JEE Main 2020 · 06 Sep 2020 · Shift 2

Q1.In the figure shown, the current in the 10 V battery is close to:

Q2.A charged particle going around in a circle can be considered to be a current loop. A particle of mass $m$ carrying charge $q$ is moving in a plane with speed $v$ under the influence of magnetic field $\vec{B}$. The magnetic moment of this moving particle:

Q3.Three rods of identical cross-section and lengths are made of three different materials of thermal conductivity ${\mathrm{K}}_1$, ${\mathrm{K}}_2$ and ${\mathrm{K}}_3$, respectively. They are joined together at their ends to make a long rod (see figure). One end of the long rod i …

Q4.Two identical electric point dipoles have dipole moments ${\vec{p}}_1=p\hat{i}$ and ${\vec{p}}_2=-p\hat{i}$ and are held on the $x$ axis at distance '$a$' from each other. When released, they move along the $x$-axis with the direction of their dipole moments remaining unchanged …

Q5.For a plane electromagnetic wave, the magnetic field at a point $x$ and time $t$ is $\vec{B}(x,t)=\left[1.2\times 10^{-7}\sin \left(0.5\times 10^{3}x+1.5\times 10^{11}t\right)\hat{k}\right]T$

The instantaneous electric field $\vec{E}$ corresponding to $\vec{B}$ is: (spe …

Q6.Two planets have masses M and 16 M and their radii are a and 2a, respectively. The separation between the centres of the planets is 10a. A body of mass m is fired from the surface of the larger planet towards the smaller planet along the line joining their centres. For the body t …

Q7.A particle moving in the $xy$ plane experiences a velocity dependent force $\vec{F}=k\left(v_y\hat{i}+v_x\hat{j}\right)$, where $v_x$ and $v_y$ are the $x$ and $y$ components of its velocity $\vec{v}$. If $\vec{a}$ is the acceleration of the particle, then which of the …

Q8.Particle $A$ of mass $m_1$ moving with velocity $(\sqrt{3}\hat{i}+\hat{j}){\mathrm{ms}}^{-1}$ collides with another particle $B$ of mass $m_2$ which is at rest initially. Let ${\vec{V}}_1$ and ${\vec{V}}_2$ be the velocities of particles $A$ and $B$ after collision respective …

Q9.When a car is at rest, its driver sees rain drops falling on it vertically. When driving the car with speed v , he sees that rain drops are coming at an angle $60^{\circ }$ from the horizontal. On further increasing the speed of the car to $(1+\beta )\mathrm{v}$, this angle change …

Q10.Given the masses of various atomic particles $m_p=1.0072u,m_n=1.0087u,m_e=0.000548\mathrm{u},{\mathrm{m}}_{\mathrm{v}}^{-}=0,{\mathrm{m}}_{\mathrm{d}}=2.0141\mathrm{u}$, where $\mathrm{p}\equiv$ proton, $\mathrm{n}\equiv$ neutron, $\mathrm{e}\equiv$ electron, …

Q11.A circuit to verify Ohm's law uses ammeter and voltmeter in series or parallel connected correctly to the resistor. In the circuit:

Q12.Consider the force F on a charge ' q ' due to a uniformly charged spherical shell of radius R carrying charge Q distributed uniformly over it. Which one of the following statements is true for F , if ' q ' is placed at distance r from the centre of the shell?

Q13.A student measuring the diameter of a pencil of circular cross-section with the help of a vernier scale records the following four readings $5.50\mathrm{mm},5.55\mathrm{mm},5.45\mathrm{mm};5.65$ mm . The average of these four readings is 5.5375 mm and the standard devia …

Q14.A double convex lens has power $P$ and same radii of curvature $R$ of both the surfaces. The radius of curvature of a surface of a plano-convex lens made of the same material with power 1.5 P is

Q15.A square loop of side 2 a 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 z -axis and passing through point ( $0,b,0$ ), ( $b\gg a$ ). The magnitude of torque on the loop about $z$-axis will …

Q16.A fluid is flowing through a horizontal pipe of varying cross-section, with speed $\mathrm{v}{\mathrm{ms}}^{-1}$ a ta point where the pressure is P Pascal. At another point where pressure is $\frac{\mathrm{P}}{2}$ Pascal its speed is $\mathrm{V}{\mathrm{ms}}^{-1}$. If the density o …

Q17.When a particle of mass $m$ is attached to a vertical spring of spring constant $k$ and released, its motion is described by $\mathrm{y}(\mathrm{t})={\mathrm{y}}_0{\sin }^2\omega \mathrm{t}$, where ' y ' is measured from the lower end of unstretched spring. Then $\omega$ is:

Q18.In a dilute gas at pressure P and temperature T, the mean time between successive collisions of a molecule varies with T as:

Q19.Assuming the nitrogen molecule is moving with r.m.s. velocity at 400 K, the de-Broglie wavelength of nitrogen molecule is close to:
(Given: nitrogen molecule weight: $4.64\times 10^{-26}$ kg, Boltzman constant: $1.38\times 10^{-23}$ J/K, Planck constant: $6.63\times 10^{-34}$ …

Q20.The liner mass density of a thin rod AB of length L varies from A to B as $\lambda (x)={\lambda }_0\left(1+\frac{x}{L}\right)$, where x is the distance from A. If M is the mass of the rod hen its moment of inertia about an axis passing through A and perpendicular to the rod is:

Q21.The out put characteristics of a transistor is shown in the figure. When ${\mathrm{V}}_{\mathrm{CE}}$ is 10 V and ${\mathrm{I}}_{\mathrm{C}}=4.0$ mA, then value of ${\beta }_{\mathrm{ac}}$ is ____.

Q22.The centre of mass of a solid hemisphere of radius 8 cm is xcm from the centre of the flat surface. Then value of x is ____.

Q23.An engine operates by taking a monatomic ideal gas through the cycle shown in the figure. The percentage efficiency of the engine is close to ____.

Q24.A Young's double-slit experiment is performed using monochromatic light of wavelength $\lambda$. The intensity of light at a point on the screen, where the path difference is $\lambda$, is K units. The intensity of the light at a point where the path difference is …

Q25.In a series LR circuit, power of 400 W is dissipated from a source of $250\mathrm{V},50\mathrm{Hz}$. The power factor of the circuit is 0.8. In order to bring the power factor to unity, a capacitor of value C is added in series to the L and R. Taking the value of C as …

Q1.For a reaction,
$4\mathrm{M}(\mathrm{s})+{\mathrm{nO}}_2(\mathrm{g})\to 2{\mathrm{M}}_2{\mathrm{O}}_{\mathrm{n}}(\mathrm{s})$,
the free energy change is plotted as a function of temperature. The temperature below which the oxide is stable could be inferred from the p …

Q2.The average molar mass of chlorine is $35.5\mathrm{g}{\mathrm{mol}}^{-1}$. The ratio of ${}^{35}\mathrm{Cl}$ to ${}^{37}\mathrm{Cl}$ in naturally occurring chlorine is close to:

Q3.Which one of the following statements is not true?

Q4.The value of ${\mathrm{K}}_{\mathrm{C}}$ is 64 at 800 K for the reaction
${\mathrm{N}}_2(\mathrm{g})+3{\mathrm{H}}_2(\mathrm{g})\rightleftharpoons 2{\mathrm{NH}}_3(\mathrm{g})$
The value of ${\mathrm{K}}_{\mathrm{C}}$ for the following reaction is: …

Q5.Dihydrogen of high purity (>99.95%) is obtained through:

Q6.The reaction of NO with ${\mathrm{N}}_2{\mathrm{O}}_4$ at 250 K gives:

Q7.The correct match between Item-I (starting material) and Item-II (reagent) for the preparation of benzaldehyde is:

Item-I
(I) Benzene
(II) Benzonitrile
(III) Benzoyl Chloride

Item-II
(P) $\mathrm{HCl}$ and ${\mathrm{SnCl}}_2,{\mathrm{H}}_3{\mathrm{O}}^{+}$
(Q) …

Q8.A crystal is made up of metal ions ' ${\mathrm{M}}_1$ ' and ' ${\mathrm{M}}_2$ ' and oxide ions. Oxide ions form a ccp lattice structure. The cation ' ${\mathrm{M}}_1$ ' occupies $50\%$ of octahedral voids and the cation ' ${\mathrm{M}}_2$ ' occupies $12.5\%$ of tet …

Q9.The element that can be refined by distillation is:

Q10.For a $d^4$ metal ion in an octahedral field, the correct electronic configuration is:

Q11.Match the following:

Test / Method
(i) Lucas Test
(ii) Dumas method
(iii) Kjeldahl's method
(iv) Hinsberg Test

Reagent
(a) ${\mathrm{C}}_6{\mathrm{H}}_5{\mathrm{SO}}_2\mathrm{Cl}/$ aq. KOH
(b) ${\mathrm{HNO}}_3/{\mathrm{AgNO}}_3$
(c) $\mathrm{CuO}/{\mathrm{CO}}_2$ …

Q12.Match the following compounds (Column-I) with their uses (Column-II):
S.
No
Column-I
S.
No.
Column-II
No.
(i) $\mathrm{Ca}(\mathrm{OH}{)}_2$
(A) casts of statues
(ii) $\mathrm{NaCl}$
(B) white wash
(iii) ${\mathrm{CaSO}}_4\cdot \frac{1}{2}{\mathrm{H}}_2\mathrm{O}$
(C) an …

Q13.Which of the following compounds can be prepared in good yield by Gabriel phthalimide synthesis?

Q14.A set of solutions is prepared using 180 g of water as a solvent and 10 g of different non-volatile solutes A, B and C. The relative lowering of vapour pressure in the presence of these solutes are in the order [Given, molar mass of A=100 g mol⁻¹; B= 200 g mol⁻¹; C=10,000 g mol⁻¹ …

Q15.For the given cell;
Cu(s)|Cu²⁺(C₁ M) || Cu²⁺(C₂ M)|Cu(s)
Change in Gibbs energy (ΔG) is negative, if

Q16.Reaction of an inorganic sulphite X with dilute H₂SO₄ generates compound Y. Reaction of Y with NaOH gives X. Further, the reaction of X with Y and water affords compound Z. Y and Z respectively, are:

Q17.The increasing order of the boiling points of the major products A, B and C of the following reactions will be:
(a)
(b)
(c)

Q18.Mischmetal is an alloy consisting mainly of:

Q19.The correct match between Item-I and Item-II is:

Item-I
(a) Natural rubber
(b) Neoprene
(c) Buna-N
(d) Buna-S

Item-II
(I) 1, 3-butadiene + styrene
(II) 1, 3-butadiene + acrylonitrile
(III) Chloroprene
(IV) Isoprene

Q20.If the solubility product of AB₂ is 3.20 × 10⁻¹¹ M³, then the solubility of AB₂ in pure water is _____ × 10⁻⁴ mol L⁻¹. [Assuming that neither kind of ion reacts with water]

Q21.For Freudlich adsorption isotherm, a plot of log(x/m) (y-axis) and log p (x-axis) gives a straight line. The intercept and slope for the line is 0.4771 and 2, respectively. The mass of gas adsorbed per gram of adsorbent if the initial pressure is 0.04 atm, is _____ × 10⁻⁴ g. (log …

Q22.A solution of phenol in chloroform when treated with aqueous NaOH gives compound P as a major product. The mass percentage of carbon in P is _____. (to the nearest integer) (Atomic mass: C=12; H=1; O=16)

Q23.The atomic number of Unnilunium is _____.

Q24.The rate of a reaction decreased by 3.555 times when the temperature was changed from $40^{\circ }\mathrm{C}$ to $30^{\circ }\mathrm{C}$. The activation energy (in $\mathrm{kJ}{\mathrm{mol}}^{-1}$) of the reaction is ____.

Q1.The integral ${\int }_1^2{e}^x\cdot x^2\left(2+{\log }_{e}x\right)dx$ equals:

Q2.The area (in sq. units) of the region enclosed by the curves $y=x^2-1$ and $y=1-x^2$ is equal to

Q3.The angle of elevation of the summit of a mountain from a point on the ground is $45^{\circ }$. After climbing up one km towards the summit at an inclination of $30^{\circ }$ from the ground, the angle of elevation of the summit is found to be $60^{\circ }$. Then the height (in km ) …

Q4.The set of all real values of $\lambda$ for which the function $f(x)=\left(1-{\cos }^{2}x\right)\cdot (\lambda +\sin x)$, $\mathrm{x}\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right)$, has exactly one maxima and exactly one minima, is

Q5.If $\alpha$ and $\beta$ are the roots of the equation $2x(2x+1)=1$, then $\beta$ is equal to:

Q6.For all twice differentiable functions
$f:R\to R$, with $f(0)=f(1)=f^{\prime }(0)=0$,

Q7.If $y=\left(\frac{2}{\pi }x-1\right)\mathrm{cosec}x$ is the solution of the differential equation, $\frac{dy}{dx}+p(x)y=\frac{2}{\pi }\mathrm{cosec}x,0<x<\frac{\pi }{2}$, then the function $p(x)$ is equal to:

Q8.Let L denote the line in the xy -plane with x and y intercepts as 3 and 1 respectively. Then the image of the point $(-1,-4)$ in this line is:

Q9.If the tangent to the curve, $y=f(x)=x{\log }_{e}x,(x>0)$ at a point ( $c,f(c)$ ) is parallel to the line - segment joining the points $(1,0)$ and $(e,e)$ then $c$ is equal to:

Q10.Let $f:R\to R$ be a function defined by $f(x)=\max \left\{x,x^2\right\}$. Let $S$ denote the set of all points in $R$, where $f$ is not differentiable. Then:

Q11.Let $\theta =\frac{\pi }{5}$ and $\mathrm{A}=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right]$. If $\mathrm{B}=\mathrm{A}+{\mathrm{A}}^4$, then $\det (\mathrm{B})$ :

Q12.A plane P meets the coordinate axes at $\mathrm{A},\mathrm{B}$ and C respectively. The centroid of $△\mathrm{ABC}$ is given to be ( $1,1,2$ ). Then the equation of the line through this centroid and perpendicular to the plane P is:

Q13.The common difference of the A.P. $b_1,b_2,\dots ,b_m$ is 2 more than the common difference of A.P. $a_1,a_2,\dots ,a_n$. If $a_{40}=-159$, $a_{100}=-399$ and $b_{100}=a_{70}$, then $b_1$ is equal to:

Q14.If the normal at an end of a latus rectum of an ellipse passes through an extremity of the minor axis, then the eccentricity $e$ of the ellipse satisfies:

Q15.For a suitably chosen real constant $a$, let a function, $f:\mathbb{R}-\{-a\}\to \mathbb{R}$ be defined by $f(x)=\frac{a-x}{a+x}$. Further suppose that for any real number $x\ne -a$ and $f(x)\ne -a$, $(f\circ f)(x)=x$. Then $f\left(-\frac{1}{2}\right)$ is equal to:

Q16.If the constant term in the binomial expansion of ${\left(\sqrt{x}-\frac{k}{x^2}\right)}^{10}$ is 405, then $|k|$ equals:

Q17.The centre of the circle passing through the point $(0,1)$ and touching the parabola $y=x^2$ at the point $(2,4)$ is:

Q18.Let $z=x+iy$ be a non-zero complex number such that $z^2=i|z{|}^2$, where $i=\sqrt{-1}$, then $z$ lies on the:

Q19.Consider the statement: "For an integer $n$, if $n^3-1$ is even, then $n$ is odd." The contrapositive statement of this statement is:

Q20.The probabilities of three events $A$, $B$ and $C$ are given by $P(A)=0.6$, $P(B)=0.4$ and $P(C)=0.5$. If $P(A\cup B)=0.8$, $P(A\cap C)=0.3$, $P(A\cap B\cap C)=0.2$, $P(B\cap C)=\beta$ and $P(A\cup B\cup C)=\alpha$, where $0.85\le \alpha \le 0.95$, then $\beta$ lies in …

Q21.Suppose that a function $f:\mathbb{R}\to \mathbb{R}$ satisfies $f(x+y)=f(x)f(y)$ for all $x,y\in \mathbb{R}$ and $f(1)=3$. If ${\sum }_{i=1}^{n}f(i)=363$, then $n$ is equal to

Q22.The sum of distinct values of $\lambda$ for which the system of equations
$(\lambda -1)x+(3\lambda +1)y+2\lambda z=0$
$(\lambda -1)x+(4\lambda -2)y+(\lambda +3)z=0$
$2x+(3\lambda +1)y+3(\lambda -1)z=0$,
has non-zero solutions, is ______.

Q23.If $\vec{x}$ and $\vec{y}$ be two non-zero vectors such that $|\vec{x}+\vec{y}|=|\vec{x}|$ and $2\vec{x}+\lambda \vec{y}$ is perpendicular to $\vec{y}$, then the value of $\lambda$ is

Q24.Consider the data on $x$ taking the values $0,2,4,8,\dots ,2^n$ with frequencies ${}^n{C}_0{,}^n{C}_1{,}^n{C}_2,\dots {,}^n{C}_n$ respectively. If the mean of this data is $\frac{728}{2^n}$, then $n$ is equal to ______.

Q25.The number of words (with or without meaning) that can be formed from all the letters of the word "LETTER" in which vowels never come together is ____.