JEE Main 2021 · 26 Feb 2021 · Shift 1

Q1.A short straight object of height 100 cm lies before the central axis of a spherical mirror whose focal length has absolute value $|\mathrm{f}|=40\mathrm{cm}$. The image of object produced by the mirror is of height 25 cm and has the same orientation of the object. One may co …

Q2.Find the gravitational force of attraction between the ring and sphere as shown in the diagram, where the plane of the ring is perpendicular to the line joining the centres. If $\sqrt{8}R$ is the distance between the centres of a ring (of mass ' $m$ ') and a sphere (mass ' M …

Q3.Find the electric field at point $P$ (as shown in figure) on the perpendicular bisector of a uniformly charged thin wire of length $L$ carrying a charge $Q$. The distance of the point $P$ from the centre of the rod is $a=\frac{\sqrt{3}}{2}L$.

Q4.In a typical combustion engine the work done by a gas molecule is given by $\mathrm{W}={\alpha }^2\beta {\mathrm{e}}^{-\frac{\beta {\mathrm{x}}^2}{\mathrm{kT}}}$, where $x$ is the displacement, $k$ is the Boltzmann constant and $T$ is the temperature. If $\alpha$ and …

Q5.A particle is moving with uniform speed along the circumference of a circle of radius of radius $R$ under the action of a central fictitious force F which is inversely proportional to ${\mathrm{R}}^3$. Its time period of revolution will be given by:

Q6.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Body ' P ' having mass M moving with speed ' $u$ ' has head - on collision elastically with another body ' Q ' having mass ' $m$ ' initially at rest. If …

Q7.Assume that a tunnel is dug along a chord of the earth, at a perpendicular distance ( $\mathrm{R}/2$ ) from the earth's centre, where ' $R$ ' is the radius of the Earth. The wall of the tunnel is frictionless. If a particle is released in this tunnel, it will execute a simp …

Q8.A large number of water drops, each of radius $r$, combine to have a drop of radius $R$. If the surface tension is T and mechanical equivalent of heat is J , the rise in heat energy per unit volume will be:

Q9.Consider the combination of 2 capacitors ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$, with ${\mathrm{C}}_2>{\mathrm{C}}_1$, when connected in parallel, the equivalent capacitance is $\frac{15}{4}$ times the equivalent capacitance of the same connected in series, Calculate the r …

Q10.Four identical solid spheres each of mass ' $m$ ' and radius ' $a$ ' are placed with their centres on the four corners of a square of side ' $b$ '. The moment of inertia of the system about side of square where the axis of rotation is parallel to the plane of the square is …

Q11.LED is constructed from $\mathrm{Ga}-\mathrm{As}-\mathrm{P}$ semiconducting material. The energy gap of this LED is 1.9 eV . Calculate the wavelength of light emitted and its colour.
$[\mathrm{h}=6.63\times 10^{-34}\mathrm{Js}$ and …

Q12.The temperature $\theta$ at the junction of two insulating sheets, having thermal resistances ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ as well as top and bottom temperatures ${\theta }_1$ and ${\theta }_2$ (as shown in figure) is given by :

Q13.If two similar spring each of spring constant ${\mathrm{K}}_1$ are joined in series, the new spring constant and time period would be changed by a factor :

Q14.A planet revolving in elliptical orbit has :
(A) a constant velocity of revolution.
(B) has the least velocity when it is nearest to the sun.
(C) its areal velocity is directly proportional to its velocity.
(D) areal velocity is inversely proportional to its velocity.
(E) To foll …

Q15.An alternating is given by the equation $\mathrm{i}={\mathrm{i}}_1\sin \omega \mathrm{t}+{\mathrm{i}}_2\cos \omega \mathrm{t}$. Then rms current will be:

Q16.If ${\lambda }_1$ and ${\lambda }_2$ are the wavelengths of the third member of Lyman and first member of the Paschen series respectively, then the value of ${\lambda }_1:{\lambda }_2$ is :

Q17.Five equal resistances are connected in a network as shown in figure. The net resistance between the points $A$ and $B$ is :

Q18.Given below are two statements : one is labelled as Assertion A and the other is labeled as Reason R.
Assertion A : An electron microscope achieve better resolving power than an optical microscope.
Reason R : The de Broglie's wavelength of the electrons emitted from an electron g …

Q19.The normal density of a material its $\rho$ and its bulk modulus of elasticity is K . The magnitude of increase in density of material, when a pressure P is applied uniformly on all sides, will be :

Q20.In a Young's double slit experiment two slits are separated by 2 mm and the screen is placed one meter away. When a light of wavelength 500 nm used, the fringe separation will be :

Q21.A container is divided into two chambers by a partition . The volume of first chamber is 4.5 litre and second chamber is 5.5 litre. The first chamber contain 3.0 moles of gas at pressure 2.0 atm and second chamber contain 4.0 moles of gas at pressure 3.0 atm . After the partition …

Q22.The circuit contains two diodes each with a forward resistance of $50\Omega$ and with infinite reverse resistance. If the battery voltage is 6 V , the current through the $120\Omega$ resistance is ____ m A.

Q23.In an electrical circuit, a battery is connected to pass 20 C of charge through it in a certain given time. The potential difference between two plates of the battery is maintained at 15 V . The work done by the battery is ____ J.

Q24.The maximum and minimum amplitude of an amplitude modulated wave is 16 V and 8 V respectively. The modulation index for this amplitude wave is $x\times 10^{-2}$. The value of $x$ is ____

Q25.A boy pushes a box of mass 2 kg with a force $\vec{F}=(20\hat{i}+10\hat{j})\mathrm{N}$ on a frictionless surface. If the box was initially at rest, then ____ m is displacement along the x -axis after 10 s .

Q26.As shown in the figure, a block of mass $\sqrt{3}\mathrm{kg}$ is kept on a horizontal rough surface of coefficient of friction $\frac{1}{3\sqrt{3}}$. The critical force to be applied on the vertical surface as shown at an angle $60^{\circ }$ with horizontal such that it does no …

Q27.In a series LCR resonant circuit, the quality factor is measured as 100 . If the inductance is increased by two fold and resistance is decreased by two fold, then the quality factor after this change will be ____ .

Q28.A person standing on a balance inside a stationary lift measures 60 kg . The weight of that person if the lift descends with uniform downward acceleration of $1.8\mathrm{m}/{\mathrm{s}}^2$ will be ____ $\mathrm{N}.\left[\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2\right]$

Q29.A radiation is emitted by 1000 W bulb and it generates an electric field and magnetic field at P , placed at a distance of 2 m . The efficiency of the bulb is $1.25\%$. The value of peak electric field at $P$ is $x\times 10^{-1}\mathrm{V}/\mathrm{m}$. Value of $x$ is ------ …

Q30.The mass per unit length of a uniform wire is $0.135\mathrm{g}/\mathrm{cm}$. A transverse wave of the form $\mathrm{y}=-0.21\sin (x+30t)$ is produced in it, where $x$ is in meter and $t$ is in second. Then, the expected value of tension in the wire is …

Q1.Match List - I with List - II.

List - I
Electronic configuration of elements
(a) $1{\mathrm{s}}^{2}2{\mathrm{s}}^2$
(b) $1s^{2}2s^{2}2p^4$
(c) $1s^{2}2s^{2}2p^3$
(d) $1s^{2}2s^{2}2p^1$

List - II
${\Delta }_i\mathrm{H}$ in $\mathrm{kJ}{\mathrm{mol}}^{-1}$ …

Q2.Which one of the following lanthanoids does not form ${\mathrm{MO}}_2$?
[ $M$ is lanthanoid metal ]

Q3.On treating a compound with warm dil. ${\mathrm{H}}_2{\mathrm{SO}}_4$, gas X is evolved which turns ${\mathrm{K}}_2{\mathrm{Cr}}_2{\mathrm{O}}_7$ paper acidified with dil. ${\mathrm{H}}_2{\mathrm{SO}}_4$ to a green compound Y. X and Y respectively are:

Q4.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Dipole - dipole interactions are the only non - covalent interactions, resulting in hydrogen bond formation.
Reason R: Fluorine is the most electronegative element a …

Q5.Given below are two statements:
Statement I: A mixture of chloroform and aniline can be separated by simple distillation.
Statement II: When separating aniline from a mixture of aniline and water by steam distillation aniline boils below its boiling point.
In the light of the abo …

Q6.Which of the following vitamin is helpful in delaying the blood clotting?

Q7.An amine on reaction with benzenesulphonyl chloride produces a compound insoluble in alkaline solution. This amine can be prepared by ammonolysis of ethyl chloride. The correct structure of amine is:

Q8.$\underset{\left({\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{Cl}}_2\right)}{\mathrm{A}}\underset{373\mathrm{K}}{\overset{\text{ Hydrolysis }}{\to }}\underset{\left({\mathrm{C}}_4{\mathrm{H}}_8\mathrm{O}\right)}{\mathrm{B}}$

B reacts with Hydroxyl amine but does not give Tollen's test. Ident …

Q9.For the given reaction:

What is 'A'?

Q10.The orbital having two radial as well as two angular nodes is:

Q11.Find $A,B$ and $C$ in the following reactions:
${\mathrm{NH}}_3+\mathrm{A}+{\mathrm{CO}}_2\to {\left({\mathrm{NH}}_4\right)}_2{\mathrm{CO}}_3$ …

Q12.Compound A used as a strong oxidizing agent is amphoteric in nature. It is the part of lead storage batteries. Compound A is :

Q13.The structure of Neoprene is :

Q14.Which of the following is 'a' FALSE statement ?
(A) Carius method is used for the estimation of nitrogen in an organic compound.
(B) Carius tube is used in the estimation of sulphur in an organic compound.
(C) Kjeldahl's method is used for the estimation of nitrogen in an organic …

Q15.Match list - I with List - II.
List - I (Ore)
(a) Kernite
(b) Cassiterite
(c) Calamine
(d) Cryolite
List - II (Element Present)
(i) Tin
(ii) Boron
(iii) Fluorine
(iv) Zinc
Choose the most appropriate answer from the options given below :

Q16.Given below are two statements :
Statements I: o- Nitrophenol is steam volatile due to intramolecular hydrogen bonding.
Statement II: o- Nitrophenol has high meliting due to hydrogen bonding.
In the light of the above statements, choose the most appropriate answer from the option …

Q17.The presence of ozone in troposphere :

Q18.Statements about heavy water are given below :
(A) Heavy water is used in exchange reactions for the study of reaction mechanisms.
(B) Heavy water is prepared by exhaustive electrolysis of water
(C) Heavy water has higher boiling point than ordinary water.
(D) Viscosity of …

Q19.Identify the major products $A$ and $B$ respectively in the following reactions of phenol :

Q20.Number of bridging CO ligands in $\left[{\mathrm{Mn}}_2(\mathrm{CO}{)}_{10}\right]$ is ____

Q21.A certain gas obeys $P\left(V_m-b\right)=RT$. The value of ${\left(\frac{\partial Z}{\partial P}\right)}_T$ is $\frac{xb}{RT}$. The value of $x$ is ____ (Integer answer) (Z : compressibility factor)

Q22.Consider the following reaction
${\mathrm{MnO}}_4^{-}+8{\mathrm{H}}^{+}+5{\mathrm{e}}^{-}\to {\mathrm{Mn}}^{+2}+4{\mathrm{H}}_2\mathrm{O},{\mathrm{E}}^{\circ }=1.51\mathrm{V}$.
The quantity of electricity required in Faraday to reduce five moles of ${\mathrm{MnO}}_4^{-}$is …

Q23.An exothermic reaction $\mathrm{X}\to \mathrm{Y}$ has an activation energy $30\mathrm{kJ}{\mathrm{mol}}^{-1}$. If energy change $\Delta \mathrm{E}$ during the reaction is $-20\mathrm{kJ}$, then the activation energy for the reverse reaction in kJ is ______ (Integer a …

Q24.A homogeneous ideal gaseous reaction ${\mathrm{AB}}_{2(\mathrm{g})}\rightleftharpoons {\mathrm{A}}_{(\mathrm{g})}+2{\mathrm{B}}_{(\mathrm{g})}$ is carried out in a 25 litre flask at $27^{\circ }\mathrm{C}$. The initial amount of $A{B}_2$ was 1 mole and the equilibrium pressure was …

Q25.Dichromate ion is treated with base, the oxidation number of Cr in the product formed is ______

Q26.3.12 g of oxygen is adsorbed on 1.2 g of platinum metal. The volume oxygen adsorbed per gram of the adsorbent at 1 atm and 300 K in L is ______
$\left[\mathrm{R}=0.0821\mathrm{L}\mathrm{atm}{\mathrm{K}}^{-1}{\mathrm{mole}}^{-1}\right]$

Q27.224 mL of ${\mathrm{SO}}_{2(\mathrm{g})}$ at 298 K and 1 atm is passed through 100 mL of 0.1 M NaOH solution. The non volatile solute produced is dissolved is 36 g of water. The lowering of vapour pressure of solution (assuming the solution is dilute) …

Q28.The number of significant figures in $50000.020\times 10^{-3}$ is ______

Q29.For a chemical reaction $\mathrm{A}+\mathrm{B}\rightleftharpoons \mathrm{C}+\mathrm{D}$
$\left({\Delta }_{\mathrm{r}}{\mathrm{H}}^{\ominus }=80\mathrm{kJ}{\mathrm{mol}}^{-1}\right)$ the entropy change ${\Delta }_{\mathrm{r}}{\mathrm{S}}^{\ominus }$ depends on the temperature T (in K) as …

Q1.If $\frac{{\sin }^{-1}x}{a}=\frac{{\cos }^{-1}x}{b}=\frac{{\tan }^{-1}y}{c};0<x<1$, then the value of $\cos \left(\frac{\pi c}{a+b}\right)$ is :

Q2.The value of $\left|\begin{array}{lll}(a+1)(a+2)& a+2& 1\\ (a+2)(a+3)& a+3& 1\\ (a+3)(a+4)& a+4& 1\end{array}\right|$ is :

Q3.The value of ${\int }_{-\pi /2}^{\pi /2}\frac{{\cos }^{2}x}{1+3^x}dx$ is :

Q4.In the circle given below, let $\mathrm{OA}=1$ unit, $\mathrm{OB}=13$ unit and $\mathrm{PQ}\perp \mathrm{OB}$. Then, the area of the triangle PQB (in square units) is :

Q5.The number of seven digit integers with sum of the digits equal to 10 and formed by using the digits 1,2 and 3 only is:

Q6.The maximum slope of the curve $y=\frac{1}{2}{x}^4-5x^3+18x^2-19x$ occurs at the point :

Q7.The value of ${\sum }_{n=1}^{100}{\int }_{n-1}^n{e}^{x-[x]}dx$, where $[x]$ is the greatest integer $\le x$, is:

Q8.The value of ${\lim }_{h\to 0}2\left\{\frac{\sqrt{3}\sin \left(\frac{\pi }{6}+h\right)-\cos \left(\frac{\pi }{6}+h\right)}{\sqrt{3}h(\sqrt{3}\cos h-\sin h)}\right\}$ is :

Q9.The intersection of three lines $x-y=0,x+2y=3$ and $2x+y=6$ is a :

Q10.Let f be any function defined on $\mathbf{R}$ and let it satisfy the condition :


If $f(0)=1$, then :

Q11.If $(1,5,35),(7,5,5),(1,\lambda ,7)$ and $(2\lambda ,1,2)$ are coplanar, then the sum of all possible values of $\lambda$ is :

Q12.Let A be a symmetric matrix of order 2 with integer entries. If the sum of the diagonal elements of $A^2$ is 1 , then the possible number of such matrices is :

Q13.The rate of growth of bacteria in a culture is proportional to the number of bacteria present and the bacteria count is 1000 at initial time $t=0$. The number of bacteria is increased by $20\%$ in 2 hours. If the population of bacteria is 2000 after …

Q14.The sum of the infinite series $1+\frac{2}{3}+\frac{7}{3^2}+\frac{12}{3^3}+\frac{17}{3^4}+\frac{22}{3^5}+\dots \dots$ is equal to :

Q15.A fair coin is tossed a fixed number of times. If the probability of getting 7 heads is equal to probability of getting 9 heads, then the probability of getting 2 heads is :

Q16.The maximum value of term independent of ' t ' in the expansion of ${\left(\mathrm{t}{\mathrm{x}}^{\frac{1}{5}}+\frac{(1-\mathrm{x}{)}^{\frac{1}{10}}}{\mathrm{t}}\right)}^{10}$ where $\mathrm{x}\in (0,1)$ is :

Q17.If $\overrightarrow{\mathrm{a}}$ and $\overrightarrow{\mathrm{b}}$ are perpendicular, then $\overrightarrow{\mathrm{a}}\times (\overrightarrow{\mathrm{a}}\times (\overrightarrow{\mathrm{a}}\times (\overrightarrow{\mathrm{a}}\times \overrightarrow{\mathrm{b}})))$ is equal t …

Q18.Consider the three planes
$P_1:3x+15y+21z=9$,
$P_2:x-3y-z=5$, and
$P_3:2x+10y+14z=5$
Then, which one of the following is true ?

Q19.Let $R=\{(P,Q)\mid P$ and $Q$ are at the same distance from the origin} be a relation, then the equivalence class of $(1,-1)$ is the set :

Q20.In an increasing geometric series, the sum of the second and the sixth term is $\frac{25}{2}$ and the product of the third and fifth term is 25. Then, the sum of $4^{\text{th }},6^{\text{th}}$ and $8^{\text{th}}$ terms is equal to :

Q21.The area bounded by the lines $y=\Vert x-1|-2|$ is ____

Q22.If $\sqrt{3}\left({\cos }^{2}x\right)=(\sqrt{3}-1)\cos x+1$, the number of solutions of the given equation when $x\in \left[0,\frac{\pi }{2}\right]$ is ____

Q23.The number of solution of the ${\log }_4(x-1)={\log }_2(x-3)$ is ____

Q24.If $y=y(x)$ is the solution of the equation $e^{\sin y}\cos y\frac{dy}{dx}+e^{\sin y}\cos x=\cos x,y(0)=0$; then $1+y\left(\frac{\pi }{6}\right)+\frac{\sqrt{3}}{2}y\left(\frac{\pi }{3}\right)+\frac{1}{\sqrt{2}}y\left(\frac{\pi }{4}\right)$ is equal to ____

Q25.Let $(\lambda ,2,1)$ be a point on the plane which passes which through the point $(4,-2,2)$. If the plane is perpendicular to the line joining the points $(-2,-21,29)$ and $(-1,-16,23)$, then ${\left(\frac{\lambda }{11}\right)}^2-\frac{4\lambda }{11}-4$ is equal to ______

Q26.The number of integral values of '$k$' for which the equation $3\sin x+4\cos x=k+1$ has a solution, $k\in R$ is ______

Q27.The sum of $162^{\text{th}}$ power of the roots of the equation $x^3-2x^2+2x-1=0$ is ______

Q28.Let $\mathrm{m},\mathrm{n}\in \mathrm{N}$ and $\gcd (2,\mathrm{n})=1$. If $30\left(\genfrac{}{}{0ex}{}{30}{0}\right)+29\left(\genfrac{}{}{0ex}{}{30}{1}\right)+\dots .+2\left(\genfrac{}{}{0ex}{}{30}{28}\right)+1\left(\genfrac{}{}{0ex}{}{30}{29}\right)=\mathrm{n}.2^{\mathrm{m}}$, then $\mathrm{n}+\mathrm{m}$ is equal to ______ …

Q29.The difference between degree and order of a differential equation that represents the family of curves given by $y^2=a\left(x+\frac{\sqrt{a}}{2}\right),a>0$ is ______

Q30.The value of the integral ${\int }_0^{\pi }|\sin 2x|dx$ is ______.