JEE Main 2022 · 25 Jun 2022 · Shift 1

Q1.If $Z=\frac{A^2{B}^3}{C^4}$, then the relative error in $Z$ will be :

Q2.$\overrightarrow{\mathrm{A}}$ is a vector quantity such that $|\overrightarrow{\mathrm{A}}|=$ nonzero constant. Which of the following expressions is true for $\overrightarrow{\mathrm{A}}$ ?

Q3.Which of the following relations is true for two unit vectors $\hat{\mathrm{A}}$ and $\hat{\mathrm{B}}$ making an angle $\theta$ to each other?

Q4.If force $\vec{F}=3\hat{i}+4\hat{j}-2\hat{k}$ acts on a particle having position vector $2\hat{i}+\hat{j}+2\hat{k}$ then, the torque about the origin will be :-

Q5.The height of any point P above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point P will be : (Given $\mathrm{g}=$ acceleration due to gravity at the surface of earth)

Q6.The terminal velocity ( ${\mathrm{v}}_{\mathrm{t}}$ ) of the spherical rain drop depends on the radius ( $r$ ) of the spherical rain drop as:-

Q7.The relation between root mean square speed $\left({\mathrm{v}}_{\mathrm{rms}}\right)$ and most probable speed ( ${\mathrm{v}}_{\mathrm{p}}$ ) for the molar mass M of oxygen gas molecule at the temperature of 300 K will be :-

Q8.In the figure, a very large plane sheet of positive charge is shown. ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are two points at distance $l$ and $2l$ from the charge distribution. If $\sigma$ is the surface charge density, then the magnitude of electric fields …

Q9.Match List-I with List-II

List-I
(A) AC generator
(B) Galvanometer
(C) Transformer
(D) Metal detector

List-II
(I) Shows deflection when current passes through it
(II) Converts mechanical energy into electrical energy
(III) Works on the principle of resonance in AC circuit
(IV) …

Q10.A long straight wire with a circular crosssection having radius R , is carrying a steady current I. The current I is uniformly distributed across this cross-section. Then the variation of magnetic field due to current I with distance $r(\mathrm{r}<\mathrm{R})$ from its centre …

Q11.If wattless current flows in the AC circuit, then the circuit is

Q12.The electric field in an electromagnetic wave is given by $\mathrm{E}=56.5\sin \omega (\mathrm{t}-\mathrm{x}/\mathrm{c}){\mathrm{NC}}^{-1}$. Find the intensity of the wave if it is propagating along $x$-axis in the free space. (Given …

Q13.The two light beams having intensities I and 9I interfere to produce a fringe pattern on a screen. The phase difference between the beams is $\frac{\pi }{2}$ at point P and $\pi$ at point Q. Then the difference between the resultant intensities at P and Q will be:

Q14.A light wave travelling linearly in a medium of dielectric constant 4, incident on the horizontal interface separating medium with air. The angle of incidence for which the total intensity of incident wave will be reflected back into the same medium will be (Given: relative perme …

Q15.Given below are two statements:
Statement I: Davisson-Germer experiment establishes the wave nature of electrons.
Statement II: If electrons have wave nature, they can interfere and show diffraction.
In the light of the above statements choose the correct answer from the options …

Q16.The ratio for the speed of the electron in the $3^{\text{rd}}$ orbit of ${\mathrm{He}}^{+}$ to the speed of the electron in the $3^{\text{rd}}$ orbit of hydrogen atom will be:

Q17.The photodiode is used to detect the optical signals. These diodes are preferably operated in reverse biased mode because:

Q18.A signal of 100 THz frequency can be transmitted with maximum efficiency by:

Q19.The difference of speed of light in the two media $A$ and $B$ $(v_A-v_B)$ is $2.6\times 10^{7}m/s$. If the refractive index of medium $B$ is 1.47, then the ratio of refractive index of medium $B$ to medium $A$ is: (Given: speed of light in vacuum …

Q20.A teacher in his physics laboratory allotted an experiment to determine the resistance (G) of a galvanometer. Students took the observations for $\frac{1}{3}$ deflection in the galvanometer. Which of the below is true for measuring value of $G$?

Q21.A uniform chain of 6 m length is placed on a table such that a part of its length is hanging over the edge of the table. The system is at rest. The co-efficient of static friction between the chain and the surface of the table is 0.5, the maximum length of the chain hanging from …

Q22.A 0.5 kg block moving at a speed of $12{\mathrm{ms}}^{-1}$ compresses a spring through a distance 30 cm when its speed is halved. The spring constant of the spring will be ______ ${\mathrm{Nm}}^{-1}$.

Q23.The velocity of upper layer of water in a river is $36{\mathrm{kmh}}^{-1}$. Shearing stress between horizontal layers of water is $10^{-3}{\mathrm{Nm}}^{-2}$. Depth of the river is ______ m. (Co-efficiency of viscosity of water is $10^{-2}Pa.s$)

Q24.A steam engine intakes 50 g of steam at $100^{\circ }\mathrm{C}$ per minute and cools it down to $20^{\circ }\mathrm{C}$. If latent heat of vaporization of steam is $540{\mathrm{cal}\mathrm{g}}^{-1}$, then the heat rejected by the steam engine per minute is ______ …

Q25.The first overtone frequency of an open organ pipe is equal to the fundamental frequency of a closed organ pipe. If the length of the closed organ pipe is 20 cm. The length of the open organ pipe is ______ cm.

Q26.The equivalent capacitance between points A and B in below shown figure will be ______ $\mu \mathrm{F}$.

Q27.A resistor develops 300 J of thermal energy in 15 s, when a current of 2 A is passed through it. If the current increases to 3 A, the energy developed in 10 s is ______ J.

Q28.The total current supplied to the circuit as shown in figure by the 5 V battery is ______ A

Q29.The current in a coil of self inductance 2.0 H is increasing according to $\mathrm{I}=2\sin ({\mathrm{t}}^2)$ A. The amount of energy spent during the period when current changes from 0 to 2 A is ______ J.

Q30.A force on an object of mass 100 g is $(10\hat{\mathrm{i}}+5\hat{\mathrm{j}})$ N. The position of that object at $\mathrm{t}=2$ s is $(\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}})$ m after starting from rest. The value of $\frac{a}{b}$ will be

Q1.Bonding in which of the following diatomic molecule(s) become(s) stronger, on the basis of MO Theory, by removal of an electron ?
(A) NO
(B) ${\mathrm{N}}_2$
(C) ${\mathrm{O}}_2$
(D) ${\mathrm{C}}_2$
(E) ${\mathrm{B}}_2$

Choose the most appropriate answer from the option …

Q2.Incorrect statement for Tyndall effect is :-

Q3.The pair, in which ions are isoelectronic with ${\mathrm{Al}}^{3+}$ is :-

Q4.Leaching of gold with dilute aqueous solution of NaCN in presence of oxygen gives complex [A], which on reaction with zinc forms the elemental gold and another complex [B]. [A] and [B], respectively are :-

Q5.Number of electron deficient molecules among the following
${\mathrm{PH}}_3,{\mathrm{B}}_2{\mathrm{H}}_6,{\mathrm{CCl}}_4,{\mathrm{NH}}_3,\mathrm{LiH}$ and ${\mathrm{BCl}}_3$ is

Q6.Which one of the following alkaline earth metal ions has the highest ionic mobility in its aqueous solution?

Q7.White precipitate of AgCl dissolves in aqueous ammonia solution due to formation of :

Q8.Cerium (IV) has a noble gas configuration. Which of the following is correct statement about it?

Q9.Among the following, which is the strongest oxidizing agent ?

Q10.The eutrophication of water body results in :

Q11.Phenol on reaction with dilute nitric acid, gives two products. Which method will be most effective for large scale separation ?

Q12.In the following structures, which one is having staggered conformation with maximum dihedral angle?

Q13.The products formed in the following reaction.

Q14.The IUPAC name of ethylidene chloride is :-

Q15.The major product in the reaction

Q16.The intermediate X, in the reaction

Q17.In the following reaction :

The compounds A and B respectively are :-

Q18.The reaction of $\mathrm{R}-\mathrm{C}-{\mathrm{NH}}_2$ with bromine and KOH gives ${\mathrm{RNH}}_2$ as the end product. Which one of the following is the intermediate product formed in this reaction?

Q19.Using very little soap while washing clothes, does not serve the purpose of cleaning of clothes because

Q20.Which one of the following is an example of artificial sweetner ?

Q21.The number of N atoms is 681 g of ${\mathrm{C}}_7{\mathrm{H}}_5{\mathrm{N}}_3{\mathrm{O}}_6$ is $\mathrm{x}\times 10^{21}$. The value of x is ____ ( ${\mathrm{N}}_{\mathrm{A}}=6.02\times 10^{23}{\mathrm{mol}}^{-1}$ ) (Nearest Integer)

Q22.The distance between ${\mathrm{Na}}^{+}$and ${\mathrm{Cl}}^{-}$ions in solid NaCl of density $43.1\mathrm{g}{\mathrm{cm}}^{-3}$ is ____ ×
$10^{-10}\mathrm{m}$. (Nearest Integer)
(Given : ${\mathrm{N}}_{\mathrm{A}}=6.02\times 10^{23}{\mathrm{mol}}^{-1}$ )

Q23.The longest wavelength of light that can be used for the ionisation of lithium atom $(\mathrm{Li})$ in its ground state is $x\times 10^{-8}\mathrm{m}$. The value of $x$ is
____. (Nearest Integer)
(Given : Energy of the electron in the first shell of the hydrogen atom …

Q24.The standard entropy change for the reaction $4\mathrm{Fe}(\mathrm{s})+3{\mathrm{O}}_2(\mathrm{g})\to 2{\mathrm{Fe}}_2{\mathrm{O}}_3(\mathrm{s})$ is $-550{\mathrm{JK}}^{-1}$ at 298 K .
[Given : The standard enthalpy change for the reaction is …

Q25.1 L aqueous solution of ${\mathrm{H}}_2{\mathrm{SO}}_4$ contains 0.02 $\mathrm{m}\mathrm{mol}{\mathrm{H}}_2{\mathrm{SO}}_4.50\%$ of this solution is diluted with deionized water to give 1 L solution (A). In solution (A), 0.01 m mol of ${\mathrm{H}}_2{\mathrm{SO}}_4$ …

Q26.The standard free energy change ( $\Delta {\mathrm{G}}^{\circ }$ ) for $50\%$ dissociation of ${\mathrm{N}}_2{\mathrm{O}}_4$ into ${\mathrm{NO}}_2$ at $27^{\circ }\mathrm{C}$ and 1 atm pressure is $-\mathrm{xJ}{\mathrm{mol}}^{-1}$. The value of x is …

Q27.In a cell, the following reactions take place
${\mathrm{Fe}}^{2+}\to {\mathrm{Fe}}^{3+}{\mathrm{e}}^{-}$

$2{\mathrm{I}}^{-}\to {\mathrm{I}}_2+2{\mathrm{e}}^{-}$ …

Q28.For a given chemical reaction


Concentration of C changes from 10 mmol ${\mathrm{dm}}^{-3}$ to $20\mathrm{mmol}{\mathrm{dm}}^{-3}$ in 10 seconds. Rate of appearance of …

Q29.If ${\left[\mathrm{Cu}{\left({\mathrm{H}}_2\mathrm{O}\right)}_4\right]}^{2+}$ absorbs a light of wavelength 600 nm for $\mathrm{d}-\mathrm{d}$ transition, then the value of octahedral crystal field splitting energy for …

Q30.Number of grams of bromine that will completely react with 5.0 g of pent-1-ene is $\_\_\_\_$ × $10^{-2}\mathrm{g}$. (Atomic mass of $\mathrm{Br}=80\mathrm{g}/\mathrm{mol}$ ) [Nearest Integer)

Q1.Let a circle C touch the lines ${\mathrm{L}}_1:4\mathrm{x}-3\mathrm{y}+{\mathrm{K}}_1=0$ and ${\mathrm{L}}_2:4\mathrm{x}-3\mathrm{y}+{\mathrm{K}}_2=0,{\mathrm{K}}_1,{\mathrm{K}}_2\in \mathrm{R}$. If a line passing through the centre of the circle C intersects …

Q2.The value of ${\int }_0^{\pi }\frac{{\mathrm{e}}^{\cos \mathrm{x}}\sin \mathrm{x}}{\left(1+{\cos }^2\mathrm{x}\right)\left({\mathrm{e}}^{\cos \mathrm{x}}+{\mathrm{e}}^{-\cos \mathrm{x}}\right)}\mathrm{dx}$ is equal to

Q3.Let $\mathrm{a},\mathrm{b}$ and c be the length of sides of a triangle ABC such that $\frac{\mathrm{a}+\mathrm{b}}{7}=\frac{\mathrm{b}+\mathrm{c}}{8}=\frac{\mathrm{c}+\mathrm{a}}{9}$. If r and R are the radius of incircle and radius of circumcircle of the triangle ABC , resp …

Q4.Let $\mathrm{f}:\mathrm{N}\to \mathrm{R}$ be a function such that $\mathrm{f}(\mathrm{x}+\mathrm{y})=2\mathrm{f}(\mathrm{x})\mathrm{f}(\mathrm{y})$ for natural numbers x and y . If $f(1)=2$, then the value of $\alpha$ for which …

Q5.Let A be a $3\times 3$ real matrix such that …

Q6.Let $f:R\to R$ be defined as $f(x)=x^3+x-5$. If $\mathrm{g}(\mathrm{x})$ is a function such that $\mathrm{f}(\mathrm{g}(\mathrm{x}))=\mathrm{x}$, $\forall \mathrm{x}\in \mathrm{R}$, then ${\mathrm{g}}^{\prime }$ (63) is equal to

Q7.Consider the following two propositions:
P1 : $\sim (\mathrm{p}\to \sim \mathrm{q})$
P2: $(\mathrm{p}\wedge \sim \mathrm{q})\wedge ((\sim \mathrm{p})\vee \mathrm{q})$
If the proposition $p\to ((\sim p)\vee q)$ is evaluated as FALSE, then:

Q8.If $\frac{1}{2\cdot 3^{10}}+\frac{1}{2^2\cdot 3^9}+\dots \frac{1}{2^{10}\cdot 3}=\frac{\mathrm{K}}{2^{10}\cdot 3^{10}}$, then the remainder when K is divided by 6 is

Q9.Let $\mathrm{f}(\mathrm{x})$ be a polynomial function such that $f(x)+f^{\prime }(x)+f^{\prime \prime }(x)=x^5+64$. Then, the value of ${\lim }_{x\to 1}\frac{f(x)}{x-1}$

Q10.Let $E_1$ and $E_2$ be two events such that the conditional probabilities $\mathrm{P}\left({\mathrm{E}}_1\mid {\mathrm{E}}_2\right)=\frac{1}{2}$, $\mathrm{P}\left({\mathrm{E}}_2\mid {\mathrm{E}}_1\right)=\frac{3}{4}$ and …

Q11.Let $\mathrm{A}=\left[\begin{array}{cc}0& -2\\ 2& 0\end{array}\right]$. If M and N are two matrices given by $M={\sum }_{k=1}^{10}{A}^{2k}$ and $N={\sum }_{k=1}^{10}{A}^{2k-1}$ then ${\mathrm{MN}}^2$ is

Q12.Let $\mathrm{g}:(0,\infty )\to \mathrm{R}$ be a differentiable function such that …

Q13.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ and $\mathrm{g}:\mathrm{R}\to \mathrm{R}$ be two functions defined by $\mathrm{f}(\mathrm{x})={\log }_{\mathrm{e}}\left({\mathrm{x}}^2+1\right)-{\mathrm{e}}^{-\mathrm{x}}+1$ and $g(x)=\frac{1-2e^{2x}}{e^x}$. Then, for …

Q14.Let $\vec{a}=a_1\hat{i}+a_2\hat{j}+a_3\hat{k}$ $a_i>0,i=1,2,3$ be a vector which makes equal angles with the coordinates axes OX, OY and OZ. Also, let the projection of $\overrightarrow{\mathrm{a}}$ on the vector $3\hat{\mathrm{i}}+4\hat{\mathrm{j}}$ be 7. Let …

Q15.Let $y=y(x)$ be the solution of the differential equation $(x+1)y^{\prime }-y=e^{3x}(x+1{)}^2$, with $y(0)=\frac{1}{3}$. Then, the point $x=-\frac{4}{3}$ for the curve $y=y(x)$ is:

Q16.If $\mathrm{y}={\mathrm{m}}_1\mathrm{x}+{\mathrm{c}}_1$ and $\mathrm{y}={\mathrm{m}}_2\mathrm{x}+{\mathrm{c}}_2,{\mathrm{m}}_1\ne {\mathrm{m}}_2$ are two common tangents of circle $x^2+y^2=2$ and parabola $y^2=x$, then the value of $8\left|m_1{m}_2\right|$ is equal …

Q17.Let Q be the mirror image of the point $\mathrm{P}(1,0,1)$ with respect to the plane $\mathrm{S}:\mathrm{x}+\mathrm{y}+\mathrm{z}=5$. If a line L passing through $(1,-1,-1)$, parallel to the line PQ meets the plane S at R, then ${\mathrm{QR}}^2$ is equal to:

Q18.If the solution curve $y=y(x)$ of the differential equation $y^{2}dx+\left(x^2-xy+y^2\right)dy=0$, which passes through the point $(1,1)$ and intersects the line $\mathrm{y}=\sqrt{3}\mathrm{x}$ at the point $(\alpha ,\sqrt{3}\alpha )$, then value of …

Q19.Let $\mathrm{x}=2\mathrm{t},\mathrm{y}=\frac{{\mathrm{t}}^2}{3}$ be a conic. Let S be the focus and B be the point on the axis of the conic such that $\mathrm{SA}\perp \mathrm{BA}$, where A is any point on the conic. If k is the ordinate of the centroid of …

Q20.Let a circle C in complex plane pass through the points ${\mathrm{z}}_1=3+4\mathrm{i},{\mathrm{z}}_2=4+3\mathrm{i}$ and ${\mathrm{z}}_3=5\mathrm{i}$. If $\mathrm{z}\left(\ne {\mathrm{z}}_1\right)$ is a point on C such that the line through z and ${\mathrm{z}}_1$ is perpendic …

Q21.The number of 3-digit odd numbers, whose sum of digits is a multiple of 7, is ______.

Q22.Let $\theta$ be the angle between the vectors $\vec{a}$ and $\vec{b}$,
where $|\vec{a}|=4,|\vec{b}|=3$ $\theta \in \left(\frac{\pi }{4},\frac{\pi }{3}\right)$. Then
$|(\vec{a}-\vec{b})\times (\vec{a}+\vec{b}){|}^2+4(\vec{a}\cdot \vec{b}{)}^2$ is equal to ______

Q23.Let the abscissae of the two points P and Q be the roots of $2{\mathrm{x}}^2-\mathrm{rx}+\mathrm{p}=0$ and the ordinates of P and Q be the roots of ${\mathrm{x}}^2-\mathrm{sx}-\mathrm{q}=0$. If the equation of the circle described on PQ as diameter is …

Q24.The number of values of $x$ in the interval $\left(\frac{\pi }{4},\frac{7\pi }{4}\right)$ for which $14{\mathrm{cosec}}^2\mathrm{x}-2{\sin }^2\mathrm{x}=21-4{\cos }^{2}x$ holds, is ____

Q25.For a natural number n, let ${\mathrm{a}}_{\mathrm{n}}=19^{\mathrm{n}}-12^{\mathrm{n}}$. Then, the value of $\frac{31{\alpha }_9-{\alpha }_{10}}{57{\alpha }_8}$ is

Q26.Let $\mathrm{f}:\mathrm{R}\to \mathrm{R}$ be a function defined by $f(x)={\left(2\left(1-\frac{x^{25}}{2}\right)\left(2+x^{25}\right)\right)}^{\frac{1}{50}}$. If the function $g(x)=f(f(f(x)))+f(f(x))$, then the greatest integer less than or equal to …

Q27.Let the lines
${\mathrm{L}}_1:\overrightarrow{\mathrm{r}}=\lambda (\hat{\mathrm{i}}+2\hat{\mathrm{j}}+3\hat{\mathrm{k}}),\lambda \in \mathrm{R}$
$L_2:\vec{r}=(\hat{i}+3\hat{j}+\hat{k})+\mu (\hat{i}+\hat{j}+5\hat{k});\mu \in R$
intersect at the point S. If a plane …

Q28.Let A be a $3\times 3$ matrix having entries from the set $\{-1,0,1\}$. The number of all such matrices A having sum of all the entries equal to 5, is ____

Q29.The greatest integer less than or equal to the sum of first 100 terms of the sequence $\frac{1}{3},\frac{5}{9},\frac{19}{27},\frac{65}{81},\dots \dots$ is equal to