JEE Main 2020 · 05 Sep 2020 · Shift 2

Q1.Two coherent sources of sound, ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ produce source waves of the same wavelength, $\lambda =1\mathrm{m}$, in phase. ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are placed 1.5 m apart (see fig). A listener located at L , directly in front of $S_2$ find …

Q2.Two different wires having lengths ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$, and respective temperature coefficient of linear expansion ${\alpha }_1$ and ${\alpha }_2$, are joined end-to-end. Then the effective temperature coefficient of linear expansion is:

Q3.In the circuit shown, charge on the $5\mu \mathrm{F}$ capacitor is:

Q4.In adiabatic process, the density of a diatomic gas becomes 32 times its initial value. The final pressure of the gas is found to be $n$ times the initial pressure. The value of $n$ is:

Q5.An infinitely long straight wire carrying current I, one side opened rectangular loop and a conductor C with a sliding connector are located in the same plane, as shown in the figure. The connector has length l and resistance R. It slides to the right with a velocity v . The resi …

Q6.An iron rod of volume $10^{-3}{\mathrm{m}}^3$ and relative permeability 1000 is placed as core in a solenoid with $10\mathrm{turns}/\mathrm{cm}$. If a current of 0.5 A is passed through the solenoid, then the magnetic moment of the rod will be:

Q7.The correct match between the entries in column I and column II are:

Radiation
(a) Microwave
(b) Gamma rays
(c) A.M. radio waves
(d) X-rays

Wavelength
(i) 100 m
(ii) $10^{-15}\mathrm{m}$
(iii) $10^{-10}\mathrm{m}$
(iv) $10^{-3}\mathrm{m}$

Q8.A radioactive nucleus decays by two difference processes. The half life for the first process is 10 s and that for the second is 100 s. The effective half life of the nucleus is closes to:

Q9.Ten charges are placed on the circumference of a circle of radius R with constant angular separation between successive charges. Alternate charges 1, 3, 5, 7, 9 have charge $(+q)$ each, while $2,4,6,8,10$ have charge $(-q)$ each. The potential $V$ and the electric field $E$ at th …

Q10.A driver in a car, approaching a vertical wall notices that the frequency of his car horn, has changed from 440 Hz to 480 Hz, when it gets reflected from the wall. If the speed of sound in air is $345\mathrm{m}/\mathrm{s}$, then the speed of the car is:

Q11.A parallel plate capacitor has plate of length '$\ell$', width '$w$' and separation of plates is '$d$'. It is connected to a battery of emf V. A dielectric slap of the same thickness 'd' and of dielectric constant $\mathrm{k}=4$ is being, inserted between the plates of the capaci …

Q12.A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate $\frac{dM(t)}{dt}=b{v}^2(t)$, where $v(t)$ its instantaneous velocity. The instantaneous acceleration of the satellite is:

Q13.The acceleration due to gravity on the earth's surface at the poles is g an and angular velocity of the earth about the axis passing through the pole is $\omega$. An object is weight at the equator and at a height $h$ above the poles by using a spring balance. If the weights are …

Q14.Two Zener diodes (A and B) having breakdown voltages of 6 V and 4 V respe4ctively, are connected as shown in the circuit below. The output voltage ${\mathrm{V}}_0$ variation wlith input voltage linearly increasing with time, is given by: ( ${\mathrm{V}}_{\text{input }}=0$ V at …

Q15.In an experiment to verify Stokes law, a small spherical ball of radius $r$ and density $\rho$ falls under gravity through a distance h in air before entering a tank of water. If the terminal velocity of the ball inside water is same as its velocity just before entering the water …

Q16.A ring is hung on a nail. It can oscillate, without slipping or sliding (i) in its plane with a time period ${\mathrm{T}}_1$ and, T (ii) back and forth in a direction perpendicular to its plane, with a period $T_2$. The ratio $\frac{T_1}{T_2}$ will be:

Q17.The velocity (v) and time (t) graph of a body in a straight line motion is shown in the figure. The point S is at 4.333 seconds. The total distance covered by the body in 6 s is:

Q18.The quantities $x=\frac{1}{\sqrt{{\mu }_0{ϵ}_0}},y=\frac{E}{B}$ and $z=\frac{l}{CR}$ are defined where $C$-capacitance, $R$ Resistance, $l$-length, $E$-Electric field, $B$-magnetic field and ${ϵ}_0$, ${\mu }_0$, - free space permittivity and permeability respective …

Q19.A galvanometer is used in laboratory for detecting the null point in electrical experiments. If, on passing a current of 6 mA it produces a deflection of $2^{\circ }$, its figure of merit is close to:

Q20.In the circuit, given in the figure currents in different branches and value of one resistor are shown. Then potential at point $B$ with respect to the point $A$ is:

Q21.A thin rod of mass 0.9 kg and length 1 m is suspended, at rest, from one end so that it can freely oscillate in the vertical plane. A particle of mass 0.1 kg moving in a straight line with velocity $80\mathrm{m}/\mathrm{s}$ hits the rod at its bottom most point and sticks to …

Q22.The surface of a metal is illuminated alternately with photons of energies ${\mathrm{E}}_1=4\mathrm{eV}$ and ${\mathrm{E}}_2=2.5\mathrm{eV}$ respectively. The ratio of maximum speeds of the photoelectrons emitted in the two cases is 2. The work function of the metal in (eV) is …

Q23.A prism of angle $\mathrm{A}=1^{\circ }$ has a refractive index $\mu =1.5$. A good estimate for the minimum angle of deviation (in degrees) is close to N/10. Value of N is ____.

Q24.Nitrogen gas is at $300^{\circ }$C temperature. The temperature (in K) at which the rms speed of a ${\mathrm{H}}_2$ molecule would be equal to the rms speed of a nitrogen molecule, is ____. (Molar mass of ${\mathrm{N}}_2$ gas 28 g).

Q25.A body of mass 2 kg, is driven by an engine delivering a constant power $1\mathrm{J}/\mathrm{s}$. The body starts from rest and moves in a straight line. After 9 seconds, the body has moved a distance (in m) ____.

Q1.An element crystallises in a face-centred cubic (fcc) unit cell with cell edge a. The distance between the centres of two nearest octahedral voids in the crystal lattice is:

Q2.Adsorption of a gas follows Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on mass $m$ of the adsorbent, the correct plot of $\frac{x}{m}$ versus $p$ is:

Q3.The compound that has the largest $\mathrm{H}-\mathrm{M}-\mathrm{H}$ bond angle ( $\mathrm{M}=\mathrm{N},\mathrm{O},\mathrm{S},\mathrm{C}$ ), is

Q4.The correct order of the ionic radii of ${\mathrm{O}}^{2-},{\mathrm{N}}^{3-},{\mathrm{F}}^{-},{\mathrm{Mg}}^{2+},{\mathrm{Na}}^{+}$ and ${\mathrm{Al}}^{3+}$ is:

Q5.Lattice enthalpy and enthalpy of solution of NaCl are $788\mathrm{kJ}{\mathrm{mol}}^{-1}$ and $4\mathrm{kJ}{\mathrm{mol}}^{-1}$, respectively. The hydration enthalpy of NaCl is:

Q6.The correct statement about probability density (except at infinite distance from nucleus) is:

Q7.The increasing order of boiling points of the following compounds is:

Q8.The final major product of the following reaction is:
(i) ${\mathrm{Ac}}_2\mathrm{O}/$ Pyridine
(ii) ${\mathrm{Br}}_2,{\mathrm{FeCl}}_3$
(iii) ${\mathrm{OH}}^{-}/\Delta$
Me

Q9.The rate constant (k) of a reaction is measured at different temperatures (T), and the data are plotted in the given figure. The activation energy of the reaction in kJ ${\mathrm{mol}}^{-1}$ is: ( $R$ is gas constant)

Q10.The major product formed in the following reaction is:
${\mathrm{CH}}_3\mathrm{CH}=\mathrm{CHCH}{\left({\mathrm{CH}}_3\right)}_2\stackrel{\mathrm{HBr}}{\to }$

Q11.Among the following compounds, geometrical isomerism is exhibited by:

Q12.Boron and silicon of very high purity can be obtained through:

Q13.The following molecule acts as an:

Q14.Which one of the following polymers is not obtained by condensation polymerisation?

Q15.Hydrogen peroxide, in the pure state, is:

Q16.Reaction of ammonia with excess ${\mathrm{Cl}}_2$ gives:

Q17.The one that is NOT suitable for the removal of permanent hardness of water is:

Q18.Consider the complex ions, trans $-{\left[\mathrm{Co}(\mathrm{en}{)}_2{\mathrm{Cl}}_2\right]}^{+}(\mathrm{A})$ and cis $-{\left[\mathrm{Co}(\mathrm{en}{)}_2{\mathrm{Cl}}_2\right]}^{+}$ (B). The correct statement regarding them is:

Q19.The number of chiral carbons present in sucrose is ____ .

Q20.Considering that ${\Delta }_0>\mathrm{P}$, the magnetic moment (in BM ) of ${\left[\mathrm{Ru}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{2+}$ would be
____ .

Q21.For a dimerization reaction,
$2\mathrm{A}(\mathrm{g})\to {\mathrm{A}}_2(\mathrm{g})$,
at $298\mathrm{K},\Delta {\mathrm{U}}^{\ominus }=-20\mathrm{kJ}{\mathrm{mol}}^{-1},\Delta {\mathrm{S}}^{\ominus }=-30{\mathrm{JK}}^{-1}{\mathrm{mol}}^{-1}$, then the …

Q22.The volume, in mL , of $0.02\mathrm{M}{\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ solution required to react with 0.288 g of ferrous oxalate in acidic medium is ____ . (Molar mass of $\mathrm{Fe}=56{\mathrm{mol}}^{-1}$ )

Q23.For a reaction $X+Y=2Z$, $1.0\mathrm{mol}$ of $X$, $1.5\mathrm{mol}$ of $Y$ and $0.5\mathrm{mol}$ of $Z$ were taken in a $1\mathrm{L}$ vessel and allowed to react. At equilibrium, the concentration of $Z$ was $1.0\mathrm{mol}{\mathrm{L}}^{-1}$. The equilibrium constant of the re …

Q1.The value of ${\left(\frac{-1+i\sqrt{3}}{1-i}\right)}^{30}$ is:

Q2.If the system of linear equations
$x+y+3z=0$
$\mathrm{x}+3\mathrm{y}+{\mathrm{k}}^2\mathrm{z}=0$
$3x+y+3z=0$
has a non-zero solution $(x,y,z)$ for some $k\in R$, then $x+\left(\frac{y}{z}\right)$ is equal to:

Q4.If for some $\alpha \in R$, the lines $L_1:\frac{x+1}{2}=\frac{y-2}{-1}=\frac{z-1}{1}$ and $L_2:\frac{x+2}{\alpha }=\frac{y+1}{5-\alpha }=\frac{z+1}{1}$ are coplanar, then the line $L_2$ passes through the point:

Q5.Let $y=y(x)$ be the solution of the differential equation $\cos x\frac{dy}{dx}+2y\sin x=\sin 2x,x\in \left(0,\frac{\pi }{2}\right)$.
If $y(\pi /3)=0$, then $y(\pi /4)$ is equal to:

Q6.If $L={\sin }^2\left(\frac{\pi }{16}\right)-{\sin }^2\left(\frac{\pi }{8}\right)$ and $M={\cos }^2\left(\frac{\pi }{16}\right)-{\sin }^2\left(\frac{\pi }{8}\right)$, then:

Q7.Which of the following point lies on the tangent to the curve $x^4{e}^y+2\sqrt{y+1}=3$ at the point $(1,0)$ ?

Q8.The derivation of ${\tan }^{-1}\left(\frac{\sqrt{1+x^2}-1}{x}\right)$ with respect to ${\tan }^{-1}\left(\frac{2x\sqrt{1-x^2}}{1-2x^2}\right)$ at $x=\frac{1}{2}$ is:

Q9.If the sum of the second, third and fourth terms of a positive term G.P. is 3 and the sum of its sixth, seventh and eights terms is 243 , then the sum of the first 50 terms of this G.P. is:

Q10.The area (in sq. units) of the region $\mathrm{A}=\{(\mathrm{x},\mathrm{y}):(\mathrm{x}-1)[\mathrm{x}]\le \mathrm{y}\le 2\sqrt{\mathrm{x}},0\le \mathrm{x}\le 2\}$, where [t] denotes the greatest integer function, is:

Q11.If $\int \frac{\cos \theta }{5+7\sin \theta -2{\cos }^2\theta }d\theta =A{\log }_e|B(\theta )|+C$, where $C$ is a constant of integration, then $\frac{\mathrm{B}(\theta )}{\mathrm{A}}$ can be:

Q12.If $\alpha$ and $\beta$ are the roots of the equation, $7x^2-3x-2=0$, then the value of $\frac{\alpha }{1-{\alpha }^2}+\frac{\beta }{1-{\beta }^2}$ is equal to:

Q13.If the length of the chord of the circle, $x^2+y^2=r^2(r>0)$ along the line $y-2x=3$ is $r$, the $r^2$ is equal to:

Q14.The statement $(P\to (q\to p))\to (p\to (p\vee q))$ is:

Q15.There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is:

Q16.If $a+x=b+y=c+z+1$, where $a,b,c,x,y,z$ are non-zero distinct real numbers then $\left|\begin{array}{ccc}x& a+y& x+a\\ y& b+y& y+b\\ z& c+y& z+c\end{array}\right|$ is equal to:

Q17.If the sum of the first 20 terms of the series ${\log }_{(7^{1/2})}x+{\log }_{(7^{1/3})}x+{\log }_{(7^{1/4})}x+\dots$ is 460, then x is equal to:

Q18.If the line $y=mx+c$ is a common tangent to the hyperbola $\frac{x^2}{100}-\frac{y^2}{64}=1$ and the circle $x^2+y^2=36$, then which one of the following is true?

Q19.If the mean and standard deviation of the data $3,5,7,a,b$ are 5 and 2 respectively, then $a$ and $b$ are the roots of the equation:

Q20.If $x=1$ is a critical point of the function $f(x)=\left(3x^2+ax-2-a\right)e^x$, then

Q21.Let $A=(a,b,c)$ and $B=(1,2,3,4)$. Then the number of elements in the set $C=\{f:A\to B\mid 2\in f(A)$ and $f$ is not one-one$\}$ is ____.

Q22.The coefficient of $x^4$ in the expansion of ${\left(1+x+x^2+x^3\right)}^6$ in powers of $x$, is ____.

Q23.If the lines $x+y=a$ and $x-y=b$ touch the curve $y=x^2-3x+2$ at the points where the curve intersects the $x$-axis, then $\frac{a}{b}$ is equal to ____.

Q24.Let the vectors $\vec{a},\vec{b},\vec{c}$ be such that $|\vec{a}|=2,|\vec{b}|=4$ and $|\vec{c}|=4$. If the projection of $\vec{b}$ on $\vec{a}$ is equal to the projection of $\vec{c}$ on $\vec{a}$ and $\vec{b}$ is perpendicular to $\vec{c}$, then the value of …

Q25.In a bombing attack, there is $50\%$ chance that a bomb will hit the target. At least two independent hits are required to destroy the target completely. Then the minimum number of bombs, that must be dropped to ensure that there is at least $99\%$ chance of completely dest …