JEE Main 2020 · 09 Jan 2020 · Shift 1

Q1.Two particles of equal mass 'm' have respective initial velocities $u\hat{i}$ and $u\left(\frac{\hat{i}+\hat{j}}{2}\right)$. They collide completely inelastically. The energy lost in the process is:

Q2.Radiation, with wavelength $6561\text{ A˚}$ falls on a metal surface to produce photoelectrons. The electrons are made to enter a uniform magnetic field of $3\times 10^{-4}\text{ T}$. If the radius of the largest circular path followed by the electrons is 10 mm, the work functi …

Q3.Water flows in a horizontal tube (see figure). The pressure of water changes by $700{\text{ Nm}}^{-2}$ between A and B where the area of cross section are $40{\text{ cm}}^2$ and $20{\text{ cm}}^2$, respectively. Find the rate of flow of water through the tube. (density of water …

Q4.The aperture diameter of a telescope is 5 m. The separation between the moon and the earth is $4\times 10^5\text{ km}$. With light of wavelength of 5500 Å, the minimum separation between objects on the surface of moon, so that they are just resolved, is close to:

Q5.A body A of mass m is moving in a circular orbit of radius R about a planet. Another body B of mass $\frac{m}{2}$ collides with A with a velocity which is half $\left(\frac{\vec{v}}{2}\right)$ the instantaneous velocity $\vec{v}$ of A. The collision is completely inelastic. Then, …

Q6.Consider two ideal diatomic gases A and B at some temperature T . Molecules of the gas A are rigid, and have a mass m . Molecules of the gas B have an additional vibrational mode and have mass $\frac{m}{4}$. The ratio of the specific heats $(C_v^A$ and …

Q7.Three harmonic waves having equal frequency v and same intensity ${\mathrm{I}}_0$, have phase angles $0,\frac{\pi }{4}$ and $-\frac{\pi }{4}$ respectively. When they are superimposed the intensity of the resultant wave is close to:

Q8.A quantity $f$ is given by $f=\sqrt{\frac{h{c}^5}{G}}$ where $c$ is speed of light, $G$ universal gravitational constant and $h$ is the Planck's constant. Dimension of $f$ is that of:

Q9.If the screw on a screw-gauge is given six rotations, it moves by 3 mm on the main scale.
If there are 50 divisions on the circular scale the least count of the screw gauge is

Q10.Three solid spheres each of mass $m$ and diameter $d$ are stuck together such that the lines connecting the centres form an equilateral triangle of side of length d . The ratio ${\mathrm{I}}_0/{\mathrm{I}}_{\mathrm{A}}$ of moment of inertia ${\mathrm{I}}_0$ of the system …

Q11.Consider a force $\vec{F}=-x\hat{i}+y\hat{j}$. The work done by this force in moving a particle from point $A(1,0)$ to $B(0,1)$ along the line segment is: (all quantities are in SI units)

Q12.A vessel of depth $2h$ is half filled with a liquid of refractive index $2\sqrt{2}$ and the upper half with another liquid of refractive index $\sqrt{2}$. The liquids are immiscible. The apparent depth of the inner surface of the bottom of vessel will be

Q13.A particle moving with kinetic energy E has de Broglie wavelength $\lambda$. If energy $\Delta \mathrm{E}$;is added to its energy, the wavelength become $\lambda /2$. Value of $\Delta \mathrm{E}$, is:

Q14.In the given circuit diagram, a wire is joining points $B$ and $D$. The current in this wire is:

Q15.A long, straight wire of radius a carries a current distributed uniformly over its crosssection. The ratio of the magnetic fields due to the wire at distance $\frac{\mathrm{a}}{3}$ and 2 a , respectively from the axis of the wire is:

Q16.The electric fields of two plane electromagnetic plane waves in vacuum are given by ${\overrightarrow{\mathrm{E}}}_1={\mathrm{E}}_0\hat{\mathrm{j}}\cos (\omega \mathrm{t}-\mathrm{kx})$ and …

Q17.An electric dipole of moment $\vec{p}=(-\hat{i}-3\hat{j}+2\hat{k})\times 10^{-29}\mathrm{cm}$ is at the origin $(0,0,0)$. The electric field due to this dipole at $\vec{r}=+\hat{i}+3\hat{j}+5\hat{k}$ (note that $\vec{r}\cdot \vec{p}=0$ ) is parallel to:

Q18.A charged particle of mass '$m$' and charge '$q$' moving under the influence of uniform electric field $E\vec{i}$ and a uniform magnetic field $\mathrm{B}\overrightarrow{\mathrm{k}}$ follows a trajectory from point $P$ to $Q$ as shown in figure. The velocities at $P$ and $Q$ ar …

Q19.Consider a sphere of radius $R$ which carries a uniform charge density $\rho$. If a sphere of radius $\frac{R}{2}$ is carved out of it, as shown the ratio $\frac{|{\vec{E}}_A|}{|{\vec{E}}_B|}$ of magnitude of electric field ${\vec{E}}_A$ and ${\vec{E}}_B$, r …

Q20.Which of the following is an equivalent cyclic process corresponding to the thermodynamic cyclic given in the figure? Where, $1\to 2$ is adiabatic. (Graphs are schematic and are not to scale)

Q21.Both the diodes used in the circuit shown are assumed to be ideal and have negligible resistance when these are forward biased. Built in potential in each diode is 0.7 V. For the input voltages shown in the figure, the voltage (in Volts) at point $A$ is ____.

Q22.One end of a straight uniform 1 m long bar is pivoted on horizontal table. It is released from rest when it makes an angle $30^{\circ }$ from the horizontal (see figure). Its angular speed when it hits the table is given as $\sqrt{\mathrm{n}}{\mathrm{s}}^{-1}$, where $n$ is an inte …

Q23.In a fluorescent lamp choke (a small transformer) 100 V of reverse voltage is produced when the choke current changes uniformly from 0.25 A to 0 in a duration of 0.025 ms. The self-inductance of the choke (in mH) is estimated to be ____.

Q24.A body of mass $\mathrm{m}=10\mathrm{kg}$ is attached to one end of a wire of length 0.3 m. The maximum angular speed (in $\mathrm{rad}{\mathrm{s}}^{-1}$) with which it can be rotated about its other end in space station is (Breaking stress of wire …

Q25.The distance $x$ covered by a particle in one dimensional motion varies with time $t$ as $x^2=a{t}^2+bt+c$. If the acceleration of the particle depends on $x$ as $x^{-n}$, where $n$ is an integer, the value of $n$ is ____.

Q1.If the magnetic moment of a dioxygen species is $1.73B.M$, it may be:

Q2.The compound that cannot act both as oxidising and reducing agent is:

Q3.$[\mathrm{Pd}(F)(Cl)(Br)(I){]}^{2-}$ has $n$ number of geometrical isomers. Then, the spin-only magnetic moment and crystal field stabilisation energy [CFSE] of $[\mathrm{Fe}(\mathrm{CN}{)}_6{]}^{n-6}$, respectively, are:
[Note: Ignore the pairing energy]

Q4.The electronic configurations of bivalent europium and trivalent cerium are: (atomic number: $\mathrm{Xe}=54,\mathrm{Ce}=58,\mathrm{Eu}=63$)

Q5.For following reactions
$\mathrm{A}\stackrel{700\mathrm{K}}{\to }$ Product
A $\underset{\text{catalyst}}{\overset{500\mathrm{K}}{\to }}$ Product
it was found that the ${\mathrm{E}}_{\mathrm{a}}$ is decreased by $30kJ/mol$ in the presence of catalyst. If the rate remains unc …

Q6.The increasing order of basicity for the following intermediates is (from weak to strong)
(i)
(ii)
(iii)
(iv)
(v)

Q7.'$X$' melts at low temperature and is a bad conductor of electricity in both liquid and solid state. $X$ is:

Q8.The de Broglie wavelength of an electron in the $4^{\text{th}}$ Bohr orbit is:

Q9.Identify (A) in the following reaction sequence:

Q10.The major product (Y) in the following reactions is:

Q11.Complex X of composition $\mathrm{Cr}({\mathrm{H}}_2\mathrm{O}{)}_6{\mathrm{Cl}}_n$ has a spin only magnetic moment of 3.83 BM. It reacts with ${\mathrm{AgNO}}_3$ and shows geometrical isomerism. The IUPAC nomenclature of X is:

Q12.The acidic, basic and amphoteric oxides, respectively, are:

Q13.The ${\mathrm{K}}_{\mathrm{sp}}$ for the following dissociation is $1.6\times 10^{-5}$


Which of the following choices is correct for a mixture of $300\mathrm{mL}$ …

Q14.A chemist has 4 samples of artificial sweetener A, B, C and D. To identify these samples, he performed certain experiments and noted the following observations:
(i) A and D both form blue-violet colour with ninhydrin.
(ii) Lassaigne extract of C gives positive ${\mathrm{AgNO}}_3$ …

Q15.The major product Z obtained in the following reaction scheme is:

Q16.Which of these will produce the highest yield in Friedel Crafts reaction?

Q17.B has a smaller first ionization enthalpy than Be. Consider the following statements:
(i) it is easier to remove $2p$ electron than $2s$ electron.
(ii) $2p$ electron of $B$ is more shielded from the nucleus by the inner core of electrons than the $2s$ electrons of Be.
(iii) $2s$ …

Q18.The correct order of heat of combustion for following alkadienes is:

Q19.If enthalpy of atomisation for ${\mathrm{Br}}_2(\mathrm{A})$ is $\mathrm{x}$ $kJ/mol$ and bond enthalpy for ${\mathrm{Br}}_2$ is $\mathrm{y}$ $kJ/mol$, the relation between them:

Q20.According to the following diagram, A reduces ${\mathrm{BO}}_2$ when the temperature is:

Q21.The molarity of ${\mathrm{HNO}}_3$ in a sample which has density $1.4$ $g/mL$ and mass percentage of $63\%$ is (Molecular Weight of ${\mathrm{HNO}}_3=63$)

Q22.The mass percentage of nitrogen in histamine is ____.

Q23.How much amount of NaCl should be added to 600 g of water ($\rho =1.00$ $g/mL$) to decrease the freezing point of water to $-0.2^{\circ }\mathrm{C}$? ____.
(The freezing point depression constant for water $=2$ $\mathrm{K}$ $\mathrm{kg}$ ${\mathrm{mol}}^{-1}$)

Q24.108 g of silver (molar mass $108$ $\mathrm{g}$ ${\mathrm{mol}}^{-1}$) is deposited at cathode from ${\mathrm{AgNO}}_3(\mathrm{aq})$ solution by a certain quantity of electricity. The volume (in L) of oxygen gas produced at 273 K and 1 bar pressure from water by the same quantity of …

Q25.The hardness of a water sample containing $10^{-3}\mathrm{M}{\mathrm{MgSO}}_4$ expressed as ${\mathrm{CaCO}}_3$ equivalents (in ppm) is ______.
(molar mass of ${\mathrm{MgSO}}_4$ is $120.38\mathrm{g}/\mathrm{mol}$)

Q1.The product $2^{\frac{1}{4}}\cdot 4^{\frac{1}{16}}\cdot 8^{\frac{1}{48}}\cdot 16^{\frac{1}{128}}\dots \dots \dots$ to $\infty$ is equal to

Q2.Let the observations $x_i(1\le i\le 10)$ satisfy the equation ${\sum }_{i=1}^{10}\left(x_i-5\right)=10$ and ${\sum }_{\mathrm{i}=1}^{10}{\left({\mathrm{x}}_{\mathrm{i}}-5\right)}^2=40$. If $\mu$ and $\lambda$ are the mean and the variance of the observations, …

Q3.If $e_1$ and $e_2$ are the eccentricities of the ellipse, $\frac{x^2}{18}+\frac{y^2}{4}=1$ and the hyperbola, $\frac{x^2}{9}-\frac{y^2}{4}=1$ respectively and $(e_1,e_2)$ is a point on the ellipse, $15x^2+3y^2=k$, then $k$ is equal to:

Q4.If the matrices $\mathrm{A}=\left[\begin{array}{ccc}1& 1& 2\\ 1& 3& 4\\ 1& -1& 3\end{array}\right],\mathrm{B}=\mathrm{adj}\mathrm{A}$ and $\mathrm{C}=3\mathrm{A}$, then $\frac{|\mathrm{adj}\mathrm{B}|}{|\mathrm{C}|}$ is equal to:

Q5.If $\mathrm{f}(\mathrm{x})=\{\begin{array}{cl}\frac{\sin (\mathrm{a}+2)\mathrm{x}+\sin \mathrm{x}}{\mathrm{x}};& x<0\\ \mathrm{b}& ;\mathrm{x}=0\\ \frac{{\left(\mathrm{x}+3{\mathrm{x}}^2\right)}^{1/3}-{\mathrm{x}}^{1/3}}{{\mathrm{x}}^{4/3}};& x>0\end{array}$ …

Q6.If the number of five digit numbers with distinct digits and 2 at the $10^{\text{th}}$ place is 336 k , then k is equal to:

Q7.In a box, there are 20 cards, out of which 10 are labeled as A and the remaining 10 are labelled as B. Cards are drawn at random, one after the other and with replacement, till a second A - card is obtained. The probability that the second A - card appears before the third B - ca …

Q8.The number of real roots of the equation, $e^{4x}+e^{3x}-4e^{2x}+e^x+1=0$ is:

Q9.A spherical iron ball of 10 cm radius is coated with a layer of ice of uniform thickness that melts at a rate of $50{\mathrm{cm}}^3/\min$. When the thickness of ice is 5 cm , then the rate (in $\mathrm{cm}/\min$ ) at which of the thickness of ice decreas …

Q10.The value of ${\int }_0^{2\pi }\frac{x{\sin }^{8}x}{{\sin }^{8}x+{\cos }^{8}x}dx$ is equal to:

Q11.Let $z$ be a complex number such that $\left|\frac{z-i}{z+2i}\right|=1$ and $|z|=\frac{5}{2}$. Then the value of $|z+3i|$ is:

Q12.Negation of the statement:
$\sqrt{5}$ is an integer or 5 is irrational' is:

Q13.Let C be the centroid of the triangle with vertices $(3,-1),(1,3)$ AND $(2,4)$. Let P be the point of intersection of the lines $x+3y-1=0$ and $3x-y+1=0$. Then the line passing through the points C and P also passes through the point:

Q14.If for some $\alpha$ and $\beta$ in R, the intersection of the following three planes
$x+4y-2z=1$
$x+7y-5z=\beta$
$x+5y+\alpha z=5$
is a line in ${\mathrm{R}}^3$, then $\alpha +\beta$ is equal to:

Q15.Let $f$ be any function continuous on $[a,b]$ and twice differentiable on (a, b). If for all $x\in (a,b),f^{\prime }(x)>0$ and $f^{\prime \prime }(x)<0$, then for any $c\in (a,b)$ $\frac{f(c)-f(a)}{f(b)-f(c)}$ is greater than:

Q16.The value of ${\cos }^3\left(\frac{\pi }{8}\right)\cdot \cos \left(\frac{3\pi }{8}\right)+{\sin }^3\left(\frac{\pi }{8}\right)\cdot \sin \left(\frac{3\pi }{8}\right)$ is:

Q17.A circle touches the $y$-axis at the point $(0,4)$ and passes through the point $(2,0)$. Which of the following lines is not a tangent to this circle?

Q18.If for all real triplets $(a,b,c)$, $f(x)=a+bx+c{x}^2$; then ${\int }_0^{1}f(x)dx$ is equal to:

Q19.If $f^{\prime }(x)={\tan }^{-1}(\sec x+\tan x),-\frac{\pi }{2}<x<\frac{\pi }{2}$, and $f(0)=0$, then $f(1)$ is equal to:

Q20.The integral $\int \frac{\mathrm{dx}}{(\mathrm{x}+4{)}^{8/7}(\mathrm{x}-3{)}^{6/7}}$ is equal to:
(where $C$ is a constant of integration)

Q21.The projection of the line segment joining the points $(1,-1,3)$ and $(2,-4,11)$ on the line joining the points $(-1,2,3)$ and $(3,-2,10)$ is ______

Q22.If the vectors, $\vec{p}=(a+1)\hat{i}+a\hat{j}+a\hat{k}$, $\vec{q}=a\hat{i}+(a+1)\hat{j}+a\hat{k}$ and $\overrightarrow{\mathrm{r}}=\mathrm{a}\hat{\mathrm{i}}+\mathrm{a}\hat{\mathrm{j}}+(\mathrm{a}+1)\hat{\mathrm{k}}$ $(\mathrm{a}\in \mathrm{R})$ are coplanar and …

Q23.If for $x\ge 0$, $y=y(x)$ is the solution of the differential equation, $(x+1)dy=\left((x+1{)}^2+y-3\right)dx$, $y(2)=0$, then $y(3)$ is equal to ______

Q24.The coefficient of $x^4$ in the expansion of ${\left(1+x+x^2\right)}^{10}$ is ______.

Q25.The number of distinct solutions of the equation, ${\log }_{\frac{1}{2}}|\sin x|=2-{\log }_{\frac{1}{2}}|\cos x|$ in the interval $[0,2\pi ]$, is ______.