JEE Main 2022 · 24 Jun 2022 · Shift 1

Q1.The bulk modulus of a liquid is $3\times 10^{10}{\mathrm{Nm}}^{-2}$. The pressure required to reduce the volume of liquid by $2\%$ is :

Q2.Given below are two statements : One is labelled as Assertion (A) and the other is labelled as Reason (R).

Assertion (A) : In an uniform magnetic field, speed and energy remains the same for a moving charged particle.

Reason (R) : Moving charged particle experiences magnetic fo …

Q3.Two identical cells each of emf 1.5 V are connected in parallel across a parallel combination of two resistors each of resistance $20\Omega$. A voltmeter connected in the circuit measures 1.2 V . The internal resistance of each cell is

Q4.Identify the pair of physical quantities which have different dimensions :

Q5.A projectile is projected with velocity of $25\mathrm{m}/\mathrm{s}$ at an angle $\theta$ with the horizontal. After t seconds its inclination with horizontal becomes zero. If R represents horizontal range of the projectile, the value of $\theta$ will be : [use …

Q6.A block of mass 10 kg starts sliding on a surface with an initial velocity of $9.8{\mathrm{ms}}^{-1}$. The coefficient of friction between the surface and bock is 0.5 . The distance covered by the block before coming to rest is : $[$ use …

Q7.A boy ties a stone of mass 100 g to the end of a 2 m long string and whirls it around in a horizontal plane. The string can withstand the maximum tension of 80 N . If the maximum speed with which the stone can revolve is $\frac{\mathrm{K}}{\pi }\mathrm{rev}./\min$. T …

Q8.A vertical electric field of magnitude $4.9\times 10^5\mathrm{N}/\mathrm{C}$ just prevents a water droplet of a mass 0.1 g from falling. The value of charge on the droplet will be : (Given $\mathrm{g}=9.8\mathrm{m}/{\mathrm{s}}^2$ )

Q9.A particle experiences a variable force $\vec{F}=\left(4x\hat{i}+3y^2\hat{j}\right)$ in a horizontal $x-y$ plane. Assume distance in meters and force is newton. If the particle moves from point $(1,2)$ to point $(2,3)$ in the $\mathrm{x}-\mathrm{y}$ plane, the Kin …

Q10.The approximate height from the surface of earth at which the weight of the body becomes $\frac{1}{3}$ of its weight on the surface of earth is : [Radius of earth $\mathrm{R}=6400\mathrm{km}$ and $\sqrt{3}=1.732$ ]

Q11.A resistance of $40\Omega$ is connected to a source of alternating current rated $220\mathrm{V},50\mathrm{Hz}$. Find the time taken by the current to change from its maximum value to rms value :

Q12.The equations of two waves are given by :


These waves are simultaneously passing through a string. The a …

Q13.A plane electromagnetic wave travels in a medium of relative permeability 1.61 and relative permittivity 6.44. If magnitude of magnetic intensity is $4.5\times 10^{-2}{\mathrm{Am}}^{-1}$ at a point, what will be the approximate magnitude of electric field intensity at that point? …

Q14.Choose the correct option from the following options given below :
(A) In the ground state of Rutherford's model electrons are in stable equilibrium. While in Thomson's model electrons always experience a net-force.
(B) An atom has a nearly continuous mass distribution in a Ruthe …

Q15.Nucleus A is having mass number 220 and its binding energy per nucleon is 5.6 MeV. It splits in two fragments 'B' and 'C' of mass numbers 105 and 115. The binding energy of nucleons in 'B' and 'C' is 6.4 MeV per nucleon. The energy Q released per fission will be :

Q16.A baseband signal of 3.5 MHz frequency is modulated with a carrier signal of 3.5 GHz frequency using amplitude modulation method. What should be the minimum size of antenna required to transmit the modulated signal ?

Q17.A Carnot engine whose heat sinks at $27^{\circ }\mathrm{C}$, has an efficiency of $25\%$. By how many degrees should the temperature of the source be changed to increase the efficiency by $100\%$ of the original efficiency ?

Q18.A parallel plate capacitor is formed by two plates each of area $30\pi {\mathrm{cm}}^2$ separated by 1 mm. A material of dielectric strength $3.6\times 10^7{\mathrm{Vm}}^{-1}$ is filled between the plates. If the maximum charge that can be stored on the capacitor without caus …

Q19.The magnetic field at the centre of a circular coil of radius r, due to current I flowing through it, is B. The magnetic field at a point along the axis at a distance $\frac{r}{2}$ from the centre is :

Q20.Two metallic blocks ${\mathrm{M}}_1$ and ${\mathrm{M}}_2$ of same area of cross-section are connected to each other (as shown in figure). If the thermal conductivity of ${\mathrm{M}}_2$ is K then the thermal conductivity of ${\mathrm{M}}_1$ will be : [Assume steady state heat con …

Q21.0.056 kg of Nitrogen is enclosed in a vessel at a temperature of $127^{\circ }\mathrm{C}$. The amount of heat required to double the speed of its molecules is ______ k cal. (Take $\mathrm{R}=2$ cal mole${}^{-1}{\mathrm{K}}^{-1}$ )

Q22.Two identical thin biconvex lenses of focal length 15 cm and refractive index 1.5 are in contact with each other. The space between the lenses is filled with a liquid of refractive index 1.25. The focal length of the combination is ______ cm.

Q23.A transistor is used in common-emitter mode in an amplifier circuit. When a signal of 10 mV is added to the base-emitter voltage, the base current changes by $10\mu \mathrm{A}$ and the collector current changes by 1.5 mA. The load resistance is $5\mathrm{k}\Omega$. The voltag …

Q24.As shown in the figure an inductor of inductance 200 mH is connected to an AC source of emf 220 V and frequency 50 Hz. The instantaneous voltage of the source is 0 V when the peak value of current is $\frac{\sqrt{a}}{\pi }\mathrm{A}$. The value of a is ______.

Q25.Sodium light of wavelengths 650 nm and 655 nm is used to study diffraction at a single slit of aperture 0.5 mm. The distance between the slit and the screen is 2.0 m. The separation between the positions of the first maxima of diffraction pattern obtained in the two cases is ____ …

Q26.When light of frequency twice the threshold frequency is incident on the metal plate, the maximum velocity of emitted electron is $v_1$. When the frequency of incident radiation is increased to five times the threshold value, the maximum velocity of emitted electron becomes $v_2$ …

Q27.From the top of a tower, a ball is thrown vertically upward which reaches the ground in 6 s. A second ball thrown vertically downward from the same position with the same speed reaches the ground in 1.5 s. A third ball released, from the rest from the same location, will reach th …

Q28.A ball of mass 100 g is dropped from a height $h=10$ cm on a platform fixed at the top of vertical spring (as shown in figure). The ball stays on the platform and the platform is depressed by a distance $\frac{h}{2}$. The spring constant is ______ ${\text{Nm}}^{-1}$. (Use …

Q29.In a potentiometer arrangement, a cell gives a balancing point at 75 cm length of wire. This cell is now replaced by another cell of unknown emf. If the ratio of the emf's of two cells respectively is $3:2$, the difference in the balancing length of the potentiometer wire in abov …

Q30.A metre scale is balanced on a knife edge at its centre. When two coins, each of mass 10 g are put one on the top of the other at the 10.0 cm mark the scale is found to be balanced at 40.0 cm mark. The mass of the metre scale is found to be $x\times 10^{-2}$ kg. The value of $x$ …

Q1.If a rocket runs on a fuel (${\mathrm{C}}_{15}{\mathrm{H}}_{30}$) and liquid oxygen, the weight of oxygen required and ${\mathrm{CO}}_2$ released for every litre of fuel respectively are: (Given: density of the fuel is $0.756\mathrm{g}/\mathrm{mL}$)

Q2.Consider the following pairs of electrons
(A) (a) $\mathrm{n}=3,1=1,{\mathrm{m}}_1=1,{\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}$
(b) $\mathrm{n}=3,1=2,{\mathrm{m}}_1=1,{\mathrm{m}}_{\mathrm{s}}=+\frac{1}{2}$
(B) (a) …

Q3.For a reaction at equilibrium
$\mathrm{A}(\mathrm{g})\rightleftharpoons \mathrm{B}(\mathrm{g})+\frac{1}{2}\mathrm{C}(\mathrm{g})$
the relation between dissociation constant (K), degree of dissociation ($\alpha$) and equilibrium pressure (p) is given by :

Q4.Given below are two statements :

Statement I : Emulsions of oil in water are unstable and sometimes they separate into two layers on standing.

Statement II :For stabilisation of an emulsion, excess of electrolyte is added.

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

Q5.Given below are the oxides:
${\mathrm{Na}}_2\mathrm{O},{\mathrm{As}}_2{\mathrm{O}}_3,{\mathrm{N}}_2\mathrm{O},\mathrm{NO}$ and ${\mathrm{Cl}}_2{\mathrm{O}}_7$
Number of amphoteric oxides is:

Q6.The highest industrial consumption of molecular hydrogen is to produce compounds of element:

Q7.Which of the following statements are correct?
(A) Both LiCl and ${\mathrm{MgCl}}_2$ are soluble in ethanol.
(B) The oxides ${\mathrm{Li}}_2\mathrm{O}$ and MgO combine with excess of oxygen to give superoxide.
(C) LiF is less soluble in water than other alkali metal fluoride …

Q8.Identify the correct statement for ${\mathrm{B}}_2{\mathrm{H}}_6$ from those given below.
(A) In ${\mathrm{B}}_2{\mathrm{H}}_6$, all B-H bonds are equivalent.
(B) In ${\mathrm{B}}_2{\mathrm{H}}_6$ there are four 3-centre-2-electron bonds.
(C) …

Q9.The most stable trihalide of nitrogen is:

Q10.Which one of the following elemental forms is not present in the enamel of the teeth?

Q11.In the given reactions sequence, the major product 'C' is:

Q12.Two statements are given below:

Statement I: The melting point of monocarboxylic acid with even number of carbon atoms is higher than that of with odd number of carbon atoms acid immediately below and above it in the series.

Statement II: The solubility of monocarboxylic acids …

Q13.Which of the following is an example of conjugated diketone?

Q14.The major product of the above reaction is

Q15.Which of the following is an example of polyester?

Q16.A polysaccharide 'X' on boiling with dil H₂SO₄ at 393 K under 2-3 atm pressure yields 'Y'. 'Y' on treatment with bromine water gives gluconic acid. 'X' contains β-glycosidic linkages only. Compound 'X' is:

Q17.Which of the following is not a broad spectrum antibiotic?

Q18.During the qualitative analysis of salt with cation y²⁺, addition of a reagent (X) to alkaline solution of the salt gives a bright red precipitate. The reagent (X) and the cation (y²⁺) present respectively are:

Q19.Atoms of element X form hcp lattice and those of element Y occupy 2/3 of its tetrahedral voids. The percentage of element X in the lattice is ______ (Nearest integer)

Q20.2O₃(g) ⇌ 3O₂(g)

At 300 K, ozone is fifty percent dissociated. The standard free energy change at this temperature and 1 atm pressure is (-) ______ J mol⁻¹ (Nearest integer)
[Given: ln 1.35 = 0.3 and R = 8.3 J K⁻¹ mol⁻¹]

Q21.The osmotic pressure of blood is 7.47 bar at 300 K.

To inject glucose to a patient intravenously, it has to be isotonic with blood. The concentration of glucose solution in g L⁻¹ is ______ (Molar mass of glucose = 180 g mol⁻¹, R = 0.083 L bar K⁻¹ mol⁻¹) (Nearest integer)

Q22.The cell potential for the following cell
Pt|H₂(g)|H⁺(aq)||Cu²⁺(0.01 M)|Cu(s)
is 0.576 V at 298 K. The pH of the solution is ______. (Nearest integer)

Q23.The rate constants for decomposition of acetaldehyde have been measured over the temperature range 700-1000 K. The data has been analysed by plotting ln k vs 10³/T graph. The value of activation energy for the reaction is ______ kJ mol⁻¹. (Nearest integer) (Given: R = 8.31 J K⁻¹ …

Q24.The difference in oxidation state of chromium in chromate and dichromate salts is ______

Q25.In the cobalt-carbonyl complex: $\left[{\mathrm{Co}}_2(\mathrm{CO}{)}_8\right]$, number of $\mathrm{Co}-\mathrm{Co}$ bonds is "X" and terminal CO ligands is "Y". $\mathrm{X}+\mathrm{Y}=$ ______

Q26.Number of electrophilic centre in the given compound is ______

Q27.The major product 'A' of the following reaction has ______ ${\mathrm{sp}}^2$ hybridized carbon atoms.

2,7-dimethylocta-2,6-diene $\stackrel{{\mathrm{H}}^{+}}{\to }$ A (major product)

Q1.Let $\mathrm{A}=\{\mathrm{z}\in \mathrm{C}:1\le |\mathrm{z}-(1+\mathrm{i})|\le 2\}$ and $\mathrm{B}=\{\mathrm{z}\in \mathrm{A}:|\mathrm{z}-(1-\mathrm{i})|=1\}$. Then, $\mathrm{B}:$

Q2.The remainder when $3^{2022}$ is divided by 5 is

Q3.The surface area of a balloon of spherical shape being inflated, increases at a constant rate. If initially, the radius of balloon is 3 units and after 5 seconds, it becomes 7 units, then its radius after 9 seconds is :

Q4.Bag A contains 2 white, 1 black and 3 red balls and bag B contains 3 black, 2 red and n white balls. One bag is chosen at random and 2 balls drawn from it at random, are found to be 1 red and 1 black. If the probability that both balls come from Bag A is $\frac{6}{11}$, then n …

Q5.Let $x^2+y^2+Ax+By+C=0$ be a circle passing through $(0,6)$ and touching the parabola $\mathrm{y}={\mathrm{x}}^2$ at (2, 4). Then $\mathrm{A}+\mathrm{C}$ is equal to

Q6.The number of values of $\alpha$ for which the system of equations :
$\mathrm{x}+\mathrm{y}+\mathrm{z}=\alpha$
$\alpha \mathrm{x}+2\alpha \mathrm{y}+3\mathrm{z}=-1$
$x+3\alpha y+5z=4$
is inconsistent, is

Q7.If the sum of the squares of the reciprocals of the roots $\alpha$ and $\beta$ of the equation $3x^2+\lambda x-1=0$ is 15, then $6{\left({\alpha }^3+{\beta }^3\right)}^2$ is equal to :

Q8.The set of all values of k for which ${\left({\tan }^{-1}\mathrm{x}\right)}^3+{\left({\cot }^{-1}\mathrm{x}\right)}^3=\mathrm{k}{\pi }^3,\mathrm{x}\in \mathrm{R}$, is the interval :

Q9.Let $S=\{\sqrt{n}:1\le n\le 50$ and $n$ is odd $\}$

Let $\mathrm{a}\in \mathrm{S}$ and $\mathrm{A}=\left[\begin{array}{ccc}1& 0& \mathrm{a}\\ -1& 1& 0\\ -\mathrm{a}& 0& 1\end{array}\right]$
If …

Q10.$f(x)=4{\log }_e(x-1)-2x^2+4x+5,x>1$, which one of the following is NOT correct ?

Q11.the tangent at the point $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ on the curve $\mathrm{y}={\mathrm{x}}^3+3{\mathrm{x}}^2+5$ passes through the origin, then $\left({\mathrm{x}}_1,{\mathrm{y}}_1\right)$ does NOT lie on the curve :

Q12.The sum of absolute maximum and absolute minimum values of the function $f(x)=\left|2x^2+3x-2\right|+\sin x\cos x$ in the interval $[0,1]$ is :

Q13.If ${\left\{{\mathrm{a}}_{\mathrm{i}}\right\}}_{\mathrm{i}=1}^{\mathrm{n}}$ where n is an even integer, is an arithmetic progression with common difference 1, and …

Q14.If $\mathrm{x}=\mathrm{x}(\mathrm{y})$ is the solution of the differential equation $y\frac{dx}{dy}=2x+y^3(y+1)e^y,x(1)=0$; then $x(e)$ is equal to :

Q15.Let $\lambda x-2y=\mu$ be a tangent to the hyperbola $a^2{x}^2-y^2=b^2$. Then ${\left(\frac{\lambda }{a}\right)}^2-{\left(\frac{\mu }{b}\right)}^2$ is equal to:

Q16.Let $\hat{a},\hat{b}$ be unit vectors. If $\vec{c}$ be a vector such that the angle between $\hat{\mathrm{a}}$ and $\overrightarrow{\mathrm{c}}$ is $\frac{\pi }{12}$, and …

Q17.If a random variable X follows the Binomial distribution $\mathrm{B}(33,\mathrm{p})$ such that $3\mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)$, then the value of …

Q18.Let
$\mathrm{S}=\left\{\theta \in [-\pi ,\pi ]-\left\{\pm \frac{\pi }{2}\right\}:\sin \theta \tan \theta +\tan \theta =\sin 2\theta \right\}$.
If $\mathrm{T}={\sum }_{\theta \in \mathrm{S}}\cos 2\theta$, then $\mathrm{T}+\mathrm{n}(\mathrm{S})$ is equal

Q19.The number of choices of $\Delta \in \{\wedge ,\vee ,\Rightarrow ,\iff \}$, such that $(\mathrm{p}\Delta \mathrm{q})\Rightarrow ((\mathrm{p}\Delta \sim \mathrm{q})\vee ((\sim \mathrm{p})\Delta \mathrm{q}))$ is a tautology, is

Q20.The number of one-one function $\mathrm{f}:\{\mathrm{a},\mathrm{b},\mathrm{c},\mathrm{d}\}\to \{0,1,2,\dots ,10\}$ such that $2\mathrm{f}(\mathrm{a})-\mathrm{f}(\mathrm{b})+3\mathrm{f}(\mathrm{c})+\mathrm{f}(\mathrm{d})=0$ is

Q21.In an examination, there are 5 multiple choice questions with 3 choices, out of which exactly one is correct There are 3 marks for each correct answer, -2 marks for each wrong answer and 0 mark if the question is not attempted. Then, the number of ways a student appearing in the …

Q22.Let $\mathrm{A}\left(\frac{3}{\sqrt{\mathrm{a}}},\sqrt{\mathrm{a}}\right)\mathrm{a}>0$, be a fixed point in the $xy$-plane. The image of $A$ in $y$-axis be $B$ and the
image of B in x -axis be C . If $\mathrm{D}(3\cos \theta ,a\sin \theta )$ is a point in the four …

Q23.Let a line having direction ratios $1,-4,2$ intersect the lines $\frac{x-7}{3}=\frac{y-1}{-1}=\frac{z+2}{1}$ and $\frac{x}{2}=\frac{y-7}{3}=\frac{z}{1}$ at the point A and B. Then $(\mathrm{AB}{)}^2$ is equal to ______.

Q24.The number of points where the function
$f(x)=\{\begin{array}{ccr}\left|2x^2-3x-7\right|& \text{ if }& x\le -1\\ \left[4x^2-1\right]& \text{ if }& -1<x<1\\ |x+1|+|x-2|& \text{ if }& x\ge 1\end{array}$
$[\mathrm{t}]$ denotes the greatest intege …

Q25.Let $f(\theta )=\sin \theta +{\int }_{-\pi /2}^{\pi /2}(\sin \theta +t\cos \theta )f(t)dt$. Then the value of $\left|{\int }_0^{\pi /2}f(\theta )d\theta \right|$ is ______.

Q26.Let $\underset{0\le x\le 2}{\mathrm{Max}}\left\{\frac{9-x^2}{5-x}\right\}=\alpha$ and $\underset{0\le x\le 2}{\mathrm{Min}}\left\{\frac{9-x^2}{5-x}\right\}=\beta$

If …

Q27.If two tangents drawn from a point $(\alpha ,\beta )$ lying on the ellipse $25x^2+4y^2=1$ to the parabola $y^2=4x$
are such that the slope of one tangent is four times the other, then the value of
$(10\alpha +5{)}^2+{\left(16{\beta }^2+50\right)}^2$ equals ______.

Q28.Let S be the region bounded by the curves $\mathrm{y}={\mathrm{x}}^3$ and $y^2=x$. The curve $y=2|x|$ divides $S$ into two regions of areas $R_1$ and $R_2$.

If max $\left\{R_1,R_2\right\}=R_2$, then $\frac{R_2}{R_1}$ is equal to ______.

Q29.If the shortest distance between the line
$\overrightarrow{\mathrm{r}}=(-\hat{\mathrm{i}}+3\mathrm{k})+\lambda (\hat{\mathrm{i}}-\mathrm{a}\hat{\mathrm{j}})$ and
$\overrightarrow{\mathrm{r}}=(-\hat{\mathrm{j}}+2\mathrm{k})+\mu (\hat{\mathrm{i}}-\hat{\mathrm{j}}+\mathrm{k})$ …