JEE Main 2021 · 18 Mar 2021 · Shift 1

Q1.An oil drop of radius 2 mm with a density $3{\mathrm{gcm}}^{-3}$ is held stationary under a constant electric field $3.55\times 10^5{\mathrm{Vm}}^{-1}$ in the Millikan's oil drop experiment. What is the number of excess electrons that the oil drop will possess?

Consider …

Q2.In Young's double slit arrangement, slits are separated by a gap of 0.5 mm, and the screen is placed at a distance of 0.5 m from them. The distance between the first and the third bright fringe formed when the slits are illuminated by a monochromatic light of $5890\mathring{A}$ is:

Q3.Match List - I with List - II.

List - I
(a) 10 km height over earth's surface
(b) 70 km height over earth's surface
(c) 180 km height over earth's surface
(d) 270 km height over earth's surface

List - II
(i) Thermosphere
(ii) Mesosphere
(iii) Stratosphere
(iv) Troposphere

Q4.The position, velocity and acceleration of a particle moving with a constant acceleration can be represented by:

Q5.In the experiment of Ohm's law, a potential difference of 5.0 V is applied across the end of a conductor of length 10.0 cm and diameter of 5.00 mm. The measured current in the conductor is 2.00 A. The maximum permissible percentage error in the resistivity of the conductor is:

Q6.A thin circular ring of mass M and radius r is rotating about its axis with an angular speed $\omega$. Two particles having mass $m$ each are now attached at diametrically opposite points. The angular speed of the ring will become:

Q7.Your friend is having eye sight problem. She is not able to see clearly a distant uniform window mesh and it appears to her non-uniform and distorted. The doctor diagnosed the problems as:

Q8.A constant power delivering machine has towed a box, which was initially at rest, along a horizontal straight line. The distance moved by the box in time '$t$' is proportional to:

Q9.What will be the average value energy along one degree of freedom for an ideal gas in thermal equilibrium at a temperature $T$ ? ( ${\mathrm{k}}_{\mathrm{B}}$ is Boltzmann constant)

Q10.Four identical long solenoids A, B, C and D are connected to each other as shown in the figure. If the magnetic field at the centre of A is 3 T ,the field at the centre of C would be: (Assume that the magnetic field is confined with in the volume of respective solenoid).

Q11.A plane electromagnetic wave of frequency 100 MHz is traveling in vacuum along the x -direction. At a particular point in space and time, $\overrightarrow{\mathrm{B}}=2.0\times 10^{-8}\hat{\mathrm{k}}\mathrm{T}$. (where, $\hat{\mathrm{k}}$ is unit vector along z -direction …

Q12.A radioactive sample disintegrates via two independent decay processes having half lives ${\mathrm{T}}_{1/2}^{(1)}$ and ${\mathrm{T}}_{1/2}^{(2)}$ respectively. The effective half-life, ${\mathrm{T}}_{1/2}$ of the nuclei is :

Q13.The time period of satellite in a circular orbit of radius $R$ is $T$. The period of another satellite in a circular orbit of radius 9 R is:

Q14.Imagine that the electron in a hydrogen atom is replaced by a muon $(\mu )$. The mass of muon particle is 207 times that of an electron and charge is equal to the charge is of an electron. The ionization potential of this hydrogen atom will be :

Q15.A loop of flexible wire of irregular shape carrying current is placed in an external magnetic field . Identify the effect of the field on the wire.

Q16.A particle is traveling 4 times as fast as an electron. Assuming the ratio of de- Broglie wavelength of a particle to that of electron is $2:1$, the mass of the particle is :

Q17.In a series LCR resonance circuit, if we change the resistance only, from a lower to higher value :

Q18.The time period of a simple pendulum is given by $\mathrm{T}=2\pi \sqrt{\frac{\ell }{g}}$. The measured value of the length of pendulum is 10 cm known to a 1 mm accuracy. The time for 200 oscillations of the pendulum is found to be 100 second using a clock of 1 s resolution. Th …

Q19.An AC source rated $220\mathrm{V},50\mathrm{Hz}$ is connected to a resistor. The time taken by the current to change from its maximum to the rms value is :

Q20.An npn transistor operates as a common emitter amplifier with a power gain of $10^6$. The input circuit resistance is $100\Omega$ and the output load resistance is $10\mathrm{k}\Omega$. The common emitter current gain ' $\beta$ ' will be ⋯------. (Round off to the Ne …

Q21.A parallel plate capacitor has plate area $100{\mathrm{m}}^2$ and plate separation of 10 m. The space between the plates is filled up to a thickness 5 m with material of dielectric constant of 10. The resultant capacitance of the system is 'x' pF.
The value of …

Q22.The voltage across the $10\Omega$ resistor in the given circuit is $x$ volt.
The value of 'x' to the nearest integer is ______

Q23.A bullet of mass 0.1 kg is fired on a wooden block to pierce through it, but it stops after moving a distance of 50 cm into it. If the velocity of bullet before hitting the wood is $10\mathrm{m}/\mathrm{s}$ and slows down with uniform deceleration, then magnitude effective …

Q24.A ball of mass 10 kg, moving with a velocity $10\sqrt{3}\mathrm{m}/\mathrm{s}$ along the x-axis, hits another ball of mass 20 kg which is at rest. After the collision, first ball comes to rest while second ball disintegrates into two equal pieces. One piece starts moving a …

Q25.A person is swimming with a speed of $10\mathrm{m}/\mathrm{s}$ at an angle of $120^0$ with the flow and reaches to a point directly opposite on the other side of the river. The speed of the flow is 'x' $\mathrm{m}/\mathrm{s}$. The value of 'x' to the nearest integer …

Q26.Two separate wires $A$ and $B$ are stretched by 2 mm and 4 mm respectively, when they are subjected to a force of 2 N. Assume that both the wires are made up of same material and the radius of wire $B$ is 4 times that of the radius of wire $A$. The length of the wires …

Q27.The circuit shown in the figure consists of a charged capacitor of capacity $3\mu \mathrm{F}$ and a charge of $30\mu \mathrm{C}$. At time $\mathrm{t}=0$, when the key is closed, the value of current flowing through the $5\mathrm{M}\Omega$ resistor is 'x' …

Q28.As shown in the figure, a particle of mass 10 kg is placed at a point A. When the particle is slightly displaced to its right, it starts moving and reaches the point $B$. The speed of the particle at $B$ is $x\mathrm{m}/\mathrm{s}$.
(Take …

Q29.A particle performs simple harmonic motion with a period of 2 second. The time taken by the particle to cover a displacement equal to half of its amplitude from the mean position is $\frac{1}{\mathrm{a}}\mathrm{s}$. The value of 'a' to the nearest integer is ______

Q1.Reagent, 1-naphthylamine and sulphanilic acid in acetic acid is used for the detection of :

Q2.Match List - I with List - II:

List - I (Class of Drug):
(a) Antacid
(b) Artificial Sweetener
(c) Antifertility
(d) Tranquilizers

List - II (Example):
(i) Novestrol
(ii) Cimetidine
(iii) Valium
(iv) Alitame

Choose the most appropriate match.

Q3.Match List - I with List - II:

List - I (Process):
(a) Deacon's process
(b) Contact process
(c) Cracking of hydrocarbons
(d) Hydrogenation of vegetable oils

List - II (Catalyst):
(i) ZSM-5
(ii) ${\mathrm{CuCl}}_2$
(iii) Particles 'Ni'
(iv) ${\mathrm{V}}_2{\mathrm{O}}_5$

Choos …

Q4.Considering the above reaction, X and Y respectively are:

Q5.Match List - I with List - II:

List - I:
(a) $\mathrm{Ca}(\mathrm{OCl}{)}_2$
(b) ${\mathrm{CaSO}}_4\cdot \frac{1}{2}{\mathrm{H}}_2\mathrm{O}$
(c) CaO
(d) ${\mathrm{CaCO}}_3$

List - II:
(i) Antacid
(ii) Cement
(iii) Bleach
(iv) Plaster of Paris

Choose the most appropriate answer from …

Q6.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R:
Assertion A : During the boiling of water having temporary hardness, $\mathrm{Mg}{\left({\mathrm{HCO}}_3\right)}_2$ is converted to ${\mathrm{MgCO}}_3$.
Reason R: The solubility …

Q7.A certain orbital has no angular nodes and two radial nodes. The orbital is:

Q8.Compound with molecular formula ${\mathrm{C}}_3{\mathrm{H}}_6\mathrm{O}$ can show:

Q9.The chemical that is added to reduce the melting point of the reaction mixture during the extraction of aluminium is:

Q10.Match List - I with List - II:

List - I (Chemicals):
(a) Alcoholic potassium hydroxide
(b) $\mathrm{Pd}/{\mathrm{BaSO}}_4$
(c) BHC (Benzene hexachloride)
(d) Polyacetylene

List - II (Use / Preparation / Constituent):
(i) electrodes in batteries
(ii) obtained by addition react …

Q11.Match List - I with List - II

List - I:
(a) Chlorophyll
(b) Vitamin - ${\mathrm{B}}_{12}$
(c) Anticancer drug
(d) Grubbs catalyst

List - II:
(i) Ruthenium
(ii) Platinum
(iii) Cobalt
(iv) Magnesium

Choose the most appropriate answer from the options given below:

Q12.Considering the above chemical reaction, identify the product " X ":

Q13.A non-reducing sugar "A" hydrolyses to give two reducing mono saccharides. Sugar A is:

Q14.The correct structures of trans-$\left[{\mathrm{NiBr}}_2{\left({\mathrm{PPh}}_3\right)}_2\right]$ and meridonial-$\left[\mathrm{Co}{\left({\mathrm{NH}}_3\right)}_3{\left({\mathrm{NO}}_2\right)}_3\right]$, respectively, are :

Q15.The ionic radius of ${\mathrm{Na}}^{+}$ion is $1.02\stackrel{\circ }{A}$. The ionic radii (in $\stackrel{\circ }{\mathrm{A}}$ ) of ${\mathrm{Mg}}^{2+}$ and ${\mathrm{Al}}^{3+}$, respectively are:

Q16.In a binary compound, atoms of element A form a hcp structure and those of element M occupy 2/3 of the tetrahedral voids of the hcp structure. The formula of the binary compound is:

Q17.Reaction of Grignard reagent, ${\mathrm{C}}_2{\mathrm{H}}_5\mathrm{MgBr}$ with ${\mathrm{C}}_8{\mathrm{H}}_8\mathrm{O}$ followed by hydrolysis gives compound "A" which reacts instantly with Lucas reagent to give compound …

Q18.Consider the above chemical reaction and identify product "A":

Q19.The number of ionisable hydrogens present in the product obtained from a reaction of phosphorus trichloride and phosphonic acid is:

Q20.The statements that are TRUE:
(A) Methane leads to both global warming and photochemical smog.
(B) Methane is generated from paddy fields.
(C) Methane is a stronger global warming gas than ${\mathrm{CO}}_2$.
(D) Methane is a part of reducing smog.

Choose the most appropriate a …

Q21.A reaction of 0.1 mole of Benzylamine with bromomethane gave 23 g of Benzyl trimethyl ammonium bromide. The number of moles of bromomethane consumed in this reaction are $\mathrm{n}\times 10^{-1}$, when $\mathrm{n}=$ ______. (Round off to the nearest integer).
[Given: Atomic …

Q22.For the reaction ${\mathrm{C}}_2{\mathrm{H}}_6\to {\mathrm{C}}_2{\mathrm{H}}_4+{\mathrm{H}}_2$ the reaction enthalpy ${\Delta }_{\mathrm{r}}\mathrm{H}=$ ______ $\mathrm{kJ}{\mathrm{mol}}^{-1}$.
(Round off to the nearest integer).
[Given: Bond enthalpies in …

Q23.In order to prepare a buffer solution of pH 5.74 , sodium acetate is added to acetic acid. If the concentration of acetic acid in the buffer is 1.0 M , the concentration of sodium acetate in the buffer is ______ M. (Round off to the nearest integer).
[Given: pKa (acetic acid) = 4 …

Q24.AX is a covalent diatomic molecule where A and X are second row elements of periodic table. Based on molecular orbital theory, the bond order of AX is 2.5. The total number of electrons in AX is ______. (Round off to the nearest integer).

Q25.For the reaction
$2{\mathrm{Fe}}^{3+}(\mathrm{aq})+2{\mathrm{I}}^{-}(\mathrm{aq})\to 2{\mathrm{Fe}}^{2+}(\mathrm{aq})+{\mathrm{I}}_2(\mathrm{s})$
The magnitude of the standard molar free energy change,
${\Delta }_{\mathrm{r}}{\mathrm{G}}_{\mathrm{m}}^{\mathrm{o}}=-$ ___ …

Q26.____ grams of 3-Hydroxy propanal ( $\mathrm{MW}=74$ ) must be dehydrated to produce 7.8 g of acrolein $(\mathrm{MW}=56)\left({\mathrm{C}}_3{\mathrm{H}}_4\mathrm{O}\right)$ if the percentage yield is 64 .
(Round off to the nearest integer).
[Given: Atomic masses : C: 12. …

Q27.$2\mathrm{NO}(\mathrm{g})+{\mathrm{Cl}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{NOCl}(\mathrm{s})$
This reaction was studied at $-10^{\circ }\mathrm{C}$ and the following data was obtained

\begin{tabular}{llll}
run & {$[\mathrm{NO}{]}_0$} & { …

Q28.2 molal solution of a weak acid HA has a freezing point of $3.885^{\circ }\mathrm{C}$. The degree of dissociation of this acid is ____ $\times 10^{-3}$. (Round off to the nearest integer).
[ Given : Molal depression constant of water …

Q29.Complete combustion of 3 g of ethane gives $x\times 10^{22}$ molecules of water. The value of $x$ is
____ . (Round off to the nearest integer).
[Use : ${\mathrm{N}}_{\mathrm{A}}=6.023\times 10^{23}$; Atomic masses in u : C:12.0,O:16.0; H:1.0]

Q30.The total number of unpaired electrons present in the complex ${\mathrm{K}}_3\left[\mathrm{Cr}(\text{ oxalate }{)}_3\right]$ is ____ .

Q1.If the equation $\mathrm{a}|\mathrm{z}{|}^2+\overline{\bar{\alpha }\mathrm{z}+\alpha \overline{\mathrm{z}}}+\mathrm{d}=0$ represents a circle where $\mathrm{a},\mathrm{d}$ are real constants, then which of the following condition is correct?

Q2.Let $A+2B=\left[\begin{array}{ccc}1& 2& 0\\ 6& -3& 3\\ -5& 3& 1\end{array}\right]$ and $2A-B=\left[\begin{array}{ccc}2& -1& 5\\ 2& -1& 6\\ 0& 1& 2\end{array}\right]$. If $\mathrm{Tr}(A)$ denotes the sum of all diagonal elements of the matrix $A$, t …

Q3.For the four circles $\mathrm{M},\mathrm{N},\mathrm{O}$ and P , following four equations are given :
Circle $\mathrm{M}:{\mathrm{x}}^2+{\mathrm{y}}^2=1$
Circle $\mathrm{N}:{\mathrm{x}}^2+{\mathrm{y}}^2-2\mathrm{x}=0$
Circle …

Q4.A vector $\vec{a}$ has components $3p$ and 1 with respect to a rectangular Cartesian system. This system is rotated through a certain angle about the origin in the counter clockwise sense. If, with respect to new system, $\vec{a}$ has components $p+1$ and $\sqrt{10}$, …

Q5.The real function $f(x)=\frac{{\mathrm{cosec}}^{-1}x}{\sqrt{x-[x]}}$, where $[x]$ denotes the greatest integer less than or equal to $x$, is defined for all $x$ belonging to :

Q6.If $\alpha ,\beta$ are natural numbers such that $100^{\alpha }-199\beta =(100)(100)+(99)(101)+(98)(102)+\dots ..+(1)(199)$, then the slope of the line passing through $(\alpha ,\beta )$ and origin is :

Q7.${\left(1+x+2x^2\right)}^{20}=a_0+a_{1}x+a_2{x}^2+\dots .+a_{40}{x}^{40}$. Then, $a_1+a_3+a_5+\dots .+a_{37}$ is equal to :

Q8.$\frac{1}{3^2-1}+\frac{1}{5^2-1}+\frac{1}{7^2-1}+\dots ..+\frac{1}{(201{)}^2-1}$ is equal to :

Q9.The solutions of the equation
$\left|\begin{array}{ccc}1+{\sin }^{2}x& {\sin }^{2}x& {\sin }^{2}x\\ {\cos }^{2}x& 1+{\cos }^{2}x& {\cos }^{2}x\\ 4\sin 2x& 4\sin 2x& 1+4\sin 2x\end{array}\right|=0,(0<x<\pi )$, are :

Q10.The equation of one of the straight lines which passes through the point $(1,3)$ and makes an angle ${\tan }^{-1}(\sqrt{2})$ with the straight line, $y+1=3\sqrt{2}x$ is :

Q11.If the functions are defined as $\mathrm{f}(\mathrm{x})=\sqrt{\mathrm{x}}$ and $\mathrm{g}(\mathrm{x})=\sqrt{1-\mathrm{x}}$, then what is the common domain of the following functions: $f+g,f-g,f/g,g/f,g-f$ where …

Q12.The number of integral values of $m$ so that the abscissa of point of intersection of lines $3x+4y=9$ and $y=mx+1$ is also an integer, is:

Q13.The differential equation satisfied by the system of parabolas $y^2=4a(x+a)$ is :

Q14.Let $\alpha ,\beta ,\gamma$ be the real roots of the equation, $x^3+a{x}^2+bx+c=0,(a,b,c\in R$ and $a,b\ne 0)$. If the system of equations(inu,v,w) given by …

Q15.The integral $\int \frac{(2x-1)\cos \sqrt{(2x-1{)}^2+5}}{\sqrt{4x^2-4x+6}}dx$ is equal to : (where c is a constant of integration)

Q16.If ${\lim }_{x\to 0}\frac{{\sin }^{-1}x-{\tan }^{-1}x}{3x^3}$ is equal to $L$, then the value of $(6L+1)$ is :

Q17.The sum of all the 4-digit distinct numbers that can be formed with the digits $1,2,2$, and 3 is:

Q18.If $f(x)=\{\begin{array}{cl}\frac{1}{|x|}& ;|x|\ge 1\\ a{x}^2+b& ;|x|<1\end{array}$ is differentiable at every point of the domain, then the values of $a$ and $b$ are respectively ;

Q19.The value of $3+\frac{1}{4+\frac{1}{3+\frac{1}{4+\frac{1}{3+\dots ..\infty }}}}$ is equal to :

Q20.Choose the correct statement about two circles whose equations are given below:

Q21.If $f(x)=\int \frac{5x^8+7x^6}{{\left(x^2+1+2x^7\right)}^2}dx,(x\ge 0),f(0)=0$ and $f(1)=\frac{1}{K}$, then the value of $K$ is

Q22.Let the plane $ax+by+cz+d=0$ bisect the line joining the points $(4,-3,1)$ and $(2,3,-5)$ at the right angles. If $a,b,c,d$ are integer, then the minimum value of $\left(a^2+b^2+c^2+d^2\right)$ is

Q23.The mean age of 25 teachers in a school is 40 years. A teacher retires at the age of 60 years and a new teacher is appointed in his place. If the mean age of the teachers in this school now is 39 years, then the age (in years) of the newly appointed teacher is:

Q24.Let $z_1,z_2$ be the roots of the equation $z^2+az+12=0$ and $z_1,z_2$ form an equilateral triangle with origin. Then, The value of $|a|$ is ____

Q25.The equation of the planes parallel to the plane $x-2y+2z-3=0$ which are at unit distance from the point $(1,2,3)$ is $ax+by+cz+d=0$. If $(b-d)=K(c-a)$, then the positive value of $K$ is ____

Q26.A square $ABCD$ has all its vertices on the curve $x^2{y}^2=1$. The midpoints of its sides also lie on the same curve. Then, the square of area of $ABCD$ is ____

Q27.Let $f(x)$ and $g(x)$ be two functions satisfying $f(x^2)+g(4-x)=4x^3$ and $g(4-x)+g(x)=0$, the value of ${\int }_{-4}^{4}f(x^2)dx$ is ____.

Q28.The number of times the digit 3 will be written when listing the integers from 1 to 1000 is ____.

Q29.The number of solutions of the equations $|\cot x|=\cot x+\frac{1}{\sin x}$ in the interval $[0,2\pi ]$ is ____