude of torque about the point $(\hat{i}+2\hat{j}+\hat{k})$ m will be $\sqrt{x}$ N-m. The value of $x$ is ______.

Q21.A particle of mass $200$ MeV$/c^2$ collides with a hydrogen atom at rest. Soon after the collision the particle comes to rest, and the atom recoils and goes to its first excited state. The initial kinetic energy of the particle (in eV) is $\frac{N}{4}$. The value of N is: (Given …

Q22.Two concentric circular coils, $C_1$ and $C_2$ are placed in the XY plane. $C_1$ has 500 turns, and a radius of $1$ cm. $C_2$ has 200 turns and radius of $20$ cm. $C_2$ carries a time dependent current $I(t)=(5t^2-2t+3)$ A where t is in s. The emf induced in $C_1$ (in mV), …

Q23.A beam of electrons of energy $E$ scatters from a target having atomic spacing of $1$ Å. The first maximum intensity occurs at $\theta =60^{\circ }$. Then $E$ (in eV) is ______.
(Planck constant $h=6.63\times 10^{-34}$ J·s, electron mass $m=9.1\times 10^{-31}$ kg)

Q24.A compound microscope consists of an objective lens of focal length 1 cm and an eye piece of focal length 5 cm with a separation of 10 cm. The distance between an object and the objective lens, at which the strain on the eye is minimum is $\frac{n}{40}$ cm. The value of n is ____ …

Q1.The structure of ${\mathrm{PCl}}_5$ in the solid state is:

Q2.In the sixth period, the orbitals that are filled are:

Q3.The increasing order of basicity of the following compounds is:

Q4.Identify the correct molecular picture showing what happens at the critical micellar concentration (CMC) of an aqueous solution of a surfactant
(● polar head; ▬ non-polar tail ; · water).

Q5.Which of the following is not an essential amino acid?

Q6.A flask contains a mixture of compounds A and B . Both compounds decompose by first - order kinetics. The half lives for A and B are 300 s and 180 s , respectively. If the concentrations of $A$ and $B$ are equal initially, the time required for the concentration of $A$ to be four …

Q7.The equation that represents the water - gas shift reactions is:

Q8.In the following reaction sequence the major products A and B are:

Q9.A diatomic molecule ${\mathrm{X}}_2$ has a body centered cubic (bcc). The density of the molecule is $6.17\mathrm{g}{\mathrm{cm}}^{-3}$. The number of molecules present in 200 g of ${\mathrm{X}}_2$ is: (Avogadro constant …

Q10.If a person is suffering from the deficiency of nor - adrenaline, what kind of drug can be suggested?

Q11.The potential energy curve for the ${\mathrm{H}}_2$ molecule as a function of internuclear distance is :

Q12.Consider the following reaction:

For each of the following cases ( $\mathrm{a},\mathrm{b}$ ) the direction in which the equilibrium shifts is:
(a) Tem …

Q13.The most appropriate reagent for conversion of $\mathrm{C}{}_2\mathrm{H}{}_5\mathrm{CN}$ into $\mathrm{CH}{}_3\mathrm{CH}{}_2\mathrm{CH}{}_2\mathrm{NH}{}_2$ is:

Q14.Which of the following derivates of alcohol is unstable is an aqueous base?

Q15.The condition that indicates a polluted environment is:

Q16.The values of the crystal field stabilization energies for a high spin $d^6$ metal ion in octahedral and tetrahedral fields, respectively, are:

Q17.The difference between the radii of $3^{\text{rd}}$ and $4^{\text{th}}$ orbits of $\mathrm{Li}{}^{2+}$ in $\Delta R_1$. The difference between the radii of $3^{\text{rd}}$ and $4^{\text{th}}$ orbits of $\mathrm{He}{}^{+}$ is $\Delta R_2$. Ratio $\Delta R_1:\Delta R_2$ is:

Q18.The increasing order of the acidity of the $\alpha$-hydrogen of the following compounds is:

(A) (see structure)
(B) (see structure)
(C) (see structure)
(D) (see structure)

Q19.The correct electronic configuration and spin - only magnetic moment (BM) of $\mathrm{Gd}{}^{3+}$ ($Z=64$), respectively, are:

Q20.An Ellingham diagram provides information about:

1. the condition of pH and potential under which a species is thermodynamically stable.
2. the standard Gibbs energies of formation of some metal oxides
3. the kinetics of the reduction process
4. standard electrode potentials of r …

Q21.The total number of coordination sites in ethylenediaminetetraacetate (EDTA ${}^{4-}$) is ____.

Q22.The minimum number of moles of ${\mathrm{O}}_2$ required for complete combustion of 1 mole of propane and 2 moles of butane is ____

Q23.An oxidation - reduction in which 3 electrons are transferred has a $\Delta {\mathrm{G}}^0$ of $17.37\mathrm{kJ}{\mathrm{mol}}^{-1}$ at $25^{\circ }\mathrm{C}$. The value of ${\mathrm{E}}_{\text{cell }}^0$ (in V is ____ $\times 10^{-2}$) …

Q24.The number of chiral carbon(s) present in peptide, lie-Arg-Pro, is ____

Q25.A soft drink was bottled with a partial pressure of ${\mathrm{CO}}_2$ of 3 bar over the liquid at room temperature. The partial pressure of ${\mathrm{CO}}_2$ over the solution approaches a value of 30 bar when 44 g of ${\mathrm{CO}}_2$ is dissolved in 1 kg of water at room …

Q1.If the four complex numbers, $z,\bar{z},\bar{z}-2\mathrm{Re}(\bar{z})$ and $z-2\mathrm{Re}(z)$ represent the vertices of a square of side 4 units in the Argand plane, then $|\mathrm{z}|$ is equal to:

Q2.The negation of the Boolean expression $x\leftrightarrow \sim y$ is equivalent to

Q3.If $2^{10}+2^9\cdot 3^1+2^8\cdot 3^2+\dots +2\cdot 3^9+3^{10}=S-2^{11}$, then $S$ is equal to

Q4.Let $\lambda \epsilon \mathrm{R}$. The system of linear equations.
$2x_1-4x_2+\lambda x_3=1$
$x_1-6x_2+x_3=2$
$\lambda {\mathrm{x}}_1-10{\mathrm{x}}_2+4{\mathrm{x}}_3=3$
Is inconsistent for:

Q5.If …

Q6.If $3^{2\sin 2\alpha -1},14$ and $3^{4-2\sin 2\alpha }$ are the first three terms of an AP for some $\alpha$, then the sixth term of this AP is:

Q7.A survey shows that $73\%$ of the persons working in an office like coffee, whereas $65\%$ like tea. If $x$ denotes the percentage of them, who like both coffee and tea, then $x$ cannot be:

Q8.If the common tangent to the parabolas $y^2=4x$ and $x^2=4y$ also touches the circle, $x^2+y^2=c^2$, then $c$ is equal to

Q9.The product of the roots of the equation $9x^2-18|x|+5=0$, is:

Q10.The value of ${\int }_{-\pi /2}^{\pi /2}\frac{1}{1+{\mathrm{e}}^{\sin \mathrm{x}}}\mathrm{dx}$ is:

Q11.If S is the sum of the first 10 terms of the series ${\tan }^{-1}\left(\frac{1}{3}\right)+{\tan }^{-1}\left(\frac{1}{7}\right)+{\tan }^{-1}\left(\frac{1}{13}\right)+{\tan }^{-1}\left(\frac{1}{21}\right)+\dots .$, then $\tan (\mathrm{S})$ is equal to:

Q12.If $(a,b,c)$ is the image of the point $(1,2,-3)$ in the line, $\frac{x+1}{2}=\frac{y-3}{-2}=\frac{z}{-1}$, then $a+b+c$ is equal to

Q13.If $y=y(x)$ is the solution of the differential equation $\frac{5+e^x}{2+y}\cdot \frac{dy}{dx}+e^x=0$ satisfying $y(0)=1$, then a value of $y\left({\log }_{e}13\right)$ is:

Q14.If $\alpha$ is the positive root of the equation, $p(x)=x^2-x-2=0$, then ${\lim }_{x\to \alpha }\frac{\sqrt{1-\cos (p(x))}}{x+\alpha -4}$ is equal to:

Q15.If the co-ordinates of two points $A$ and $B$ are $(\sqrt{7},0)$ and $(-\sqrt{7},0)$ respectively and $P$ is any point on the conic $9x^2+16y^2=144$, then $PA+PB$ is equal to:

Q16.If the function $f(x)=\{\begin{array}{lc}{k}_1(x-\pi {)}^2-1& x\le \pi \\ k_2\cos x& x>\pi \end{array}$ is twice differentiable, then the ordered pair $(k_1,k_2)$ is equal to:

Q17.If the minimum and the maximum values of the function $f:\left[\frac{\pi }{4},\frac{\pi }{2}\right]\to \mathbb{R}$, defined by …

Q18.The mean and variance of 7 observations are 8 and 16, respectively. If five observations are $2,4,10,12,14$, then the absolute difference of the remaining two observations is:

Q19.If the point $P$ on the curve, $4x^2+5y^2=20$ is farthest from the point $Q(0,-4)$ then $P{Q}^2$ is equal to:

Q20.If the volume of a parallelepiped, whose coterminus edges are given by the vectors $\vec{a}=\hat{i}+\hat{j}+n\hat{k},\vec{b}=2\hat{i}+4\hat{j}-n\hat{k}$ and $\vec{c}=\hat{i}+n\hat{j}+3\hat{k}(n\ge 0)$, is 158 cu.units, then:

Q21.The natural number $m$, for which the coefficient of $x$ in the binomial expansion of ${\left(x^m+\frac{1}{x^2}\right)}^{22}$ is 1540, is ______

Q22.Let $f(x)=x\cdot \left[\frac{x}{2}\right]$, for $-10<x<10$, where $[t]$ denotes the greatest integer function. Then the number of points of discontinuity of $f$ is equal to ______

Q23.If the line, $2x-y+3=0$ is at a distance $\frac{1}{\sqrt{5}}$ and $\frac{2}{\sqrt{5}}$ from the lines $4x-2y+\alpha =0$ and $6x-3y+\beta =0$, respectively, then the sum of all possible values of $\alpha$ and $\beta$ is ______.

Q24.Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five, is ______.

Q25.The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is ____.