JEE Main 2022 · 29 Jul 2022 · Shift 2

Q1.Two identical metallic spheres A and B when placed at certain distance in air repel each other with a force of F. Another identical uncharged sphere C is first placed in contact with A and then in contact with B and finally placed at midpoint between spheres A and B. The force ex …

Q2.Two identical thin metal plates has charge ${\mathrm{q}}_1$ and ${\mathrm{q}}_2$ respectively such that ${\mathrm{q}}_1>{\mathrm{q}}_2$. The plates were brought close to each other to form a parallel plate capacitor of capacitance C. The potential difference between them is :

Q3.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Alloys such as constantan and manganin are used in making standard resistance coils.

Reason R: Constantan and manganin have very small value of temperature coeffic …

Q4.A 1 m long wire is broken into two unequal parts X and Y. The X part of the wire is streched into another wire W. Length of W is twice the length of X and the resistance of W is twice that of Y. Find the ratio of length of X and Y.

Q5.A wire X of length 50 cm carrying a current of 2 A is placed parallel to a long wire Y of length 5 m. The wire Y carries a current of 3 A. The distance between two wires is 5 cm and currents flow in the same direction. The force acting on the wire Y is :

Q6.A juggler throws balls vertically upwards with same initial velocity in air. When the first ball reaches its highest position, he throws the next ball. Assuming the juggler throws n balls per second, the maximum height the balls can reach is

Q7.A circuit element X when connected to an a.c. supply of peak voltage 100 V gives a peak current of 5 A which is in phase with the voltage. A second element Y when connected to the same a.c. supply also gives the same value of peak current which lags behind the voltage by …

Q8.An unpolarised light beam of intensity $2{\mathrm{I}}_0$ is passed through a polaroid P and then through another polaroid Q which is oriented in such a way that its passing axis makes an angle of $30^{\circ }$ relative to that of P. The intensity of the emergent light is

Q9.An $\alpha$ particle and a proton are accelerated from rest through the same potential difference. The ratio of linear momenta acquired by above two particals will be :

Q10.Read the following statements:
(A) Volume of the nucleus is directly proportional to the mass number.
(B) Volume of the nucleus is independent of mass number.
(C) Density of the nucleus is directly proportional to the mass number.
(D) Density of the nucleus is directly proportion …

Q11.An object of mass 1 kg is taken to a height from the surface of earth which is equal to three times the radius of earth. The gain in potential energy of the object will be
[If, $g=10{\mathrm{ms}}^{-2}$ and radius of earth $=6400\mathrm{km}$]

Q12.A ball is released from a height $h$. If $t_1$ and $t_2$ be the time required to complete first half and second half of the distance respectively. Then, choose the correct relation between $t_1$ and $t_2$.

Q13.Two bodies of masses ${\mathrm{m}}_1=5\mathrm{kg}$ and ${\mathrm{m}}_2=3\mathrm{kg}$ are connected by a light string going over a smooth light pulley on a smooth inclined plane as shown in the figure. The system is at rest. The force exerted by the inclined plane on the b …

Q14.If momentum of a body is increased by $20\%$, then its kinetic energy increases by :

Q15.The torque of a force $5\hat{i}+3\hat{j}-7\hat{k}$ about the origin is $\tau$. If the force acts on a particle whose position vector is $2\hat{i}+2\hat{j}+\hat{k}$, then the value of $\tau$ will be :

Q16.A thermodynamic system is taken from an original state D to an intermediate state E by the linear process shown in the figure. Its volume is then reduced to the original volume from E to F by an isobaric process. The total work done by the gas from D to E to F will be

Q17.The vertical component of the earth's magnetic field is $6\times 10^{-5}\mathrm{T}$ at any place where the angle of dip is $37^{\circ }$. The earth's resultant magnetic field at that place will be (Given $\tan 37^{\circ }=\frac{3}{4}$)

Q18.The root mean square speed of smoke particles of mass $5\times 10^{-17}\mathrm{kg}$ in their Brownian motion in air at NTP is approximately. [Given $\mathrm{k}=1.38\times 10^{-23}{\mathrm{JK}}^{-1}$]

Q19.Light enters from air into a given medium at an angle of $45^{\circ }$ with interface of the air-medium surface. After refraction, the light ray is deviated through an angle of $15^{\circ }$ from its original direction. The refractive index of the medium is :

Q20.A tube of length 50 cm is filled completely with an incompressible liquid of mass 250 g and closed at both ends. The tube is then rotated in horizontal plane about one of its ends with a uniform angular velocity $\mathrm{x}\sqrt{\mathrm{F}}\mathrm{rad}{\mathrm{s}}^{-1}$. If F …

Q21.Nearly $10\%$ of the power of a 110 W light bulb is converted to visible radiation. The change in average intensities of visible radiation, at a distance of 1 m from the bulb to a distance of 5 m is $a\times 10^{-2}\mathrm{W}/{\mathrm{m}}^2$. The value of 'a' will be

Q22.A metal wire of length 0.5 m and cross-sectional area $10^{-4}{\mathrm{m}}^2$ has breaking stress $5\times 10^8{\mathrm{Nm}}^{-2}$. A block of 10 kg is attached at one end of the string and is rotating in a horizontal circle. The maximum linear velocity of block will be \ …

Q23.The velocity of a small ball of mass 0.3 g and density $8\mathrm{g}/\mathrm{cc}$ when dropped in a container filled with glycerine becomes constant after some time. If the density of glycerine is $1.3\mathrm{g}/\mathrm{cc}$, then the value of viscous force acting on t …

Q24.A modulating signal $2\sin \left(6.28\times 10^6\right)t$ is added to the carrier signal $4\sin \left(12.56\times 10^9\right)t$ for amplitude modulation. The combined signal is passed through a non-linear square law device. The output is then passed through a band pass …

Q25.The speed of a transverse wave passing through a string of length 50 cm and mass 10 g is $60{\mathrm{ms}}^{-1}$. The area of cross-section of the wire is $2.0{\mathrm{mm}}^2$ and its Young's modulus is $1.2\times 10^{11}{\mathrm{Nm}}^{-2}$. The extension of the wire over its na …

Q26.The metallic bob of simple pendulum has the relative density 5. The time period of this pendulum is 10 s. If the metallic bob is immersed in water, then the new time period becomes $5\sqrt{x}$ s. The value of $x$ will be ______.

Q27.A 8 V Zener diode along with a series resistance R is connected across a 20 V supply (as shown in the figure). If the maximum Zener current is 25 mA, then the minimum value of $R$ will be ______ $\Omega$.

Q28.Two radioactive materials A and B have decay constants $25\lambda$ and $16\lambda$ respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of B to that of A will be "e" after a time $\frac{1}{a\lambda }$. The value of a is ______.

Q29.A capacitor of capacitance $500\mu \mathrm{F}$ is charged completely using a dc supply of 100 V. It is now connected to an inductor of inductance 50 mH to form an LC circuit. The maximum current in LC circuit will be ______ A.

Q1.Consider the reaction
$4{\mathrm{HNO}}_3(l)+3\mathrm{KCl}(\mathrm{s})\to {\mathrm{Cl}}_2(\mathrm{g})+\mathrm{NOCl}(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}(\mathrm{g})+3{\mathrm{KNO}}_3(\mathrm{s})$

The amount of ${\mathrm{HNO}}_3$ required to produce 110.0 g o …

Q2.Given below are the quantum numbers for 4 electrons.
A. $\mathrm{n}=3,l=2,{\mathrm{m}}_1=1,{\mathrm{m}}_{\mathrm{s}}=+1/2$
B. $\mathrm{n}=4,l=1,{\mathrm{m}}_1=0,{\mathrm{m}}_{\mathrm{s}}=+1/2$
C. …

Q3.$\mathrm{C}(\mathrm{s})+{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{CO}}_2(\mathrm{g})+400\mathrm{kJ}$
$\mathrm{C}(\mathrm{s})+\frac{1}{2}{\mathrm{O}}_2(\mathrm{g})\to \mathrm{CO}(\mathrm{g})+100\mathrm{kJ}$
When coal of purity $60\%$ is allowed to bu …

Q4.200 mL of 0.01 M HCl is mixed with 400 mL of $0.01\mathrm{M}{\mathrm{H}}_2{\mathrm{SO}}_4$. The pH of the mixture is ____ .

Q5.Given below are the critical temperatures of some of the gases :

The gas showing least adsorption on a …

Q6.In liquation process used for tin $(\mathrm{Sn})$, the metal :

Q7.Given below are two statements.

Statement I : Stannane is an example of a molecular hydride.
Statement II : Stannane is a planar molecule.
In the light of the above statement, choose the most appropriate answer from the options given below :

Q8.Portland cement contains ' X ' to enhance the setting time. What is ' X '?

Q9.When borax is heated with CoO on a platinum loop, blue coloured bead formed is largely due to :

Q10.Which of the following 3d-metal ion will give the lowest enthalpy of hydration ( ${\Delta }_{\text{hyd }}\mathrm{H}$ ) when dissolved in water?

Q11.Octahedral complexes of copper (II) undergo structural distortion (Jahn-Teller). Which one of the given copper (II) complexes will show the maximum structural distortion?
(en-ethylenediamine; ${\mathrm{H}}_2\mathrm{N}-{\mathrm{CH}}_2-{\mathrm{CH}}_2-{\mathrm{NH}}_2$ )

Q12.Dinitrogen is a robust compound, but reacts at high altitude to form oxides. The oxide of nitrogen that can damage plant leaves and retard photosynthesis is :

Q13.Correct structure of $\gamma$-methylcyclohexane carbaldehyde is :

Q14.Compound 'A' undergoes following sequence of reactions to give compound 'B'. The correct structure and chirality of compound 'B' is:
[where Et is $-{\mathrm{C}}_2{\mathrm{H}}_5$]

Q15.Given below are two statements.

Statement I : The compound A is optically active.

Statement II : B is mirror image of above compound A.
In the light of the above statement, choose the most appropriate answer from the options given below.

Q16.When ethanol is heated with conc. ${\mathrm{H}}_2{\mathrm{SO}}_4$, a gas is produced. The compound formed, when this gas is treated with cold dilute aqueous solution of Baeyer's reagent, is :

Q17.The Hinsberg reagent is :

Q18.Which of the following is NOT a natural polymer?

Q19.Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Amylose is insoluble in water.
Reason R : Amylose is a long linear molecule with more than 200 glucose units.

In the light of the above statements, choose the corr …

Q20.A compound 'X' is a weak acid and it exhibits colour change at pH close to the equivalence point during neutralization of NaOH with ${\mathrm{CH}}_3\mathrm{COOH}$. Compound 'X' exists in ionized form in basic medium. The compound 'X' is :

Q21.'x' g of molecular oxygen (${\mathrm{O}}_2$) is mixed with 200 g of neon (Ne). The total pressure of the nonreactive mixture of ${\mathrm{O}}_2$ and Ne in the cylinder is 25 bar. The partial pressure of Ne is 20 bar at the same temperature and volume. The value of 'x' is ____ …

Q22.Consider, ${\mathrm{PF}}_5,{\mathrm{BrF}}_5,{\mathrm{PCl}}_3,{\mathrm{SF}}_6,{\left[{\mathrm{ICl}}_4\right]}^{-},{\mathrm{ClF}}_3$ and ${\mathrm{IF}}_5$.

Amongst the above molecule(s)/ion(s), the number of molecule(s)/ion(s) having ${\mathrm{sp}}^3{\mathrm{d}}^2$ hybrid …

Q23.1.80 g of solute A was dissolved in $62.5{\mathrm{cm}}^3$ of ethanol and freezing point of the solution was found to be 155.1 K. The molar mass of solute A is ______ $\mathrm{g}{\mathrm{mol}}^{-1}$.
[Given: Freezing point of ethanol is 156.0 K.
Density of ethanol is …

Q24.For a cell, $\mathrm{Cu}(\mathrm{s})\mid {\mathrm{Cu}}^{2+}(0.001\mathrm{M})\mid \mid {\mathrm{Ag}}^{+}(0.01\mathrm{M})\mid \mathrm{Ag}(\mathrm{s})$ the cell potential is found to be 0.43 V at 298 K. The magnitude of standard electrode potential for …

Q25.Assuming $1\mu \mathrm{g}$ of trace radioactive element X with a half life of 30 years is absorbed by a growing tree. The amount of X remaining in the tree after 100 years is ____ $\times 10^{-1}\mu \mathrm{g}$.
[Given : $\ln 10=2.303;\log 2=0.30$ ]

Q26.Sum of oxidation state (magnitude) and coordination number of cobalt in $\mathrm{Na}[\mathrm{Co}(\text{bpy}){\mathrm{Cl}}_4]$ is ____.
(Given bpy =

Q27.Consider the following sulphure based oxoacids.
${\mathrm{H}}_2{\mathrm{SO}}_3,{\mathrm{H}}_2{\mathrm{SO}}_4,{\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_8$ and ${\mathrm{H}}_2{\mathrm{S}}_2{\mathrm{O}}_7$.
Amongst these oxoacids, the number of those with peroxo(O-O) bo …

Q28.A 1.84 mg sample of polyhydric alcoholic compound ' X ' of molar mass $92.0\mathrm{g}/\mathrm{mol}$ gave 1.344 mL of ${\mathrm{H}}_2$ gas at STP. The number of alcoholic hydrogens present in compound ' X ' is ____.

Q29.The number of stereoisomers formed in a reaction of $(\pm )\mathrm{Ph}(\mathrm{C}=\mathrm{O})\mathrm{C}(\mathrm{OH})(\mathrm{CN})\mathrm{Ph}$ with HCN is ____.

Q30.The number of chlorine atoms in bithionol is ____.

Q1.If $\mathrm{z}\ne 0$ be a complex number such that $\left|\mathrm{z}-\frac{1}{\mathrm{z}}\right|=2$, then the maximum value of |z| is:

Q2.Which of the following matrices can NOT be obtained from the matrix $\left[\begin{array}{cc}-1& 2\\ 1& -1\end{array}\right]$ by a single elementary row operation?

Q3.If the system of equations
$x+y+z=6$
$2x+5y+\alpha z=\beta$
$x+2y+3z=14$
has infinitely many solutions, then $\alpha +\beta$ is equal to:

Q4.Let the function
$f(x)=\{\begin{array}{cc}\frac{{\log }_e(1+5x)-{\log }_e(1+\alpha x)}{x}& ;\text{ if }x\ne 0\\ 10& ;\text{ if }x=0\end{array}$
be continuous at $\mathrm{x}=0$.
Then $\alpha$ is equal to:

Q5.If $[t]$ denotes the greatest integer $\le t$, then the value of ${\int }_0^1\left[2\mathrm{x}-\left|3{\mathrm{x}}^2-5\mathrm{x}+2\right|+1\right]\mathrm{dx}$ is:

Q6.Let ${\left\{a_{\mathrm{n}}\right\}}_{\mathrm{n}=0}^{\infty }$ be a sequence such that $a_0=a_1=0$ and $a_{\mathrm{n}+2}=3a_{\mathrm{n}+1}-2a_{\mathrm{n}}+1,\forall \mathrm{n}\ge 0$.
Then $a_{25}{a}_{23}-2a_{25}{a}_{22}-2a_{23}{a}_{24}+4a_{22}{a}_{24}$ is equal to:

Q7.${\sum }_{\mathrm{r}=1}^{20}\left({\mathrm{r}}^2+1\right)(\mathrm{r}!)$ is equal to:

Q8.For $\mathrm{I}(\mathrm{x})=\int \frac{{\sec }^2\mathrm{x}-2022}{{\sin }^{2022}\mathrm{x}}\mathrm{dx}$, if $\mathrm{I}\left(\frac{\pi }{4}\right)=2^{1011}$, then

Q9.If the solution curve of the differential equation $\frac{dy}{dx}=\frac{x+y-2}{x-y}$ passes through the point $(2,1)$ and $(\mathrm{k}+1,2),\mathrm{k}>0$, then

Q10.Let $y=y(x)$ be the solution curve of the differential equation $\frac{dy}{dx}+\left(\frac{2x^2+11x+13}{x^3+6x^2+11x+6}\right)\mathrm{y}=\frac{(\mathrm{x}+3)}{\mathrm{x}+1},\mathrm{x}>-1$, which passes through the point $(0,1)$. Then $\mathrm{y}(1)$ is equal to:

Q11.Let ${\mathrm{m}}_1,{\mathrm{m}}_2$ be the slopes of two adjacent sides of a square of side a such that ${\mathrm{a}}^2+11\mathrm{a}+3\left({\mathrm{m}}_1^2+{\mathrm{m}}_2^2\right)=220$. If one vertex of the square is …

Q12.The number of elements in the set $S=\left\{x\in \mathbb{R}:2\cos \left(\frac{x^2+x}{6}\right)=4^x+4^{-x}\right\}$ is:

Q13.Let $\mathrm{A}(\alpha ,-2),\mathrm{B}(\alpha ,6)$ and $\mathrm{C}\left(\frac{\alpha }{4},-2\right)$ be vertices of a $△\mathrm{ABC}$. If $\left(5,\frac{\alpha }{4}\right)$ is the circumcentre of $\Delta \mathrm{ABC}$, then which of the following is NOT correct about …

Q14.Let Q be the foot of perpendicular drawn from the point $\mathrm{P}(1,2,3)$ to the plane $\mathrm{x}+2\mathrm{y}+\mathrm{z}=14$. If R is a point on the plane such that $\angle \mathrm{PRQ}=60^{\circ }$, then the area of $△\mathrm{PQR}$ is equal to:

Q15.If $(2,3,9),(5,2,1),(1,\lambda ,8)$ and $(\lambda ,2,3)$ are coplanar, then the product of all possible values of $\lambda$ is:

Q16.Bag I contains 3 red, 4 black and 3 white balls and Bag II contains 2 red, 5 black and 2 white balls. One ball is transferred from Bag I to Bag II and then a ball is drawn from Bag II. The ball so drawn is found to be black in colour. Then the probability, that the transferred ba …

Q17.Let $\mathrm{S}=\{\mathrm{z}=\mathrm{x}+\mathrm{iy}:|\mathrm{z}-1+\mathrm{i}|\ge |\mathrm{z}|,|\mathrm{z}|<2,|\mathrm{z}+\mathrm{i}|=|\mathrm{z}-1|\}$. Then the set of all values of $x$, for which $\mathrm{w}=2\mathrm{x}+\mathrm{iy}\in \mathrm{S}$ for some …

Q18.Let $\overrightarrow{\mathrm{a}},\overrightarrow{\mathrm{b}},\overrightarrow{\mathrm{c}}$ be three coplanar concurrent vectors such that angles between any two of them is same. If the product of their magnitudes is 14 and …

Q19.The domain of the function $f(x)={\sin }^{-1}\left(\frac{x^2-3x+2}{x^2+2x+7}\right)$ is :

Q20.The statement $(p\Rightarrow q)\vee (p\Rightarrow r)$ is NOT equivalent to:

Q21.The sum and product of the mean and variance of a binomial distribution are 82.5 and 1350 respectively. Then the number of trials in the binomial distribution is:

Q22.Let $\alpha ,\beta$ ($\alpha >\beta$) be the roots of the quadratic equation ${\mathrm{x}}^2-\mathrm{x}-4=0$. If ${\mathrm{P}}_{\mathrm{n}}={\alpha }^{\mathrm{n}}-{\beta }^{\mathrm{n}},\mathrm{n}\in \mathbb{N}$, then …

Q23.Let $\mathrm{X}=\left[\begin{array}{l}1\\ 1\\ 1\end{array}\right]$ and $\mathrm{A}=\left[\begin{array}{ccc}-1& 2& 3\\ 0& 1& 6\\ 0& 0& -1\end{array}\right]$. For $\mathrm{k}\in \mathbb{N}$, if ${\mathrm{X}}^{\prime }{\mathrm{A}}^k\mathrm{X}=33$, then k is equal to:

Q24.The number of natural numbers lying between 1012 and 23421 that can be formed using the digits $2,3,4,5,6$ (repetition of digits is not allowed) and divisible by 55 is:

Q25.If ${\sum }_{\mathrm{k}=1}^{10}{\mathrm{K}}^2{\left({}^{10}{\mathrm{C}}_{\mathrm{K}}\right)}^2=22000\mathrm{L}$, then L is equal to ____.

Q26.If $[\mathrm{t}]$ denotes the greatest integer $\le \mathrm{t}$, then number of points, at which the function $\mathrm{f}(\mathrm{x})=4|2\mathrm{x}+3|+9\left[\mathrm{x}+\frac{1}{2}\right]-12[\mathrm{x}+20]$ is not differentiable in the open interval $(-20,20)$, is ____.

Q27.If the tangent to the curve $y=x^3-x^2+x$ at the point $(a,b)$ is also tangent to the curve $y=5x^2+2\mathrm{x}-25$ at the point $(2,-1)$, then $|2\mathrm{a}+9\mathrm{b}|$ is equal to ____.

Q28.Let AB be a chord of length 12 of the circle $(x-2{)}^2+(y+1{)}^2=\frac{169}{4}$.

If tangents drawn to the circle at points A and B intersect at the point P, then five times the distance of point P from chord AB is equal to ____.

Q29.Let $\vec{a}$ and $\vec{b}$ be two vectors such that $|\vec{a}+\vec{b}{|}^2=|\vec{a}{|}^2+2|\vec{b}{|}^2$, $\vec{a}\cdot \vec{b}=3$ and $|\vec{a}\times \vec{b}{|}^2=75$. Then $|\overrightarrow{\mathrm{a}}{|}^2$ is equal to ____.

Q30.Let
$\mathrm{S}=\left\{(\mathrm{x},\mathrm{y})\in \mathbb{N}\times \mathbb{N}:9(\mathrm{x}-3{)}^2+16(\mathrm{y}-4{)}^2\le 144\right\}$
and $\mathrm{T}=\left\{(\mathrm{x},\mathrm{y})\in \mathbb{R}\times \mathbb{R}:(\mathrm{x}-7{)}^2+(\mathrm{y}-4{)}^2\le 36\right\}$.
Th …