JEE Main 2022 · 26 Jun 2022 · Shift 1

Q1.An expression for a dimensionless quantity P is given by $\mathrm{P}=\frac{\alpha }{\beta }{\log }_{\mathrm{e}}\left(\frac{\mathrm{kt}}{\beta \mathrm{x}}\right)$; where $\alpha$ and $\beta$ are constants, x is distance; k is Boltzmann constant and $t$ is the temperature. The …

Q2.A person is standing in an elevator. In which situation, he experiences weight loss ?

Q3.An object is thrown vertically upwards. At its maximum height, which of the following quantity becomes zero ?

Q4.A ball is released from rest from point P of a smooth semi-spherical vessel as shown in figure. The ratio of the centripetal force and normal reaction on the ball at point Q is A while angular position of point Q is $\alpha$ with respect to point P. Which of the following graph …

Q5.A thin circular ring of mass $M$ and radius $R$ is rotating with a constant angular velocity $2{\mathrm{rads}}^{-1}$ in a horizontal plane about an axis vertical to its plane and passing through the center of the ring. If two objects each of mass $m$ be attached gently to …

Q6.The variation of acceleration due to gravity (g) with distance ( $r$ ) from the center of the earth is correctly represented by : (Given $\mathrm{R}=$ radius of earth)

Q7.The efficiency of a Carnot's engine, working between steam point and ice point, will be :

Q8.Time period of a simple pendulum in a stationary lift is ' T '. If the lift accelerates with $\frac{\mathrm{g}}{6}$ vertically upwards then the time period will be :
(where $\mathrm{g}=$ acceleration due to gravity)

Q9.A thermally insulated vessel contains an ideal gas of molecular mass M and ratio of specific heats 1.4. Vessel is moving with speed v and is suddenly brought to rest. Assuming no heat is lost to the surrounding and vessel temperature of the gas increases by : ($\mathrm{R}=$ uni …

Q10.Two capacitors having capacitance ${\mathrm{C}}_1$ and ${\mathrm{C}}_2$ respectively are connected as shown in figure. Initially, capacitor ${\mathrm{C}}_1$ is charged to a potential difference V volt by a battery. The battery is then removed and the charged capacitor …

Q11.Assertion (A) : Non-polar amterials do not have my permanent dipole moment.

Reason (R) : When an non-polar material is placed in a electric field. the centre of the positive charge distribution of it's individual atom or molecule coinsides with the centre of the negative charge …

Q12.The magnetic flux through a coil perpendicular to its plane is varying according to the relation $\varphi =\left(5t^3+4t^2+2t-5\right)$ Weber. If the resistance of the coil is 5 ohm, then the induced current through the coil at $t=2\sec$ will be:

Q13.An aluminium wire is stretched to make its length, 0.4% larger. Then percentage change in resistance is:

Q14.A proton and an alpha particle of the same velocity enter in a uniform magnetic field which is acting perpendicular to their direction of motion. The ratio of the circular paths described by the alpha particle and proton is:

Q15.If electric field intensity of a uniform plane electro magnetic wave is given as $\mathrm{E}=-301.6\sin (\mathrm{kz}-\omega \mathrm{t}){\hat{\mathrm{a}}}_{\mathrm{x}}+452.4\sin (\mathrm{kz}-\omega \mathrm{t}){\hat{a}}_y\frac{V}{m}$

Then, magnetic intensity H of this wave in …

Q16.In free space, an electromagnetic wave of 3 GHz frequency strikes over the edge of an object of size $\frac{\lambda }{100}$, where $\lambda$ is the wavelength of the wave in free space. The phenomenon, which happens there will be:

Q17.An electron with speed v and a photon with speed c have the same de-Broglie wavelength. If the kinetic energy and momentum of electron are ${\mathrm{E}}_{\mathrm{e}}$ and ${\mathrm{p}}_{\mathrm{e}}$ and that of photon are ${\mathrm{E}}_{\mathrm{ph}}$ and ${\mathrm{p}}_{\mathrm{ph}}$ resp …

Q18.How many alpha and beta particles are emitted when Uranium ${}_{92}{\mathrm{U}}^{238}$ decays to lead ${}_{82}{\mathrm{Pb}}^{206}$ ?

Q19.The I-V characteristics of a p-n junction diode in forward bias is shown in the figure. The ratio of dynamic resistance, corresponding to forward bias voltages of 2 V and 4 V respectively, is :

Q20.Choose the correct statement for amplitude modulation:

Q21.A fighter jet is flying horizontally at a certain altitude with a speed of 200 m/s. When it passes directly overhead an anti-aircraft gun, bullet is fired from the gun, at an angle $\theta$ with the horizontal, to hit the jet. If the bullet speed is 400 m/s, the value of $\theta$ …

Q22.A ball of mass 0.5 kg is dropped from the height of 10 m. The height, at which the magnitude of velocity becomes equal to the magnitude of acceleration due to gravity, is ____ m. (Use g = 10 m/s²).

Q23.The elastic behaviour of material for linear stress and linear strain, is shown in the figure. The energy density for a linear strain of $5\times 10^{-4}$ is ____ kJ/m³. Assume that material is elastic upto the linear strain of $5\times 10^{-4}$.

Q24.The elongation of a wire on the surface of the earth is $10^{-4}$ m. The same wire of same dimensions is elongated by $6\times 10^{-5}$ m on another planet. The acceleration due to gravity on the planet will be ____ m/s². (Take acceleration due to gravity on the surface of earth …

Q25.A $10\Omega ,20\mathrm{mH}$ coil carrying constant current is connected to a battery of 20 V through a switch is opened current becomes zero in $100\mu \mathrm{s}$. The average emf induced in the coil is ____ V.

Q26.A light ray is incident, at an incident angle ${\theta }_1$, on the system of two plane mirrors ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ having an inclination angle $75^{\circ }$ between them (as shown in figure). After reflecting from mirror ${\mathrm{M}}_1$ it gets reflect …

Q27.In a vernier callipers, each cm on the main scale is divided into 20 equal parts. If tenth vernier scale division coincides with nineth main scale division. Then the value of vernier constant will be ____ $\times 10^{-2}\mathrm{mm}$.

Q28.As per the given circuit, the value of current through the battery will be ____ A.

Q29.A $110\mathrm{V},50\mathrm{Hz},\mathrm{AC}$ source is connected in the circuit (as shown in figure). The current through the resistance $55\Omega$, at resonance in the circuit, will be ____ A.

Q30.An ideal fluid of density $800{\mathrm{kgm}}^{-3}$, flows smoothly through a bent pipe (as shown in figure) that tapers in cross-sectional area from a to $\frac{\mathrm{a}}{2}$. The pressure difference between the wide and narrow sections of pipe is 4100 Pa. At wider section, …

Q1.A commercially sold conc. HCl is $35\%\mathrm{HCl}$ by mass. If the density of this commercial acid is 1.46 $\mathrm{g}/\mathrm{mL}$, the molarity of this solution is :
(Atomic mass : $\mathrm{Cl}=35.5\mathrm{amu},\mathrm{H}=1\mathrm{amu}$ )

Q2.An evacuated glass vessel weighs 40.0 g when empty, 135.0 g when filled with a liquid of density $0.95\mathrm{g}{\mathrm{mL}}^{-1}$ and 40.5 g when filled with an ideal gas at 0.82 atm at 250 K . The molar mass of the gas in $\mathrm{g}{\mathrm{mol}}^{-1}$ is :
(Given : …

Q3.If the radius of the $3^{\text{rd }}$ Bohr's orbit of hydrogen atom is $r_3$ and the radius of $4^{\text{th }}$ Bohr's orbit is $r_4$. Then :

Q4.Consider the ions/molecule
${\mathrm{O}}_2^{+},{\mathrm{O}}_2,{\mathrm{O}}_2^{-},{\mathrm{O}}_2^{2-}$
For increasing bond order the correct option is :

Q5.The ${\left(\frac{\partial E}{\partial T}\right)}_P$ of four different types of half cells are as follows (in $\mathrm{V}{\mathrm{K}}^{-1}$): A $=1\times 10^{-4}$, B $=2\times 10^{-4}$, C $=0.1\times 10^{-4}$, D $=0.2\times 10^{-4}$ (where E is the electromotive force). Which of the above ha …

Q6.Choose the correct stability order of group 13 elements in their +1 oxidation state.

Q7.Given below are two statements :

Statement I : According to the Ellingham diagram, any metal oxide with higher $\Delta {\mathrm{G}}^{\circ }$ is more stable than the one with lower $\Delta {\mathrm{G}}^{\circ }$.
Statement II : The metal involved in the formation of oxide placed l …

Q8.Consider the following reaction :


The dihedral angle in product $\mathbf{A}$ in its solid phase at 110 K is :

Q9.The correct order of melting point is :

Q10.The correct order of melting points of hydrides of group 16 elements is :

Q11.Consider the following reaction :

A + alkali $\to$ B (Major Product)
If B is an oxoacid of phosphorus with no $\mathrm{P}-\mathrm{H}$ bond, then A is :

Q12.Polar stratospheric clouds facilitate the formation of :

Q13.Given below are two statements :

Statement I: In 'Lassaigne's Test, when both nitrogen and sulphur are present in an organic compound, sodium thiocyanate is formed.
Statement II : If both nitrogen and sulphur are present in an organic compound, then the excess of sodium used in …

Q14.$({\mathrm{C}}_7{\mathrm{H}}_5{\mathrm{O}}_2{)}_2\stackrel{\mathrm{h}\nu }{\to }[\mathrm{X}]+2{\dot{\mathrm{C}}}_6{\mathrm{H}}_5+2{\mathrm{CO}}_2$

Consider the above reaction and identify the intermediate ' X '

Q15.Consider the above reaction sequence and identify the product $\mathbf{B}$.

Q16.Which will have the highest enol content?

Q17.Among the following structures, which will show the most stable enamine formation?
(Where Me is $-{\mathrm{CH}}_3$ )

Q18.Which of the following sets are correct regarding polymer ?
(A) Copolymer : Buna-S
(B) Condensation polymer : Nylon-6,6
(C) Fibre : Nylon-6,6
(D) Thermosetting polymer : Terylene
(E) Homopolymer : Buna-N

Choose the correct answer from given options below:

Q19.A chemical which stimulates the secretion of pepsin is :

Q20.Which statement is not true with respect to nitrate ion test?

Q21.For complete combustion of methanol
${\mathrm{CH}}_3\mathrm{OH}(\mathrm{l})+\frac{3}{2}{\mathrm{O}}_2(\mathrm{g})\to {\mathrm{CO}}_2(\mathrm{g})+2{\mathrm{H}}_2\mathrm{O}(\mathrm{l})$
the amount of heat produced as measured by bomb calorimeter is …

Q22.A 0.5 percent solution of potassium chloride was found to freeze at $-0.24^{\circ }\mathrm{C}$. The percentage dissociation of potassium chloride is ____. (Nearest integer)
(Molal depression constant for water is 1.80 K kg ${\mathrm{mol}}^{-1}$ and molar mass of KCl is …

Q23.50 mL of $0.1\mathrm{M}{\mathrm{CH}}_3\mathrm{COOH}$ is being titrated against 0.1 M NaOH . When 25 mL of NaOH has been added, the pH of the solution will be
____ $\times 10^{-2}$. (Nearest integer)
(Given : …

Q24.A flask is filled with equal moles of A and B. The half lives of A and B are 100 s and 50 s respectively and are independent of the initial concentration. The time required for the concentration of A to be four times that of B is
____ s.
(Given $:\ln 2=0.693$ )

Q25.2.0 g of ${\mathrm{H}}_2$ gas is adsorbed on 2.5 g of platinum powder at 300 K and 1 bar pressure. The volume of the gas adsorbed per gram of the adsorbent is
____ mL.
(Given : $\mathrm{R}=0.083\mathrm{L}$ bar ${\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$ )

Q26.The spin-only magnetic moment value of the most basic oxide of vanadium among ${\mathrm{V}}_2{\mathrm{O}}_3$, ${\mathrm{V}}_2{\mathrm{O}}_4$ and ${\mathrm{V}}_2{\mathrm{O}}_5$ is ______ B.M. (Nearest Integer)

Q27.The spin-only magnetic moment value of an octahedral complex among ${\mathrm{CoCl}}_3\cdot 4{\mathrm{NH}}_3$, ${\mathrm{NiCl}}_2\cdot 6{\mathrm{H}}_2\mathrm{O}$ and ${\mathrm{PtCl}}_4\cdot 2\mathrm{HCl}$, which upon reaction with excess of ${\mathrm{AgNO}}_3$ gives 2 moles of AgC …

Q28.On complete combustion 0.30 g of an organic compound gave 0.20 g of carbon dioxide and 0.10 g of water. The percentage of carbon in the given organic compound is ______ (Nearest Integer)

Q29.Compound 'P' on nitration with dil. ${\mathrm{HNO}}_3$ yields two isomers (A) and (B). These isomers can be separated by steam distillation. Isomers (A) and (B) show the intramolecular and intermolecular hydrogen bonding respectively. Compound (P) on reaction with conc. …

Q30.The number of oxygens present in a nucleotide formed from a base, that is present only in RNA is ______.

Q1.Let $f(x)=\frac{x-1}{x+1},x\in R-\{0,-1,1)$. If $f^{n+1}(x)=f\left(f^n(x)\right)$ for all $\mathrm{n}\in \mathrm{N}$, then ${\mathrm{f}}^6(6)+{\mathrm{f}}^7(7)$ is equal to:

Q2.Let $\mathrm{A}=\left\{\mathrm{z}\in \mathrm{C}:\left|\frac{\mathrm{z}+1}{\mathrm{z}-1}<1\right|\right\}$
and $B=\left\{z\in C:\arg \left(\frac{z-1}{z+1}\right)=\frac{2\pi }{3}\right\}$.
Then $\mathrm{A}\cap \mathrm{B}$ is :

Q3.Let A be a $3\times 3$ invertible matrix. If $|\mathrm{adj}(24\mathrm{A})|=|\mathrm{adj}(3\mathrm{adj}(2\mathrm{A}))|$, then $|\mathrm{A}{|}^2$ is equal to :

Q4.The ordered pair (a, b), for which the system of linear equations
$3\mathrm{x}-2\mathrm{y}+\mathrm{z}=\mathrm{b}$
$5\mathrm{x}-8\mathrm{y}+9\mathrm{z}=3$
$2\mathrm{x}+\mathrm{y}+\mathrm{az}=-1$
has no solution, is :

Q5.The remainder when $(2021{)}^{2023}$ is divided by 7 is :

Q6.${\lim }_{x\to \frac{1}{\sqrt{2}}}\frac{\sin \left({\cos }^{-1}x\right)-x}{1-\tan \left({\cos }^{-1}x\right)}$ is equal to :

Q7.Let $\mathrm{f},\mathrm{g}:\mathrm{R}\to \mathrm{R}$ be two real valued functions defined as $f(x)=\{\begin{array}{cc}-|x+3|& ,x<0\\ e^x& ,x\ge 0\end{array}$ and …

Q8.The sum of the absolute minimum and the absolute maximum values of the function $f(x)=\left|3x-x^2+2\right|-x$ in the interval $[-1,2]$ is :

Q9.Let S be the set of all the natural numbers, for which the line $\frac{\mathrm{x}}{\mathrm{a}}+\frac{\mathrm{y}}{\mathrm{b}}=2$ is a tangent to the curve ${\left(\frac{\mathrm{x}}{\mathrm{a}}\right)}^{\mathrm{n}}+{\left(\frac{\mathrm{y}}{\mathrm{b}}\right)}^{\mathrm{n}}=2$ at the …

Q10.Let R be the point $(3,7)$ and let P and Q be two points on the line $\mathrm{x}+\mathrm{y}=5$ such that PQR is an equilateral triangle. Then the area of $△\mathrm{PQR}$ is :

Q11.Let C be a circle passing through the points $\mathrm{A}(2,-1)$ and $\mathrm{B}(3,4)$. The line segment AB is not a diameter of C . If r is the radius of C and its centre lies on the circle $(x-5{)}^2+(y-1{)}^2=\frac{13}{2}$, then $r^2$ is equal to :

Q12.Let the normal at the point P on the parabola $y^2=6x$ pass through the point $(5,-8)$. If the tangent at P to the parabola intersects its directrix at the point Q, then the ordinate of the point Q is:

Q13.If the two lines $l_1:\frac{x-2}{3}=\frac{y+1}{-2},z=2$ and $l_2:\frac{x-1}{1}=\frac{2y+3}{\alpha }=\frac{z+5}{2}$ perpendicular, then an angle between the lines $l_2$ and $l_3:\frac{1-x}{3}=\frac{2y-1}{-4}=\frac{z}{4}$ is:

Q14.Let the plane $2x+3y+z+20=0$ be rotated through a right angle about its line of intersection with the plane $x-3y+5z=8$. If the mirror image of the point $\left(2,-\frac{1}{2},2\right)$ in the rotated plane is $B(a,b,c)$, then:

Q15.If $\vec{a}\cdot \vec{b}=1,\vec{b}\cdot \vec{c}=2$ and $\vec{c}\cdot \vec{a}=3$, then the value of $[\vec{a}\times (\vec{b}\times \vec{c}),\vec{b}\times (\vec{c}\times \vec{a}),\vec{c}\times (\vec{b}\times \vec{a})]$ is:

Q16.Let a biased coin be tossed 5 times. If the probability of getting 4 heads is equal to the probability of getting 5 heads, then the probability of getting atmost two heads is:

Q17.The mean of the numbers $a,b,8,5,10$ is 6 and their variance is 6.8. If M is the mean deviation of the numbers about the mean, then 25M is equal to:

Q18.Let $f(x)=2{\cos }^{-1}x+4{\cot }^{-1}x-3x^2-2x+10,x\in [-1,1]$. If $[a,b]$ is the range of the function then $4a-b$ is equal to:

Q19.Let $\Delta ,\nabla \in \{\wedge ,\vee \}$ be such that $p\nabla q\Rightarrow ((p\Delta q)\nabla r)$ is a tautology.

Then $(p\nabla q)\Delta r$ is logically equivalent to:

Q20.The sum of the cubes of all the roots of the equation $x^4-3x^3-2x^2+3x+1=10$ is ______.

Q21.There are ten boys $B_1,B_2,\dots ,B_{10}$ and five girls $G_1,G_2,\dots ,G_5$ in a class. Then the number of ways of forming a group consisting of three boys and three girls, if both $B_1$ and $B_2$ together should not be the members of a group, is __ …

Q22.Let the common tangents to the curves $4(x^2+y^2)=9$ and $y^2=4x$ intersect at the point Q. Let an ellipse, centered at the origin O, has lengths of semi-minor and semi-major axes equal to OQ and 6, respectively. If e and $l$ respectively denote the eccentricity and t …

Q23.Let $f(x)=\max \{|x+1|,|x+2|,\dots ,|x+5|\}$. Then ${\int }_{-6}^{0}f(x)dx$ is equal to ______.

Q24.Let the solution curve $y=y(x)$ of the differential equation $(4+x^2)dy-2x(x^2+3y+4)dx=0$ pass through the origin. Then $y(2)$ is equal to ____.

Q25.If ${\sin }^2(10^{\circ })\sin (20^{\circ })\sin (40^{\circ })\sin (50^{\circ })\sin (70^{\circ })=\alpha -\frac{1}{16}\sin (10^{\circ })$, then $16+{\alpha }^{-1}$ is equal to ____.

Q26.Let $A=\{n\in \mathbb{N}:\text{H.C.F.}(n,45)=1\}$ and $B=\{2k:k\in \{1,2,\dots ,100\}\}$. Then the sum of all the elements of $A\cap B$ is ____.

Q27.The value of the integral $\frac{48}{{\pi }^4}{\int }_0^{\pi }\left(\frac{3\pi x^2}{2}-x^3\right)\frac{\sin x}{1+{\cos }^{2}x}dx$ is equal to ____.

Q28.Let $A={\sum }_{i=1}^{10}{\sum }_{j=1}^{10}\min \{i,j\}$ and $B={\sum }_{i=1}^{10}{\sum }_{j=1}^{10}\max \{i,j\}$. Then $A+B$ is equal to ____.

Q29.Let $S=(0,2\pi )-\left\{\frac{\pi }{2},\frac{3\pi }{4},\frac{3\pi }{2},\frac{7\pi }{4}\right\}$. Let $y=y(x)$, $x\in S$, be the solution curve of the differential equation $\frac{dy}{dx}=\frac{1}{1+\sin 2x}$, $y\left(\frac{\pi }{4}\right)=\frac{1}{2}$. If the sum of absc …