JEE Main 2020 · 08 Jan 2020 · Shift 2

Q1.A simple pendulum is being used to determine the vale of gravitational acceleration $g$ at a certain place. The length of the pendulum is 25.0 cm and a stop watch with 1 s resolution measures the time taken for 40 oscillations to be 50 s. The accuracy in $g$ is:

Q2.A Carnot engine having an efficiency of $\frac{1}{10}$ is being used as a refrigerator. If the work done on the refrigerator is 10 J, the amount of heat absorbed from the reservoir at lower temperature is:

Q3.Consider two charged metallic spheres $S_1$ and $S_2$ of radii $R_1$ and $R_2$, respectively. The electric fields $E_1$ (on $S_1$) and $E_2$ (on $S_2$) on their surfaces are such that $E_1/E_2=R_1/R_2$. Then the ratio of $V_1$ (on $S_1$)$/V_2$ (on …

Q4.As shown in the figure, a battery of emf $\epsilon$ is connected to an inductor $L$ and resistance $R$ in series. The switch is closed at $t=0$. The total charge that flows from the battery, between $t=0$ and $t=t_c$ ($t_c$ is the time constant of the circuit) is

Q5.A very long wire $ABADMNDC$ is shown in figure carrying current $I$. $AB$ and $BC$ parts are straight, long and at right angle. At $D$ wire forms a circular turn $DMND$ of radius $R$. $AB$, $BC$ parts are tangential to circular turn at $N$ and $D$. Magnetic field at the centre of …

Q6.A uniform sphere of mass 500 g rolls without slipping on a plane horizontal surface with its centre moving at a speed of $5.00\mathrm{cm}/\mathrm{s}$. Its kinetic energy is:

Q7.In a double-slit experiment, at a certain point on the screen the path difference between the two interfering waves is $\frac{1}{8}$ th of a wavelength. The ratio of the intensity of light at that point to that at the centre of a bright fringe is:

Q8.A particle of mass $m$ is dropped from a height $h$ above the ground. At the same time another particle of same mass is thrown vertically upwards from the ground with a speed of $\sqrt{2\mathrm{gh}}$.
If they collide head-on completely inelastically, the time taken for the combi …

Q9.A particle moves such that its position vector $\vec{r}(t)=\cos \omega t\hat{i}+\sin \omega t\hat{j}$ where $\omega$ is a constant and $t$ is time. Then which of the following statements is true for the velocity $\vec{v}(t)$ and acceleration $\vec{a}(t)$ of the particle:

Q10.Consider a mixture of $n$ moles of helium gas and $2n$ moles of oxygen gas (molecules taken to be rigid) as an ideal gas. Its ${\mathrm{C}}_{\mathrm{P}}/{\mathrm{C}}_{\mathrm{V}}$ value will be

Q11.A capacitor is made of two square plates each of side 'a' making a very small angle α between them, as shown in figure. The capacitance will be close to:

Q12.Two liquids of densities ${\rho }_1$ and ${\rho }_2$ (${\rho }_2=2{\rho }_1$) are filled up behind a square wall of side 10 m as shown in figure. Each liquid has a height of 5 m. The ratio of the forces due to these liquids exerted on upper part MN to that at the lower part NO is (A …

Q13.A plane electromagnetic wave of frequency 25 GHz is propagating in vacuum along the z-direction. At a particular point in space and time, the magnetic field is given by $\vec{B}=5\times 10^{-8}\hat{j}\mathrm{T}$. The corresponding electric field $\vec{E}$ is (speed of light …

Q14.An electron (mass $m$) with initial velocity $\vec{v}=v_0\hat{i}+v_0\hat{j}$ is in an electric field $\vec{E}=-E_0\hat{k}$. If ${\lambda }_0$ is initial de-Broglie wavelength of electron, its de-Broglie wavelength at time $t$ is given by

Q15.A transverse wave travels on a taut steel wire with a velocity of v when tension in it is $2.06\times 10^4\mathrm{N}$. When the tension is changed to T, the velocity changed to $\mathrm{v}/2$. The value of T is close to:

Q16.An object is gradually moving away from the focal point of a concave mirror along the axis of the mirror. The graphical representation of the magnitude of linear magnification (m) versus distance of the object from the mirror (x) is correctly given by (Graphs are drawn schematica …

Q17.A particle of mass $m$ and charge $q$ is released from rest in a uniform electric field. If there is no other force on the particle, the dependence of its speed v on the distance x travelled by it is correctly given by (graphs are schematic and not drawn to scale)

Q18.As shown in figure when a spherical cavity (centered at O) of radius 1 is cut out of a uniform sphere of radius R (centred at C ), the centre of mass of remaining (shaded) part of sphere is at G, i.e. on the surface of the cavity. R can be determined by the equation:

Q19.In the given circuit, value of Y is

Q20.A galvanometer having a coil resistance $100\Omega$ gives a full scale deflection when a current of 1 mA is passed through it. What is the value of the resistance which can convert this galvanometer into a voltmeter giving full scale deflection for a potential difference of 10 V …

Q21.A ball is dropped form the top of a 100 m high tower on a planet. In the last $\frac{1}{2}\mathrm{s}$ before hitting the ground, it covers a distance of 19 m. Acceleration due to gravity (in ${\mathrm{ms}}^{-2}$) near the surface on that planet is ____.

Q22.The first member of the Balmer series of hydrogen atom has a wavelength of $6561\mathring{A}$. The wavelength of the second member of the Balmer series (in nm) is ____.

Q23.The series combination of two batteries, both of the same emf 10 V, but different internal resistance of $20\Omega$ and $5\Omega$, is connected to the parallel combination of two resistors 30 $\Omega$ and $\mathrm{R}\Omega$. The voltage difference across the battery of interna …

Q24.An asteroid is moving directly towards the centre of the earth. When at a distance of 10 R ($R$ is the radius of the earth) from the earths centre, it has a speed of $12\mathrm{km}/\mathrm{s}$. Neglecting the effect of earths atmosphere, what will be the speed of the asteroid w …

Q25.Three containers ${\mathrm{C}}_1$, ${\mathrm{C}}_2$ and ${\mathrm{C}}_3$ have water at different temperatures. The table below shows the final temperature T when different amounts of water (given in liters) are taken from each container and mixed (assume no loss of heat during th …

Q1.The increasing order of the atomic radii of the following elements is:
(a) C
(b) O
(c) F
(d) Cl
(e) Br

Q2.Kjeldahl's method cannot be used to estimate nitrogen for which of the following compounds?

Q3.Consider the following plots of rate constant versus $\frac{1}{\mathrm{T}}$ for four different reactions. Which of the following order is correct for the activation energies of these reactions?

Q4.For the following Assertion and Reason, the correct option is :

Assertion : The pH of water increase with increase in temperature.
Reason : The dissociation of water into ${\mathrm{H}}^{+}$and ${\mathrm{OH}}^{-}$ is an exothermic reaction

Q5.White phosphorus on reaction with concentrated NaOH solution in an inert atmosphere of ${\mathrm{CO}}_2$ gives phosphine and compound $(\mathrm{X})$. $(\mathrm{X})$ on acidification with HCl gives compound $(\mathrm{Y})$. The basicity of compound $(\mathrm{Y})$ is :

Q6.The major product $[\mathrm{B}]$ in the following sequence is:

Q7.Among (a) - (d), the complexes that can display geometrical isomerism are:
(a) $\left[\mathrm{Pt}{\left({\mathrm{NH}}_3\right)}_3\right]{\mathrm{Cl}}^{+}$
(b) ${\left[\mathrm{Pt}\left({\mathrm{NH}}_3\right){\mathrm{Cl}}_5\right]}^{-}$
(c) …

Q8.For the following Assertion and Reason, the correct option is :

Assertion: For hydrogenation reactions, the catalytic activity increases from Group 5 to Group 11 metals with maximum activity shown by Group 7-9 elements.
Reason : The reactants are most strongly adsorbed on group …

Q9.The major product in the following reaction is

Q10.Among the reactions (a)-(d), the reaction(s) that does/do not occur in the blast furnace during the extraction of iron is/are:
(a) $\mathrm{CaO}+{\mathrm{SiO}}_2⟶{\mathrm{CaSiO}}_3$
(b) …

Q11.A metal (A) on heating in nitrogen gas gives compound B. B on treatment with ${\mathrm{H}}_2\mathrm{O}$ gives a colourless gas which when passed through ${\mathrm{CuSO}}_4$ solution gives a dark blue-violet coloured solution. A and B respectively, are:

Q12.Two monomers in maltose are:

Q13.The correct order of the calculated spin-only magnetic moments of complexes (A) to (D) is :
(a) $\mathrm{Ni}(\mathrm{CO}{)}_4$
(b) $\left[\mathrm{Ni}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]{\mathrm{Cl}}_2$
(c) …

Q14.An unsaturated hydrocarbon $X$ absorbs two hydrogen molecules on catalytic hydrogenation, and also gives following reaction: …

Q15.Hydrogen has three isotopes (a), (b) and (c). If the number of neutron(s) in (a), (b) and (c) respectively, are (x), (y) and (z), the sum of (x), (y) and (z) is:

Q16.Which of the following compound is likely to show both Frenkel and Schottky defects in its crystalline form?

Q17.Arrange the following bonds according to their average bond energies in descending order:
$\mathrm{C}-\mathrm{Cl},\mathrm{C}-\mathrm{Br},\mathrm{C}-\mathrm{F},\mathrm{C}-\mathrm{I}$

Q18.Preparation of Bakelite proceeds via reactions:

Q19.The radius of the second Bohr orbit, in terms of the Bohr radius, ${\mathrm{a}}_0$, in ${\mathrm{Li}}^{2+}$ is

Q20.Among the compounds A and B with molecular formula ${\mathrm{C}}_9{\mathrm{H}}_{18}{\mathrm{O}}_3,\mathrm{A}$ is having higher boiling point the $B$. The possible structures of $A$ and $B$ are:

Q21.Complexes $\left({\mathrm{ML}}_5\right)$ of metals Ni and Fe have ideal square pyramidal and trigonal bipyramidal geometries, respectively. The sum of the $90^{\circ },120^{\circ }$ and $180^{\circ }\mathrm{L}-\mathrm{M}-\mathrm{L}$ angles in the two complexes is ____

Q22.At constant volume, 4 mol of an ideal gas when heated from 300 K to 500 K changes its internal energy by 5000 J . The molar heat capacity at constant volume is ____

Q23.In the following sequence of reactions the maximum number of atoms present in molecule ' $C$ ' in one plane is …

Q24.For an electrochemical cell $\mathrm{Sn}(\mathrm{s})\left|{\mathrm{Sn}}^{2+}(\mathrm{aq},1\mathrm{M})\right|\left|{\mathrm{Pb}}^{2+}(\mathrm{aq},1\mathrm{M})\right|\mathrm{Pb}(\mathrm{s})$ the ratio $\frac{\left[{\mathrm{Sn}}^{2+}\right]}{\left[{\mathrm{Pb}}^{2+}\right]}$ when t …

Q25.${\mathrm{NaClO}}_3$ is used, even in spacecraft, to produce ${\mathrm{O}}_2$. The daily consumption of pure ${\mathrm{O}}_2$ by a person is 492 L at $1\mathrm{atm},300\mathrm{K}$. How much amount of ${\mathrm{NaClO}}_3$, in grams, is required to produce …

Q1.If the $10^{\text{th}}$ term of an A.P. is $\frac{1}{20}$ and its $20^{\text{th}}$ term is $\frac{1}{10}$, then the sum of its first 200 terms is:

Q2.Which of the following statement is a tautology?

Q3.The mean and variance of 20 observations are found to be 10 and 4, respectively. On rechecking, it was found that an observation 9 was incorrect and the correct observation was 11. Then the correct variance is:

Q4.The mirror image of the point ($1,2,3$) in a plane is $\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$. Which of the following points lies on this plane?

Q5.If a hyperbola passes through the point $P(10,16)$ and it has vertices at $(\pm 6,0)$ then the equation of the normal to it at $P$ is:

Q6.If a line, $y=mx+c$ is a tangent to the circle, $(x-3{)}^2+y^2=1$ and it is perpendicular to a line $L_1$, where $L_1$ is the tangent to the circle, $x^2+y^2=1$ at the point $\left(\frac{1}{\sqrt{2}},\frac{1}{\sqrt{2}}\right)$; then:

Q7.The area (in sq. units) of the region $\left\{(x,y)\in R^2\le y\le 3-2x\right\}$, is

Q8.Let S be the set of all functions $\int :[0,1]\to \mathrm{R}$, which are continuous on $[0,1]$ and differentiable on $(0,1)$. Then for every $\int$ in $S$, there exists $\mathrm{ac}\in (0,1)$, depending on $f$, such that:

Q9.Let $\vec{a}=\hat{i}-2\hat{j}+\hat{k}$ and $\vec{b}=\hat{i}-\hat{j}+\hat{k}$ be two vectors. If $\vec{c}$ is a vector such that $\vec{b}\times \vec{c}=\vec{b}\times \vec{a}$ and $\vec{c}\cdot \vec{a}=0$, then $\vec{c}\cdot \vec{b}$ is equal to:

Q10.Let $f:(1,3)\to R$ be a function defined by $f(x)=\frac{x[x]}{1+x^2}$, where $[x]$ denotes the greatest integer $\le \mathrm{X}$. Then the range of f is:

Q11.Let $\alpha =\frac{-1+i\sqrt{3}}{2}$. If $a=(1+\alpha ){\sum }_{k=0}^{100}{\alpha }^{2k}$ and $b={\sum }_{k=0}^{100}{\alpha }^{3k}$, then $a$ and $b$ are the roots of the quadratic equation:

Q12.${\lim }_{\mathrm{x}\to 0}\frac{{\int }_0^{\mathrm{x}}\mathrm{t}\sin (10\mathrm{t})\mathrm{dt}}{\mathrm{x}}$ is equal to:

Q13.The system of linear equations
$\lambda x+2y+2z=5$
$2\lambda x+3y+5z=8$
$4x+\lambda y+6z=10$ has:

Q14.If $\alpha$ and $\beta$ be the coefficients of $x^4$ and $x^2$ respectively in the expansion of ${\left(x+\sqrt{x^2-1}\right)}^6+{\left(x-\sqrt{x^2-1}\right)}^6$, then:

Q15.The differential equation of the family of curves, $x^2=4b(y+b),b\in R$, is:

Q16.The length of the perpendicular from the origin, on the normal to the curve, $x^2+2xy-3y^2=0$ at the point $(2,2)$ is:

Q17.If $A=\left(\begin{array}{cc}2& 2\\ 9& 4\end{array}\right)$ and $I=\left(\begin{array}{cc}1& 0\\ 0& 1\end{array}\right)$, then $10A^{-1}$ is equal to:

Q18.Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that A or B occurs is $\frac{1}{2}$, then the probability of both of them occur together is:

Q19.If $I={\int }_1^2\frac{dx}{\sqrt{2x^3-9x^2+12x+4}}$, then:

Q20.Let S be the set of all real roots of the equation, $3^x(3^x-1)+2=|3^x-1|+|3^x-2|$. Then S:

Q21.Let $f(x)$ be a polynomial of degree 3 such that $f(-1)=10,f(1)=-6,f(x)$ has a critical point at $x=-1$ and $f^{\prime }(x)$ has a critical point at $x=1$. Then $f(x)$ has a local minima at $x=$

Q22.Let a line $y=mx$ $(m>0)$ intersect the parabola, $y^2=x$ at a point P, other than the origin. Let the tangent to it at P meet the $x$-axis at the point Q. If area $(△OPQ)=4$ sq. units, then $m$ is equal to

Q23.The sum ${\sum }_{n=1}^7\frac{n(n+1)(2n+1)}{4}$ is equal to

Q24.The number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word 'EXAMINATION' is

Q25.If $\frac{\sqrt{2}\sin \alpha }{\sqrt{1+\cos 2\alpha }}=\frac{1}{7}$ and $\sqrt{\frac{1-\cos 2\beta }{2}}=\frac{1}{\sqrt{10}},\alpha ,\beta \in \left(0,\frac{\pi }{2}\right)$, then $\tan (\alpha +2\beta )$ is equal to ______.