JEE Main 2022 · 27 Jun 2022 · Shift 1

Q1.A projectile is launched at an angle '$\alpha$' with the horizontal with a velocity $20{\mathrm{ms}}^{-1}$. After 10 s, its inclination with horizontal is '$\beta$'. The value of $\tan \beta$ will be : $\left(\mathrm{g}=10{\mathrm{ms}}^{-2}\right)$

Q2.A girl standing on road holds her umbrella at $45^{\circ }$ with the vertical to keep the rain away. If she starts running without umbrella with a speed of $15\sqrt{2}km{h}^{-1}$, the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl …

Q3.A sliver wire has mass $(0.6\pm 0.006)\mathrm{g}$, radius $(0.5\pm 0.005)\mathrm{mm}$ and length $(4\pm 0.04)\mathrm{cm}$. The maximum percentage error in the measurement of its density will be :

Q4.A system of two blocks of masses $\mathrm{m}=2\mathrm{kg}$ and $\mathrm{M}=8\mathrm{kg}$ is placed on a smooth table as shown in figure. The coefficient of static friction between two blocks is 0.5. The maximum horizontal force F that can be applied to the block of mass M …

Q5.Two blocks of masses 10 kg and 30 kg are placed on the same straight line with coordinates $(0,0)\mathrm{cm}$ and ( $\mathrm{x},0$ ) cm respectively. The block of 10 kg is moved on the same line through a distance of 6 cm towards the other block. The distance through which …

Q6.A $72\Omega$ galvanometer is shunted by a resistance of $8\Omega$. The percentage of the total current which passes through the galvanometer is :

Q7.Given below are two statements :
Statement I: The law of gravitation holds good for any pair of bodies in the universe.
Statement II : The weight of any person becomes zero when the person is at the centre of the earth.
In the light of the above statements, choose the correct ans …

Q8.What percentage of kinetic energy of a moving particle is transferred to a stationary particle when it strikes the stationary particle of 5 times its mass? (Assume the collision to be head-on elastic collision)

Q9.The velocity of a small ball of mass ' $m$ ' and density ${\mathrm{d}}_1$, when dropped in a container filled with glycerine, becomes constant after some time. If the density of glycerine is ${\mathrm{d}}_2$, then the viscous force acting on the ball, will be :

Q10.The susceptibility of a paramagnetic material is 99. The permeability of the material in $\mathrm{Wb}/\mathrm{A}-\mathrm{m}$ is :
[Permeability of free space ${\mu }_0=4\pi \times 10^{-7}\mathrm{Wb}/\mathrm{A}-\mathrm{m}$ ]

Q11.The current flowing through an ac circuit is given by
$I=5\sin (120\pi t)A$
How long will the current take to reach the peak value starting from zero?

Q12.An $\alpha$ particle and a carbon 12 atom has same kinetic energy K. The ratio of their de-Broglie wavelength $\left({\lambda }_a:{\lambda }_{C12}\right)$ is :

Q13.A force of 10 N acts on a charged particle placed between two plates of a charged capacitor. If one plate of capacitor is removed, then the force acting on that particle will be :

Q14.The displacement of simple harmonic oscillator after 3 seconds starting from its mean position is equal to half of its amplitude. The time period of harmonic motion is :

Q15.An observer moves towards a stationary source of sound with a velocity equal to one-fifth of the velocity of sound. The percentage change in the frequency will be :

Q16.Consider a light ray travelling in air is incident into a medium of refractive index $\sqrt{2n}$. The incident angle is twice that of refracting angle. Then, the angle of incidence will be :

Q17.A hydrogen atom in is ground state absorbs 10.2 eV of energy. The angular momentum of electron of the hydrogen atom will increase by the value of : (Given, Plank's constant $=6.6\times 10^{-34}\mathrm{Js}$)

Q18.Identify the correct Logic Gate for the following output $(\mathrm{Y})$ of two inputs A and B .

Q19.A mixture of hydrogen and oxygen has volume $2000{\mathrm{cm}}^3$, temperature 300 K , pressure 100 kPa and mass 0.76 g The ratio of number of moles of hydrogen to number of moles of oxygen in the mixture will be :

Q20.In a carnot engine, the temperature of reservoir is $527^{\circ }\mathrm{C}$ and that of sink is 200 K . If the workdone by the engine when it transfers heat from reservoir to sink is 12000 kJ , the quantity of heat absorbed by the engine from reservoir is ____ …

Q21.A $220\mathrm{V},50\mathrm{Hz}\mathrm{AC}$ source is connected to a 25 V , 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be ____。

Q22.In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be __\ …

Q23.A beam of monochromatic light is used to excite the electron in ${\mathrm{Li}}^{++}$from the first orbit to the third orbit. The wavelength of monochromatic light is found to be $x\times 10^{-10}m$. The value of x is ____ .
[Given hc $=1242\mathrm{eV}\mathrm{nm}$ ]

Q24.A cell, shunted by a $8\Omega$ resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by $4\Omega$ resistance. The value of internal resistance of the cell will be ______ $\Omega$.

Q25.The current density in a cylindrical wire of radius 4 mm is $4\times 10^6{\text{A m}}^{-2}$. The current through the outer portion of the wire between radial distance $\frac{R}{2}$ and R is ______ $\pi \text{A}$.

Q26.A capacitor of capacitance 50 pF is charged by 100 V source. It is then connected to another uncharged identical capacitor. Electrostatic energy loss in the process is ______ nJ.

Q27.The height of a transmitting antenna at the top of a tower is 25 m and that of receiving antenna is 49 m. The maximum distance between them, for satisfactory communication in LOS (Line-Of-Sight) is $K\sqrt{5}\times 10^2$ m. The value of $K$ is ______.
[Assume radius of Ea …

Q28.The area of cross-section of a large tank is $0.5{\text{m}}^2$. It has a narrow opening near the bottom having area of cross-section $1{\text{cm}}^2$. A load of 25 kg is applied on the water at the top in the tank. Neglecting the speed of water in the tank, the velocity o …

Q29.A pendulum of length 2 m consists of a wooden bob of mass 50 g. A bullet of mass 75 g is fired towards the stationary bob with a speed v. The bullet emerges out of the bob with a speed $\frac{v}{3}$ and the bob just completes the vertical circle. The value of $v$ is ______ …

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

Assertion (A) : At $10^{\circ }\mathrm{C}$, the density of a 5 M solution of KCl [atomic masses of K and Cl are 39 $\&35.5\mathrm{g}{\mathrm{mol}}^{-1}$]. The solution is …

Q2.Based upon VSEPR theory, match the shape (geometry) of the molecules in List-I with the molecules in List-II and select the most appropriate option

List-I (Shape):
(A) T-shaped
(B) Trigonal planar
(C) Square planar
(D) See-saw

List-II (Molecules):
(I) ${\mathrm{XeF}}_4$
(II) …

Q3.Match List-I with List-II

List-I:
(A) Spontaneous process
(B) Process with $\Delta \mathrm{P}=0$, $\Delta \mathrm{T}=0$
(C) $\Delta {\mathrm{H}}_{\text{reaction}}$
(D) Exothermic process

List-II:
(I) $\Delta \mathrm{H}<0$
(II) $\Delta {\mathrm{G}}_{\mathrm{T},\mathrm{P}}<0$
(III) …

Q4.Match List-I with List-II

List-I:
(A) Lyophilic colloid
(B) Emulsion
(C) Positively charged colloid
(D) Negatively charged colloid

List-II:
(I) Liquid-liquid colloid
(II) protective colloid
(III) ${\mathrm{FeCl}}_3+\mathrm{NaOH}$
(IV) ${\mathrm{FeCl}}_3+$ hot water

Choose the …

Q5.Given below are two statements: one is labelled as Assertion (A) and the other is labelled as Reason(R)

Assertion (A): The ionic radii of ${\mathrm{O}}^{2-}$ and ${\mathrm{Mg}}^{2+}$ are same.

Reason (R) : Both ${\mathrm{O}}^{2-}$ and ${\mathrm{Mg}}^{2+}$ are isoelectronic species

In …

Q6.Match List-I with List-II

List-I:
(A) Concentration of gold ore
(B) Leaching of alumina
(C) Froth stabiliser
(D) Blister copper

List-II:
(I) Aniline
(II) NaOH
(III) ${\mathrm{SO}}_2$
(IV) NaCN

Choose the correct answer from the options given below.

Q7.Addition of ${\mathrm{H}}_2{\mathrm{SO}}_4$ to ${\mathrm{BaO}}_2$ produces:

Q8.${\mathrm{BeCl}}_2$ reacts with ${\mathrm{LiAlH}}_4$ to give

Q9.Match List-I with List-II

List-I (Si-Compounds):
(A) ${\left({\mathrm{CH}}_3\right)}_4\mathrm{Si}$
(B) $\left({\mathrm{CH}}_3\right)\mathrm{Si}(\mathrm{OH}{)}_3$
(C) ${\left({\mathrm{CH}}_3\right)}_2\mathrm{Si}(\mathrm{OH}{)}_2$
(D) …

Q10.Heating white phosphorus with conc. NaOH solution gives mainly

Q11.Which of the following will have maximum stabilization due to crystal field?

Q12.Given below are two statements:

Statement I: Classical smog occurs in cool humid climate. It is a reducing mixture of smoke, fog and sulphur dioxide

Statement II: Photochemical smog has components, ozone, nitric oxide, acrolein, formaldehyde, PAN etc.

In the light of above sta …

Q13.Which of the following is structure of a separating funnel?

Q14.'$\mathbf{A}$' and '$\mathbf{B}$' respectively are:
…

Q15.Which of the following reactions will yield benzaldehyde as a product?

Q16.Given below are two statements:

Statements-I : In Hofmann degradation reaction, the migration of only an alkyl group takes place from carbonyl carbon of the amide to the nitrogen atom.

Statement-II : The group is migrated in Hofmann degradation reaction to electron deficient at …

Q17.Match List-I with List-II

List-I (Polymer)
(A) Bakelite
(B) Glyptal
(C) PVC
(D) Polystyrene

List-II (Used in)
(I) Radio and television Cabinets
(II) Electrical switches
(III) Paints and Lacquers
(IV) Water pipes

Choose the correct answer from the options given below:

Q18.L-isomer of a compound 'A' $({\mathrm{C}}_4{\mathrm{H}}_8{\mathrm{O}}_4)$ gives a positive test with $[\mathrm{Ag}({\mathrm{NH}}_3{)}_2{]}^{+}$. Treatment of 'A' with acetic anhydride yield triacetate derivative. Compound 'A' produces an optically active compound (B) and an optic …

Q19.Match List-I with List-II

List-I
(A) (see structure)
(B) (see structure)
(C) ${\mathrm{C}}_{17}{\mathrm{H}}_{35}{\mathrm{COO}}^{-}{\mathrm{Na}}^{+}+{\mathrm{Na}}_2{\mathrm{CO}}_3+$ Rosinate
(D) …

Q20.Metal deficiency defect is shown by ${\mathrm{Fe}}_{0.93}\mathrm{O}$. In the crystal, some ${\mathrm{Fe}}^{2+}$ cations are missing and loss of positive charge is compensated by the presence of ${\mathrm{Fe}}^{3+}$ ions. The percentage of ${\mathrm{Fe}}^{2+}$ ions in the …

Q21.If the uncertainty in velocity and position of a minute particle in space are, $2.4\times 10^{-26}({\mathrm{ms}}^{-1})$ and $10^{-7}(\mathrm{m})$ respectively. The mass of the particle in g is ______ (Nearest integer)
(Given : $\mathrm{h}=6.626\times 10^{-34}\mathrm{Js}$)

Q22.2 g of a non-volatile non-electrolyte solute is dissolved in 200 g of two different solvents A and B whose ebullioscopic constants are in the ratio of $1:8$. The elevation in boiling points of A and B are in the ratio $\frac{x}{y}(x:y)$. The value of $y$ is ______ (Nearest inte …

Q23.$2\mathrm{NOCl}(\mathrm{g})\rightleftharpoons 2\mathrm{NO}(\mathrm{g})+{\mathrm{Cl}}_2(\mathrm{g})$

In an experiment, 2.0 moles of NOCl was placed in a one-litre flask and the concentration of NO after equilibrium established, was found to be 0.4 $\mathrm{mol}/\mathrm{L}$. …

Q24.The limiting molar conductivities of $\mathrm{NaI},{\mathrm{NaNO}}_3$ and ${\mathrm{AgNO}}_3$ are 12.7, 12.0 and $13.3\mathrm{mS}{\mathrm{m}}^2{\mathrm{mol}}^{-1}$, respectively (all at $25^{\circ }\mathrm{C}$ ). The limiting molar conductivity of AgI at this temperatu …

Q25.The rate constant for a first order reaction is given by the following equation:
$\ln \mathrm{k}=33.24-\frac{2.0\times 10^4\mathrm{K}}{\mathrm{T}}$
The Activation energy for the reaction is given by
____ $\mathrm{kJ}{\mathrm{mol}}^{-1}$. (In Nearest integer)
(Given: …

Q26.The number of statement(s) correct from the following for copper (at no. 29) is/are ____
(A) Cu (II) complexes are always paramagnetic
(B) $\mathrm{Cu}(\mathrm{I})$ complexes are generally colourless
(C) $\mathrm{Cu}(\mathrm{I})$ is easily oxidized
(D) In Fehling solution …

Q27.Acidified potassium permanganate solution oxidises oxalic acid. The spin-only magnetic moment of the manganese product formed from the above reaction is ____ B.M. (Nearest Integer)

Q28.Two elements A and B which form 0.15 moles of ${\mathrm{A}}_2\mathrm{B}$ and ${\mathrm{AB}}_3$ type compounds. If both ${\mathrm{A}}_2\mathrm{B}$ and ${\mathrm{AB}}_3$ weigh equally, then the atomic weight of A is
____ times of atomic weight of B .

Q29.Total number of possible stereoisomers of dimethyl cyclopentane is ____

Q1.The area of the polygon, whose vertices are the non-real roots of the equation $\bar{z}=i{z}^2$ is :

Q2.Let the system of linear equations $x+2y+z=2$, $\alpha x+3y-z=\alpha$, $-\alpha x+y+2z=-\alpha$ be inconsistent.

Then $\alpha$ is equal to :

Q3.If $x={\sum }_{n=0}^{\infty }{a}^n$, $y={\sum }_{n=0}^{\infty }{b}^n$, $z={\sum }_{n=0}^{\infty }{c}^n$, where $a,b,c$ are in A.P. and $|a|<1$, $|b|<1$, $|c|<1$, $abc\ne 0$, then

Q4.Let $\frac{dy}{dx}=\frac{ax-by+a}{bx+cy+a}$, where $a,b,c$ are constants, represent a circle passing through the point $(2,5)$. Then the shortest distance of the point $(11,6)$ from this circle is :

Q5.Let $a$ be an integer such that ${\lim }_{x\to 7}\frac{18-[1-x]}{[x-3a]}$ exists, where $[t]$ is greatest integer $\le t$. Then $a$ is equal to :

Q6.The number of distinct real roots of $x^4-4x+1=0$ is :

Q7.The lengths of the sides of a triangle are $10+x^2$, $10+x^2$ and $20-2x^2$. If for $x=k$, the area of the triangle is maximum, then $3k^2$ is equal to :

Q8.If ${\cos }^{-1}\left(\frac{y}{2}\right)={\log }_e{\left(\frac{x}{5}\right)}^5$, $|y|<2$, then :

Q9.$\int \frac{\left(x^2+1\right)e^x}{(x+1{)}^2}dx=f(x)e^x+C$, Where $C$ is a constant, then $\frac{d^{3}f}{d{x}^3}$ at $x=1$ is equal to :

Q10.The value of the integral ${\int }_{-2}^2\frac{|x^3+x|}{\left(e^{x|x|}+1\right)}dx$ is equal to :

Q11.If $\frac{dy}{dx}+\frac{2^{x-y}\left(2^y-1\right)}{2^x-1}=0$, $x,y>0$, $y(1)=1$, then $y(2)$ is equal to :

Q12.In an isosceles triangle ABC , the vertex A is $(6,1)$ and the equation of the base BC is $2x+y=4$. Let the point B lie on the line $x+3y=7$. If $(\alpha ,\beta )$ is the centroid $△ABC$, then $15(\alpha +\beta )$ is equal to :

Q13.Let the eccentricity of an ellipse $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$, be $\frac{1}{4}$. If this ellipse passes through the point $\left(-4\sqrt{\frac{2}{5}},3\right)$, then ${\mathrm{a}}^2+{\mathrm{b}}^2$ is equal to :

Q14.If two straight lines whose direction cosines are given by the relations $l+m-n=0,3l^2+m^2+cnl=0$ are parallel, then the positive value of c is :

Q15.Let $\vec{a}=\hat{i}+\hat{j}-\hat{k}$ and $\vec{c}=2\hat{i}-3\hat{j}+2\hat{k}$. Then the number of vectors $\vec{b}$ such that $\vec{b}\times \vec{c}=\vec{a}$ and $|\vec{b}|\in \{1,2,\dots ,10\}$ is :

Q16.Five numbers ${\mathrm{x}}_1,{\mathrm{x}}_2,{\mathrm{x}}_3,{\mathrm{x}}_4,{\mathrm{x}}_5$ are randomly selected from the numbers $1,2,3,\dots ,18$ and are arranged in the increasing order ( ${\mathrm{x}}_1<{\mathrm{x}}_2<{\mathrm{x}}_3<{\mathrm{x}}_4<{\mathrm{x}}_5$ ) …

Q17.Let X be a random variable having binomial distribution $\mathrm{B}(7,\mathrm{p})$. If $\mathrm{P}(\mathrm{X}=3)=5\mathrm{P}(\mathrm{X}=4)$, then the sum of the mean and the variance of X is :

Q18.The value of $\cos \left(\frac{2\pi }{7}\right)+\cos \left(\frac{4\pi }{7}\right)+\cos \left(\frac{6\pi }{7}\right)$ is equal to :

Q19.${\sin }^{-1}\left(\sin \frac{2\pi }{3}\right)+{\cos }^{-1}\left(\cos \frac{7\pi }{6}\right)+{\tan }^{-1}\left(\tan \frac{3\pi }{4}\right)$ is equal to :

Q20.The Boolean expression $(\sim (p\wedge q))\vee q$ is equivalent to :

Q21.Let $f:R\to R$ be a function defined $f(x)=\frac{2e^{2x}}{e^{2x}+e}$.

Then $f\left(\frac{1}{100}\right)+f\left(\frac{2}{100}\right)+f\left(\frac{3}{100}\right)+\dots +f\left(\frac{99}{100}\right)$ is equal to ____.

Q22.If the sum of all the roots of the equation $e^{2x}-11e^x-45e^{-x}+\frac{81}{2}=0$ is ${\log }_e\mathrm{P}$, then p is equal to ____.

Q23.The positive value of the determinant of the matrix A, whose $\mathrm{Adj}(\mathrm{Adj}(A))=\left(\begin{array}{ccc}14& 28& -14\\ -14& 14& 28\\ 28& -14& 14\end{array}\right)$, is ____.

Q24.The number of ways, 16 identical cubes, of which 11 are blue and rest are red, can be placed in a row so that between any two red cubes there should be at least 2 blue cubes, is ____.

Q25.If the coefficient of $x^{10}$ in the binomial expansion of ${\left(\frac{\sqrt{x}}{5^{\frac{1}{4}}}+\frac{\sqrt{5}}{x^{\frac{1}{3}}}\right)}^{60}$ is $5^{k}l$, where $l,k\in \mathbb{N}$ and $l$ is coprime to 5, then k is equal to ______.

Q26.Let $A_1=\{(x,y):|x|\le y^2,|x|+2y\le 8\}$ and $A_2=\{(x,y):|x|+|y|\le k\}$. If $27$(Area $A_1$)$=5$(Area $A_2$), then k is equal to:

Q27.If the sum of the first ten terms of the series $\frac{1}{5}+\frac{2}{65}+\frac{3}{325}+\frac{4}{1025}+\frac{5}{2501}+\dots$ is $\frac{m}{n}$, where m and n are co-prime numbers, then $m+n$ is equal to ______.

Q28.A rectangle R with end points of one of its sides as $(1,2)$ and $(3,6)$ is inscribed in a circle. If the equation of a diameter of the circle is $2x-y+4=0$, then the area of R is ______.

Q29.A circle of radius 2 unit passes through the vertex and the focus of the parabola $y^2=2x$ and touches the parabola $y={\left(x-\frac{1}{4}\right)}^2+\alpha$, where $\alpha >0$. Then $(4\alpha -8{)}^2$ is equal to ______.

Q30.Let the mirror image of the point $(a,b,c)$ with respect to the plane $3x-4y+12z+19=0$ be $(a-6,\beta ,\gamma )$. If $a+b+c=5$, then $7\beta -9\gamma$ is equal to ______.