JEE Main 2022 · 28 Jun 2022 · Shift 1

Q1.Given below are two statements : One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Product of Pressure (P) and time (t) has the same dimension as that of coefficient of viscosity.
Reason R:
Coefficient of viscosity …

Q2.A particle of mass m is moving in a circular path of constant radius $r$ such that its centripetal acceleration (a) is varying with time t as $\mathrm{a}={\mathrm{k}}^2{\mathrm{rt}}^2$. where k is a constant. The power delivered to the particle by the force acting on it is given …

Q3.A radar sends an electromagnetic signal of electric field $(E_0)=2.25\mathrm{V}/\mathrm{m}$ and magnetic field $(B_0)=1.5\times 10^{-8}\mathrm{T}$ which strikes a target on line of sight at a distance of 3 km in a medium. After that, a part of signal (echo) reflects ba …

Q4.The refracting angle of a prism is A and refractive index of the material of the prism is $\cot (A/2)$. Then the angle of minimum deviation will be -

Q5.The aperture of the objective is 24.4 cm. The resolving power of this telescope, if a light of wavelength $2440\mathring{A}$ is used to see the object will be

Q6.The de Broglie wavelengths for an electron and a photon are ${\lambda }_e$ and ${\lambda }_p$ respectively. For the same kinetic energy of electron and photon, which of the following presents the correct relation between the de Broglie wavelengths of two?

Q7.The Q-value of a nuclear reaction and kinetic energy of the projectile particle, $K_p$ are related as:

Q8.In the following circuit, the correct relation between output (Y) and inputs A and B will be:

Q9.For using a multimeter to identify diode from electrical components, choose the correct statement out of the following about the diode:

Q10.Given below are two statements: One is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: n-p-n transistor permits more current than a p-n-p transistor.
Reason R: Electrons have greater mobility as a charge carrier.
Choose the correct answer from the opt …

Q11.The velocity of sound in a gas, in which two wavelengths 4.08 m and 4.16 m produce 40 beats in 12s, will be:

Q12.A pendulum is suspended by a string of length 250 cm. The mass of the bob of the pendulum is 200 g. The bob is pulled aside until the string is at $60^{\circ }$ with vertical as shown in the figure. After releasing the bob, the maximum velocity attained by the bob will be ______ …

Q13.A meter bridge setup is shown in the figure. It is used to determine an unknown resistance R using a given resistor of $15\Omega$. The galvanometer (G) shows null deflection when tapping key is at 43 cm mark from end A. If the end correction for end A is 2 cm, then the determine …

Q14.Current measured by the ammeter (A) in the reported circuit when no current flows through $10\Omega$ resistance. will be ____ A.

Q15.An AC source is connected to an inductance of 100 mH, a capacitance of $100\mu \mathrm{F}$ and a resistance of $120\Omega$ as shown in figure. The time in which the resistance having a thermal capacity $2\mathrm{J}{/}^{\circ }\mathrm{C}$ will get heated by …

Q16.The position vector of 1 kg object is $\overrightarrow{\mathrm{r}}=(3\hat{\mathrm{i}}-\hat{\mathrm{j}})\mathrm{m}$ and its velocity $\overrightarrow{\mathrm{v}}=(3\hat{\mathrm{j}}+\hat{\mathrm{k}}){\mathrm{ms}}^{-1}$. The magnitude of its angular momentum is …

Q17.A man of 60 kg is running on the road and suddenly jumps into a stationary trolly car of mass 120 kg. Then, the trolly car starts moving with velocity $2{\mathrm{ms}}^{-1}$. The velocity of the running man was ____ ${\mathrm{ms}}^{-1}$ when he jumps into the car.

Q18.A hanging mass M is connected to a four times bigger mass by using a string-pulley arrangement, as shown in the figure. The bigger mass is placed on a horizontal ice-slab and being pulled by 2 Mg force. In this situation, tension in the string is $\frac{\mathrm{X}}{5}$ Mg for …

Q19.The total internal energy of two mole monoatomic ideal gas at temperature $\mathrm{T}=300\mathrm{K}$ will be ____ J. (Given $\mathrm{R}=8.31\mathrm{J}/\mathrm{mol}\cdot \mathrm{K}$)

Q20.A singly ionized magnesium atom (A24) ion is accelerated to kinetic energy 5 keV and is projected perpendicularly into a magnetic field B of the magnitude 0.5 T. The radius of path formed will be ____ cm.

Q21.A telegraph line of length 100 km has a capacity of $0.01\mu \mathrm{F}/\mathrm{km}$ and it carries an alternating current at 0.5 kilo cycle per second. If minimum impedance is required, then the value of the inductance that needs to be introduced in series is ____ mH. ( …

Q22.Motion of a particle in x-y plane is described by a set of equations $x=4\sin (\omega t)$ m and $y=4\cos (\omega t)$ m. The path of the particle will be:

Q23.Match List-I with List-II:
List-I: (A) M.I. of a solid sphere of radius R about any tangent (B) M.I. of a hollow sphere of radius R about any tangent (C) M.I. of a circular ring of radius R about its diameter (D) M.I. of a circular disc of radius R about any diameter
List-II …

Q24.Two planets A and B of equal mass have periods of revolution T_A and T_B such that T_A = 2 T_B. They revolve in circular orbits of radii r_A and r_B respectively. Which of the following is the correct relationship of their orbits?

Q1.The incorrect statement about the imperfections in solids is :

Q2.The Zeta potential is related to which property of colloids?

Q3.Element "E" belongs to the period 4 and group 16 of the periodic table. The valence shell electron configuration of the element, which is just above 'E' in the group is

Q4.Given are two statements one is labelled as Assertion A and other is labelled as Reason R.
Assertion A: Magnesium can reduce ${\mathrm{Al}}_2{\mathrm{O}}_3$ at a temperature below $1350^{\circ }\mathrm{C}$, while above $1350^{\circ }\mathrm{C}$ aluminium can reduce MgO.
Reason R: T …

Q5.Dihydrogen reacts with CuO to give

Q6.Nitrogen gas is obtained by thermal decomposition of

Q7.Given below are two statements:
Statement-I: The pentavalent oxide of group-15 element, ${\mathrm{E}}_2{\mathrm{O}}_5$, is less acidic than trivalent oxide, ${\mathrm{E}}_2{\mathrm{O}}_3$, of the same element.
Statement-II: The acidic character of trivalent oxide of group 15 elem …

Q8.Which one of the lanthanoids given below is the most stable in divalent form?

Q9.Given below are two statements:
Statement I: $[\mathrm{Ni}(\mathrm{CN}{)}_4{]}^{2-}$ is square planar and diamagnetic complex with ${\mathrm{dsp}}^2$ hybridization for Ni but $[\mathrm{Ni}(\mathrm{CO}{)}_4]$ is tetrahedral, paramagnetic and with ${\mathrm{sp}}^3$-hybridization for Ni …

Q10.Which amongst the following is not a pesticide?

Q11.Which one of the following techniques is not used to spot components of a mixture separated on thin layer chromatographic plate?

Q12.Which of the following structures are aromatic in nature?

Q13.The major product (P) in the reaction

(see reaction scheme)

[Ph is $-\mathrm{C}{}_6\mathrm{H}{}_5$] is

Q14.The correct structure of product 'A' formed in the following reaction.

$\mathrm{PhCHO}+\mathrm{Ph}\cdot \mathrm{CHO}\underset{\mathrm{in}\mathrm{D}{}_2\mathrm{O}}{\overset{\mathrm{NaOD}}{\to }}\mathrm{A}+\mathrm{Ph}-\stackrel{\mathrm{O}}{\mathrm{C}}-\mathrm{O}{}^{-}$

(Ph is $-\mathrm{C}{}_6\mathrm{H}{}_5$)

Q15.Which one of the following compounds is inactive towards $\mathrm{S}{}_{\mathrm{N}}1$ reaction?

Q16.Identify the major product formed in the following sequence of reactions:

(see reaction scheme)

Q17.A primary aliphatic amine on reaction with nitrous acid in cold (273 K) and there after raising temperature of reaction mixture to room temperature (298 K). Gives a/an

Q18.Which one of the following is NOT a copolymer?

Q19.Stability of $\alpha$-Helix structure of proteins depends upon

Q20.The formula of the purple colour formed in Laissaigne's test for sulphur using sodium nitroprusside is

Q21.A 2.0 g sample containing $\mathrm{MnO}{}_2$ is treated with HCl liberating $\mathrm{Cl}{}_2$. The $\mathrm{Cl}{}_2$ gas is passed into a solution of KI and 60.0 mL of 0.1 M $\mathrm{Na}{}_2\mathrm{S}{}_2\mathrm{O}{}_3$ is required to titrate the liberated iodine. The percentage of $\mathrm{MnO}{}_2$ in the sample is ______.
(Nearest int …

Q22.If the work function of a metal is $6.63\times 10^{-19}$ J, the maximum wavelength of the photon required to remove a photoelectron from the metal is ______ nm. (Nearest integer)
[Given: $h=6.63\times 10^{-34}$ J s, and $c=3\times 10^8$ m s${}^{-1}$]

Q23.The hybridization of P exhibited in $\mathrm{PF}{}_5$ is ${\mathrm{sp}}^x{\mathrm{d}}^y$. The value of $y$ is ______.

Q24.4.0 L of an ideal gas is allowed to expand isothermally into vacuum until the total volume is 20 L. The amount of heat absorbed in this expansion is ______ L atm.

Q25.The vapour pressures of two volatile liquids A and B at $25^{\circ }\mathrm{C}$ are 50 Torr and 100 Torr, respectively. If the liquid mixture contains 0.3 mole fraction of A, then the mole fraction of liquid B in the vapour phase is $\frac{x}{17}$. The value of $x$ is ______.

Q26.The solubility product of a sparingly soluble salt ${\mathrm{A}}_2{\mathrm{X}}_3$ is $1.1\times 10^{-23}$. If specific conductance of the solution is $3\times 10^{-5}\mathrm{S}{\mathrm{m}}^{-1}$, the limiting molar conductivity of the solution is …

Q27.The quantity of electricity in Faraday needed to reduce 1 mol of ${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}$ to ${\mathrm{Cr}}^{3+}$ is ______.

Q28.For a first order reaction $\mathrm{A}\to \mathrm{B}$, the rate constant, $\mathrm{k}=5.5\times 10^{-14}{\mathrm{s}}^{-1}$. The time required for $67\%$ completion of reaction is $\mathrm{x}\times 10^{-1}$ times the half life of reaction. The value of $x$ is ______.
(N …

Q29.Number of complexes which will exhibit synergic bonding amongst, $[\mathrm{Cr}(\mathrm{CO}{)}_6]$, $[\mathrm{Mn}(\mathrm{CO}{)}_5]$ and $[{\mathrm{Mn}}_2(\mathrm{CO}{)}_{10}]$ is ______.

Q30.In the estimation of bromine, 0.5 g of an organic compound gave 0.40 g of silver bromide. The percentage of bromine in the given compound is ______ % (nearest integer)
(Relative atomic masses of Ag and Br are 108u and 80u, respectively).

Q1.If

Where …

Q2.Let a function $\mathrm{f}:\mathbb{N}\to \mathbb{N}$ be defined by …

Q3.If the system of linear equations
$2x+3y-z=-2$
$x+y+z=4$
$\mathrm{x}-\mathrm{y}+|\lambda |\mathrm{z}=4\lambda -4$
where $\lambda \in \mathbb{R}$, has no solution, then

Q4.Let A be a matrix of order $3\times 3$ and $\det (\mathrm{A})=2$. Then $\det \left(\det (\mathrm{A})\mathrm{adj}\left(5\mathrm{adj}\left({\mathrm{A}}^3\right)\right)\right)$ is equal to

Q5.The total number of 5-digit numbers, formed by using the digits $1,2,3,5,6,7$ without repetition, which are multiple of 6, is

Q6.Let ${\mathrm{A}}_1,{\mathrm{A}}_2,{\mathrm{A}}_3,\dots$ be an increasing geometric progression of positive real numbers. If $A_1{A}_3{A}_5{A}_7=\frac{1}{1296}$ and $A_2+A_4=\frac{7}{36}$, then, the value of ${\mathrm{A}}_6+{\mathrm{A}}_8+{\mathrm{A}}_{10}$ is equal …

Q7.Let $[t]$ denote the greatest integer less than or equal to $t$. Then, the value of the integral ${\int }_0^1\left[-8x^2+6x-1\right]dx$ is equal to

Q8.Let $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ be defined as …

Q9.The area of the region
$\mathrm{S}=\left\{(\mathrm{x},\mathrm{y}):{\mathrm{y}}^2\le 8\mathrm{x},\mathrm{y}\ge \sqrt{2}\mathrm{x},\mathrm{x}\ge 1\right\}$ is

Q10.Let the solution curve $y=y(x)$ of the differential equation,

pass through the points $(1,0)$ and $(2\alpha ,\alpha ),\alpha >0$.
Then …

Q11.Let $y=y(x)$ be the solution of the differential equation $x\left(1-x^2\right)\frac{dy}{dx}+\left(3x^{2}y-y-4x^3\right)=0,x>1$, with $y(2)=-2$. Then $y(3)$ is equal to

Q12.The number of real solutions of $x^7+5x^3+3x+1=0$ is equal to

Q13.Let the eccentricity of the hyperbola $\mathrm{H}:\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2}-\frac{{\mathrm{y}}^2}{{\mathrm{b}}^2}=1$ be $\sqrt{\frac{5}{2}}$ and length of its latus rectum be $6\sqrt{2}$, If $\mathrm{y}=2\mathrm{x}+\mathrm{c}$ is a tangent to the hyperbola …

Q14.If the tangents drawn at the point $\mathrm{O}(0,0)$ and $P(1+\sqrt{5},2)$ on the circle $x^2+y^2-2x-4y=0$ intersect at the point Q , then the area of the triangle OPQ is equal to

Q15.If two distinct point $\mathrm{Q},\mathrm{R}$ lie on the line of intersection of the planes $-x+2y-z=0$ and $3x-5y+2z=0$ and $PQ=PR=\sqrt{18}$ where the point P is $(1,-2,3)$, then the area of the triangle PQR is equal to

Q16.The acute angle between the planes ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$, when $P_1$ and $P_2$ are the planes passing through the intersection of the planes $5x+8y+13z-29=0$ and $8x-7y+z-20=0$ and the points $(2,1,3)$ and ( $0,1,2$ ), respectively, is

Q17.Let the plane $\mathrm{P}:\overrightarrow{\mathrm{r}}\cdot \overrightarrow{\mathrm{a}}=\mathrm{d}$ contain the line of intersection of two planes $\overrightarrow{\mathrm{r}}\cdot (\hat{\mathrm{i}}+3\hat{\mathrm{j}}-\hat{\mathrm{k}})=6$ and …

Q18.The probability, that in a randomly selected 3-digit number at least two digits are odd, is

Q19.Let AB and PQ be two vertical poles, 160 m apart from each other. Let C be the middle point of B and Q , which are feet of these two poles. Let $\frac{\pi }{8}$ and $\theta$ be the angles of elevation from C to P and A , respectively. If the height of pole PQ is twice the heig …

Q20.Let $\mathrm{p},\mathrm{q},\mathrm{r}$ be three logical statements. Consider the compound statements
$S_1:((\sim p)\vee q)\vee ((\sim p)\vee r)$ and
${\mathrm{S}}_2:\mathrm{p}\to (\mathrm{q}\vee \mathrm{r})$
Then, which of the following is NOT true ?

Q21.Let ${\mathrm{R}}_1$ and ${\mathrm{R}}_2$ be relations on the set $\{1,2,\dots ,50\}$ such that
${\mathrm{R}}_1=\{\left(\mathrm{p},{\mathrm{p}}^{\mathrm{n}}\right):\mathrm{p}$ is a prime and $\mathrm{n}\ge 0$ is an integer $\}$
and …

Q22.The number of real solutions of the equation ${\mathrm{e}}^{4\mathrm{x}}+4{\mathrm{e}}^{3\mathrm{x}}-58{\mathrm{e}}^{2\mathrm{x}}+4{\mathrm{e}}^{\mathrm{x}}+1=0$ is ____ .

Q23.The mean and standard deviation of 15 observations are found to be 8 and 3 respectively. On rechecking it was found that, in the observations, 20 was misread as 5 . Then, the correct variance is equal to ____ .

Q24.If $\vec{a}=2\hat{i}+\hat{j}+3\hat{k},\vec{b}=3\hat{i}+3\hat{j}+\hat{k}$ and $\overrightarrow{\mathrm{c}}={\mathrm{c}}_1\hat{\mathrm{i}}+{\mathrm{c}}_2\hat{\mathrm{j}}+{\mathrm{c}}_3\hat{\mathrm{k}}$ are coplanar vectors and …

Q25.A ray of light passing through the point $P(2,3)$ reflects on the x-axis at point A and the reflected ray passes through the point $Q(5,4)$. Let R be the point that divides the line segment AQ internally into the ratio $2:1$. Let the co-ordinates of the foot of the perpendicular …

Q26.Let $\ell$ be a line which is normal to the curve $y=2x^2+x+2$ at a point P on the curve. If the point $Q(6,4)$ lies on the line $\ell$ and O is origin, then the area of the triangle OPQ is equal to ____.

Q27.Let $A=\{1,a_1,a_2,\dots ,a_{18},77\}$ be a set of integers with $1<a_1<a_2<\dots <a_{18}<77$. Let the set $A+A=\{x+y:x,y\in A\}$ contain exactly 39 elements. Then, the value of $a_1+a_2+\dots +a_{18}$ is equal to ____.

Q28.The number of positive integers k such that the constant term in the binomial expansion of ${\left(2x^3+\frac{3}{x^k}\right)}^{12}$, $x\ne 0$ is $2^8\cdot \ell$, where $\ell$ is an odd integer, is ____.

Q29.The number of elements in the set $\{z=a+ib\in \mathbb{C}:a,b\in \mathbb{Z}$ and $1<|z-3+2i|<4\}$ is ____.

Q30.Let the lines $y+2x=\sqrt{11}+7\sqrt{7}$ and $2y+x=2\sqrt{11}+6\sqrt{7}$ be normal to a circle $C:(x-h{)}^2+(y-k{)}^2=r^2$. If the line $\sqrt{11}y-3x=\frac{5\sqrt{77}}{3}+11$ is tangent to the circle C, then the value of $(5h-8k{)}^2+5r^2$ is equal to ____.