JEE Main 2022 · 27 Jun 2022 · Shift 2

Q1.The SI unit of a physical quantity is pascal-second. The dimensional formula of this quantity will be

Q2.The distance of the Sun from earth is $1.5\times 10^{11}\mathrm{m}$ and its angular diameter is (2000) s when observed from the earth. The diameter of the Sun will be :

Q3.When a ball is dropped into a lake from a height 4.9 m above the water level, it hits the water with a velocity v and then sinks to the bottom with the constant velocity v. It reaches the bottom of the lake 4.0 s after it is dropped. The approximate depth of the lake is :

Q4.One end of a massless spring of spring constant k and natural length $l_0$ is fixed while the other end is connected to a small object of mass m lying on a frictionless table. The spring remains horizontal on the table. If the object is made to rotate at an angular velocity …

Q5.A stone tide to a string of length L is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of change in its velocity, as it reaches a position where th …

Q6.Four spheres each of mass m form a square of side d (as shown in figure). A fifth sphere of mass M is situated at the centre of square. The total gravitational potential energy of the system is :

Q7.For a perfect gas, two pressures ${\mathrm{P}}_1$ and ${\mathrm{P}}_2$ are shown in figure. The graph shows:

Q8.According to kinetic theory of gases,
A. The motion of the gas molecules freezes at $0^{\circ }\mathrm{C}$
B. The mean free path of gas molecules decreases if the density of molecules is increased.
C. The mean free path of gas molecules increases if temperature is increased kee …

Q9.A lead bullet penetrates into a solid object and melts. Assuming that $40\%$ of its kinetic energy is used to heat it, the initial speed of bullet is:
(Given, initial temperature of the bullet $=127^{\circ }\mathrm{C}$, Melting point of the bullet $=327^{\circ }\mathrm{C}$ …

Q10.The equation of a particle executing simple harmonic motion is given by $x=\sin \pi \left(t+\frac{1}{3}\right)m$. At $\mathrm{t}=1\mathrm{s}$, the speed of particle will be
(Given : $\pi =3.14$ )

Q11.Three identical charged balls each of charge 2 C are suspended from a common point P by silk threads of 2 m each (as shown in figure). They form an equilateral triangle of side 1 m .

The ratio of net force on a charged ball to the force between any two charged balls will be :

Q12.Two long parallel conductors ${\mathrm{S}}_1$ and ${\mathrm{S}}_2$ are separated by a distance 10 cm and carrying currents of 4A and 2A respectively. The conductors are placed along x-axis in X-Y plane. There is a point P located between the conductors (as shown in figure).

A ch …

Q13.If $\mathrm{L}$, $\mathrm{C}$ and R are the self inductance, capacitance and resistance respectively, which of the following does not have the dimension of time?

Q14.Given below are two statements:

Statement I: A time varying electric field is a source of changing magnetic field and vice-versa. Thus a disturbance in electric or magnetic field creates EM waves.

Statement II: In a material medium. The EM wave travels with speed …

Q15.A convex lens has power P. It is cut into two halves along its principal axis. Further one piece (out of the two halves) is cut into two halves perpendicular to the principal axis (as shown in figure). Choose the incorrect option for the reported pieces.

Q16.If a wave gets refracted into a denser medium, then which of the following is true?

Q17.Given below are two statements:

Statement I: In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit ( ${\mathrm{E}}_1$ ) to higher energy orbit ( ${\mathrm{E}}_2$ ), is given as $\mathrm{hf}={\mathrm{E}}_1-{\mathrm{E}}_2$.

Statement- …

Q18.For a transistor to act as a switch, it must be operated in

Q19.We do not transmit low frequency signal to long distances because
(a) The size of the antenna should be comparable to signal wavelength which is unreal solution for a signal of longer wavelength.
(b) Effective power radiated by a long wavelength baseband signal would be high.
(c) …

Q20.A mass of 10 kg is suspended vertically by a rope of length 5 m from the roof. A force of 30 N is applied at the middle point of rope in horizontal direction. The angle made by upper half of the rope with vertical is $\theta ={\tan }^{-1}\left(\mathrm{x}\times 10^{-1}\right)$. The …

Q21.A rolling wheel of 12 kg is on an inclined plane at position P and connected to a mass of 3 kg through a string of fixed length and pulley as shown in figure. Consider PR as friction free surface.

The velocity of centre of mass of the wheel when it reaches at the bottom Q of the …

Q22.A diatomic gas $(\gamma =1.4)$ does 400 J of work when it is expanded isobarically. The heat given to the gas in the process is ______ J.

Q23.A particle executes simple harmonic motion. Its amplitude is 8 cm and time period is 6 s. The time it will take to travel from its position of maximum displacement to the point corresponding to half of its amplitude, is ______ s.

Q24.A paralle plate capacitor is made up of stair like structure with a palte area A of each stair and that is connected with a wire of length b, as shown in the figure. The capacitance of the arrangement is $\frac{x}{15}\frac{{\epsilon }_{0}A}{b}$. The value of $x$ is ______.

Q25.The current density in a cylindrical wire of radius $r=4.0$ mm is $1.0\times 10^6$ A/m${}^2$. The current through the outer portion of the wire between radial distances $r/2$ and r is $x\pi$ A; where x is ______.

Q26.In the given circuit 'a' is an arbitrary constant. The value of m for which the equivalent circuit resistance is minimum, will be $\sqrt{\frac{x}{2}}$. The value of $x$ is ______.

Q27.A deuteron and a proton moving with equal kinetic energy enter into to a uniform magnetic field at right angle to the field. If $r_d$ and $r_p$ are the radii of their circular paths respectively, then the ratio $\frac{r_d}{r_p}$ will be $\sqrt{x}:1$ where x is ______.

Q28.A metallic rod of length 20 cm is palced in NorthSouth direction and is moved at a constant speed of 20 m/s towards East. The horizontal component of the Earth's magnetic field at that place is $4\times 10^{-3}$ T and the angle of dip is $45^{\circ }$. The emf induced in the rod …

Q29.The cut-off voltage of the diodes (shown in figure) in forward bias is 0.6 V. The current through the resister of $40\Omega$ is ______ mA.

Q1.Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas ?

Q2.Identify the incorrect statement for ${\mathrm{PCl}}_5$ from the following.

Q3.Statement I: Leaching of gold with cyanide ion in absence of air / ${\mathrm{O}}_2$ leads to cyano complex of $\mathrm{Au}(\mathrm{III})$.

Statement II : Zinc is oxidized during the displacement reaction carried out for gold extraction.

In the light of the above statements, cho …

Q4.The correct order of increasing intermolecular hydrogen bond strength is

Q5.The correct order of increasing ionic radii is

Q6.The gas produced by treating an aqueous solution of ammonium chloride with sodium nitrite is

Q7.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : Flourine forms one oxoacid.
Reason R : Flourine has smallest size amongst all halogens and is highly electronegative

In the light of the above statements, choose …

Q8.In 3d series, the metal having the highest ${\mathrm{M}}^{2+}/\mathrm{M}$ standard electrode potential is

Q9.The $f$ orbitals are half and completely filled, respectively in lanthanide ions
(Given: Atomic no. Eu, 63; Sm, 62; Tm, 69; Tb, 65; Yb, 70; Dy, 66)

Q10.Arrange the following coordination compounds in the increasing order of magnetic moments. (Atomic numbers: $\mathrm{Mn}=25;\mathrm{Fe}=26$)
(A) ${\left[{\mathrm{FeF}}_6\right]}^{3-}$
(B) ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$
(C) ${\left[{\mathrm{MnCl}}_6\right]}^{3-}$ (h …

Q11.On the surface of polar stratospheric clouds, hydrolysis of chlorine nitrate gives A and B while its reaction with HCl produces B and $\mathrm{C}.\mathrm{A},\mathrm{B}$ and C are, respectively

Q12.Which of the following is most stable?

Q13.What will be the major product of following sequence of reactions?

Q14.Product 'A' of following sequence of reactions is
Ethylbenzene (Major product)

Q15.Decarboxylation of all six possible forms of diaminobenzoic acids ${\mathrm{C}}_6{\mathrm{H}}_3{\left({\mathrm{NH}}_2\right)}_2\mathrm{COOH}$ yields three products $\mathrm{A},\mathrm{B}$ and C. Three acids give a product 'A', two acids gives a product 'B' and one acid give a …

Q16.Which is true about Buna-N?

Q17.Given below are two statements.

Statments I: Maltose has two $\alpha$-D-glucose units linked at ${\mathrm{C}}_1$ and ${\mathrm{C}}_4$ and is a reducing sugar.

Statement II: Maltose has two monosaccharides: $\alpha$-D-glucose and $\beta$-D-glucose linked at ${\mathrm{C}}_1$ and …

Q18.116 g of a substance upon dissociation reaction, yields 7.5 g of hydrogen, 60 g of oxygen and 48.5 g of carbon. Given that the atomic masses of H, O and C are 1, 16 and 12 respectively. The data agrees with how many formulae of the following?
(A) ${\mathrm{CH}}_3\mathrm{COOH}$
( …

Q19.Consider the following sets of quantum numbers:

The number of correct sets of quantum numbers is ______.

Q20.BeO reacts with HF in presence of ammonia to give [A] which on thermal decomposition produces [B] and ammonium fluoride. Oxidation state of Be in [A] is ____

Q21.When 5 moles of He gas expand isothermally and reversibly at 300 K from 10 litre to 20 litre, the magnitude of the maximum work obtained is ____ J. [nearest integer]
(Given: $\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ and $\log 2=0.3010$)

Q22.A solution containing $2.5\times 10^{-3}\mathrm{kg}$ of a solute dissolved in $75\times 10^{-3}\mathrm{kg}$ of water boils at 373.535 K. The molar mass of the solute is ______ ${\mathrm{g}\mathrm{mol}}^{-1}$. [nearest integer]
(Given: …

Q23.pH value of 0.001 M NaOH solution is ______.

Q24.For the reaction taking place in the cell:
$\mathrm{Pt}(\mathrm{s})|{\mathrm{H}}_2(\mathrm{g})|{\mathrm{H}}^{+}(\mathrm{aq})||{\mathrm{Ag}}^{+}(\mathrm{aq})|\mathrm{Ag}(\mathrm{s})$ ${\mathrm{E}}_{\text{Cell}}^{\circ }=+0.5332\mathrm{V}$.
The value of …

Q25.It has been found that for a chemical reaction with rise in temperature by 9 K the rate constant gets doubled. Assuming a reaction to be occurring at 300 K, the value of activation energy is found to be ______ ${\mathrm{kJ}\mathrm{mol}}^{-1}$. [nearest integer]
(Given $\ln 10=2.3$, …

Q26.If the initial pressure of a gas is 0.03 atm, the mass of the gas adsorbed per gram of the adsorbent is ______ $\times 10^{-2}\mathrm{g}$.

Q27.0.25 g of an organic compound containing chlorine gave 0.40 g of silver chloride in Carius estimation. The percentage of chlorine present in the compound is ______. [in nearest integer]
(Given: Molar mass of Ag is $108{\mathrm{g}\mathrm{mol}}^{-1}$ and that of Cl is …

Q1.The number of points of intersection of $|z-(4+3i)|=2$ and $|z|+|z-4|=6,z\in C$ is :

Q2.Let $f(x)=\left|\begin{array}{ccc}a& -1& 0\\ ax& a& -1\\ a{x}^2& ax& a\end{array}\right|,a\in R$. Then the sum of the squares of all the values of $a$ for which $2f^{\prime }(10)-f^{\prime }(5)+100=0$ is :

Q3.Let for some real numbers $\alpha$ and $\beta$, $a=\alpha -i\beta$. If the system of equations $4ix+(1+i)y=0$ and $8\left(\cos \frac{2\pi }{3}+i\sin \frac{2\pi }{3}\right)x+\bar{a}y=0$ has more than one solution then $\frac{\alpha }{\beta }$ is equal to :

Q4.Let A and B be two $3\times 3$ matrices such that $AB=I$ and $|A|=\frac{1}{8}$ then $|\mathrm{adj}(B\mathrm{adj}(2A))|$ is equal to

Q5.Let $S=2+\frac{6}{7}+\frac{12}{7^2}+\frac{20}{7^3}+\frac{30}{7^4}+\dots$. then $4S$ is equal to

Q6.If $a_1,a_2,a_3\dots$ and $b_1,b_2,b_3\dots$ are A.P. and $a_1=2,a_{10}=3,a_1{b}_1=1=a_{10}{b}_{10}$ then $a_4{b}_4$ is equal to

Q7.If $m$ and $n$ respectively are the number of local maximum and local minimum points of the function $f(x)={\int }_0^{x^2}\frac{t^2-5t+4}{2+e^t}dt$, then the ordered pair $(m,n)$ is equal to

Q8.Let $f$ be a differentiable function in $\left(0,\frac{\pi }{2}\right)$. If ${\int }_{\cos x}^1{t}^{2}f(t)dt={\sin }^{3}x+\cos x-1$, then $\frac{1}{\sqrt{3}}{f}^{\prime }\left(\frac{1}{\sqrt{3}}\right)$ is equal to :

Q9.The integral ${\int }_0^1\frac{1}{7^{\left[\frac{1}{x}\right]}}dx$, where $[.]$ denotes the greatest integer function is equal to

Q10.If the solution curve of the differential equation $\left(\left({\tan }^{-1}y\right)-x\right)dy=\left(1+y^2\right)dx$ passes through the point $(1,0)$ then the abscissa of the point on the curve whose ordinate is $\tan (1)$ is :

Q11.If the equation of the parabola, whose vertex is at $(5,4)$ and the directrix is $3x+y-29=0$, is $x^2+a{y}^2+bxy+cx+dy+k=0$ then
$a+b+c+d+k$ is equal to

Q12.The set of values of $k$ for which the circle $C:4x^2+4y^2-12x+8y+k=0$ lies inside the fourth quadrant and the point $\left(1,-\frac{1}{3}\right)$ lies on or inside the circle $C$ is :

Q13.Let the foot of the perpendicular from the point $(1,2,4)$ on the line $\frac{x+2}{4}=\frac{y-1}{2}=\frac{z+1}{3}$ be $P$. Then the distance of P from the plane $3x+4y+12z+23=0$

Q14.The shortest distance between the lines $\frac{x-3}{2}=\frac{y-2}{3}=\frac{z-1}{-1}$ and $\frac{x+3}{2}=\frac{y-6}{1}=\frac{z-5}{3}$ is :

Q15.Let $\vec{a}$ and $\vec{b}$ be the vectors along the diagonal of a parallelogram having area $2\sqrt{2}$. Let the angle between $\vec{a}$ and $\vec{b}$ be acute. $|\vec{a}|=1$ and $|\vec{a}\cdot \vec{b}|=|\vec{a}\times \vec{b}|$. If …

Q16.The mean and variance of the data 4, 5, 6, 6, 7, 8, $x$, $y$ where $x<y$ are 6, and $\frac{9}{4}$ respectively. Then $x^4+y^2$ is equal to

Q17.If a point $A(x,y)$ lies in the region bounded by the y-axis, straight lines $2y+x=6$ and $5x-6y=30$, then the probability that $y<1$ is :

Q18.The value of $\cot \left({\sum }_{n=1}^{50}{\tan }^{-1}\left(\frac{1}{1+n+n^2}\right)\right)$ is

Q19.$\alpha =\sin 36^{\circ }$ is a root of which of the following equation

Q20.Which of the following statement is a tautology?

Q21.Let $S=\{1,2,3,4,5,6,7,8,9,10\}$. Define $f:S\to S$ as $f(n)=\{\begin{array}{ll}2n,& \text{if }n=1,2,3,4,5\\ 2n-11& \text{if }n=6,7,8,9,10\end{array}$.

Let $g:S\to S$ be a function such that …

Q22.Let $\alpha ,\beta$ be the roots of the equation $x^2-4\lambda x+5=0$ and $\alpha ,\gamma$ be the roots of the equation $x^2-(3\sqrt{2}+2\sqrt{3})x+7+3\lambda \sqrt{3}=0$.

If $\beta +\gamma =3\sqrt{2}$, then $(\alpha +2\beta +\gamma {)}^2$ is equal to :

Q23.Let A be a matrix of order $2\times 2$, whose entries are from the set $\{0,1,2,3,4,5\}$. If the sum of all the entries of A is a prime number $p$, $2<p<8$, then the number of such matrices A is :

Q24.If the sum of the coefficients of all the positive powers of x, in the binomial expansion of ${\left(x^n+\frac{2}{x^5}\right)}^7$ is 939, then the sum of all the possible integral values of n is :

Q25.Let $[\mathrm{t}]$ denote the greatest integer $\le \mathrm{t}$ and $\{\mathrm{t}\}$ denote the fractional part of t. Then integral value of $\alpha$ for which the left hand limit of the function …

Q26.If $\mathrm{y}(\mathrm{x})={\left({\mathrm{x}}^{\mathrm{x}}\right)}^{\mathrm{x}},\mathrm{x}>0$ then $\frac{{\mathrm{d}}^2\mathrm{x}}{{\mathrm{dy}}^2}+20$ at $\mathrm{x}=1$ is equal to:

Q27.If the area of the region $\left\{(\mathrm{x},\mathrm{y}):{\mathrm{x}}^{\frac{2}{3}}+{\mathrm{y}}^{\frac{2}{3}}\le 1,\mathrm{x}+\mathrm{y}\ge 0,\mathrm{y}\ge 0\right\}$ is A, then $\frac{256\mathrm{A}}{\pi }$ is

Q28.Let v be the solution of the differential equation
$\left(1-x^2\right)dy=\left(xy+\left(x^3+2\right)\sqrt{1-x^2}\right)dx,-1<x<1$
and $y(0)=0$ if ${\int }_{-\frac{1}{2}}^{\frac{1}{2}}\sqrt{1-x^2}y(x)dx=k$ then $k^{-1}$ is equal to :

Q29.Let a circle C of radius 5 lie below the x-axis. The line $L_1:4x+3y+2=0$ passes through the centre $P$ of the circle C and intersects the line ${\mathrm{L}}_2:3\mathrm{x}-4\mathrm{y}-11=0$ at Q. The line ${\mathrm{L}}_2$ touches C at the point Q. Then the distance of P fro …

Q30.Let $\mathrm{S}=\left\{{\mathrm{E}}_1,{\mathrm{E}}_2\dots {\mathrm{E}}_8\right\}$ be a sample space of random experiment such that $\mathrm{P}\left({\mathrm{E}}_{\mathrm{n}}\right)=\frac{\mathrm{n}}{36}$ for every $\mathrm{n}=1,2\dots 8$. Then the number of elements in the set …