JEE Main 2022 · 24 Jun 2022 · Shift 2

Q1.Identify the pair of physical quantities that have same dimensions :

Q2.The distance between Sun and Earth is R. The duration of year if the distance between Sun and Earth becomes 3 R will be :

Q3.A stone of mass m , tied to a string is being whirled in a vertical circle with a uniform speed. The tension in the string is :

Q4.Two identical charged particles each having a mass 10 g and charge $2.0\times 10^{-7}$ C are placed on a horizontal table with a separation of L between them such that they stay in limited equilibrium. If the coefficient of friction between each particle and the table is 0.25 , …

Q5.A Carnot engine takes 5000 kcal of heat from a reservoir at $727^{\circ }$C and gives heat to a sink at $127^{\circ }$C. The work done by the engine is :

Q6.Two massless springs with spring constants 2 k and 9 k , carry 50 g and 100 g masses at their free ends. These two masses oscillate vertically such that their maximum velocities are equal. Then, the ratio of their respective amplitudes will be :

Q7.What will be the most suitable combination of three resistors $A=2\Omega$, $B=4\Omega$, $C=6\Omega$ so that $\left(\frac{22}{3}\right)\Omega$ is equivalent resistance of combination?

Q8.The soft-iron is a suitable material for making an electromagnet. This is because soft-iron has :

Q9.A proton, a deuteron and an $\alpha$-particle with same kinetic energy enter into a uniform magnetic field at right angle to magnetic field. The ratio of the radii of their respective circular paths is :

Q10.Given below are two statements :

Statement-I : The reactance of an ac circuit is zero. It is possible that the circuit contains a capacitor and an inductor.
Statement-II : In ac circuit, the average power delivered by the source never becomes zero.

In the light of the above sta …

Q11.Potential energy as a function of r is given by $U=\frac{A}{r^{10}}-\frac{B}{r^5}$, where r is the interatomic distance, A and B are positive constants. The equilibrium distance between the two atoms will be :

Q12.An object of mass 5 kg is thrown vertically upwards from the ground. The air resistance produces a constant retarding force of 10 N throughout the motion. The ratio of time of ascent to the time of descent will be equal to : [Use $g=10$ ms${}^{-2}$]

Q13.A fly wheel is accelerated uniformly from rest and rotates through 5 rad in the first second. The angle rotated by the fly wheel in the next second, will be :

Q14.A 100 g of iron nail is hit by a 1.5 kg hammer striking at a velocity of $60{\mathrm{ms}}^{-1}$. What will be the rise in the temperature of the nail if one fourth of energy of the hammer goes into heating the nail?
[Specific heat capacity of iron …

Q15.If the charge on a capacitor is increased by 2 C, the energy stored in it increases by $44\%$. The original charge on the capacitor is (in C) :

Q16.A long cylindrical volume contains a uniformly distributed charge of density $\rho$. The radius of cylindrical volume is $R$. A charge particle (q) revolves around the cylinder in a circular path. The kinetic of the particle is :

Q17.An electric bulb is rated as 200 W. What will be the peak magnetic field at 4 m distance produced by the radiations coming from this bulb? Consider this bulb as a point source with $3.5\%$ efficiency.

Q18.The light of two different frequencies whose photons have energies 3.8 eV and 1.4 eV respectively, illuminate a metallic surface whose work function is 0.6 eV successively. The ratio of maximum speeds of emitted electrons for the two frequencies respectivly will be :

Q19.Two light beams of intensities in the ratio of $9:4$ are allowed to interfere. The ratio of the intensity of maxima and minima will be :

Q20.In Bohr's atomic model of hydrogen, let K. P and E are the kinetic energy, potential energy and total energy of the electron respectively. Choose the correct option when the electron undergoes transitions to a higher level :

Q21.A body is projected from the ground at an angle of $45^{\circ }$ with the horizontal. Its velocity after 2 s is $20{\mathrm{ms}}^{-1}$. The maximum height reached by the body during its motion is ______ m. (use $\mathrm{g}=10{\mathrm{ms}}^{-2}$)

Q22.An antenna is placed in a dielectric medium of dielectric constant 6.25. If the maximum size of that antenna is 5.0 mm, it can radiate a signal of minimum frequency of ______ GHz.
(Given ${\mu }_{\mathrm{r}}=1$ for dielectric medium)

Q23.A potentiometer wire of length 10 m and resistance $20\Omega$ is connected in series with a 25 V battery and an external resistance $30\Omega$. A cell of emf E in secondary circuit is balanced by 250 cm long potentiometer wire. The value of E (in volt) is $\frac{x}{10}$. The va …

Q24.Two travelling waves of equal amplitudes and equal frequencies move in opposite directions along a string. They interfere to produce a stationary wave whose equation is given by
$y=\left(10\cos \pi x\sin \frac{2\pi t}{T}\right)\mathrm{cm}$
The amplitude of the particle at …

Q25.In the given circuit- the value of current ${\mathrm{I}}_{\mathrm{L}}$ will be $\_\_\_\_$ mA.
(When ${\mathrm{R}}_{\mathrm{L}}=1\mathrm{k}\Omega$)

Q26.A sample contains $10^{-2}\mathrm{kg}$ each of two substances A and B with half lives 4 s and 8 s respectively. The ratio of then atomic weights is $1:2$. The ratio of the amounts of $A$ and $B$ after $16s$ is $\frac{x}{100}$. the value of $x$ is $\_\_\_\_$.

Q27.A ray of ligh is incident at an angle of incidence $60^{\circ }$ on the glass slab of refractive index $\sqrt{3}$. After refraction, the light ray emerges out from other parallel faces and lateral shift between incident ray and emergent ray is $4\sqrt{3}\mathrm{cm}$. The thickn …

Q28.A circular coil of 1000 turns each with area $1{\mathrm{m}}^2$ is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of 0.07 T. The maximum voltage generation will be $\_\_\_\_$ V.

Q29.A monoatomic gas performs a work of $\frac{\mathrm{Q}}{4}$ where Q is the heat supplied to it. The molar heat capaticy of the gas will be $\_\_\_\_$ R during this transformation.

Where $R$ is the gas constant.

Q30.In an experment ot verify Newton's law of cooling, a graph is plotted between, the temperature difference $(\Delta T)$ of the water and surroundings and time as shown in figure. The initial temperature of water is taken as $80^{\circ }C$. The value of $t_2$ as mentioned in the …

Q1.120 g of an organic compound that contains only carbon and hydrogen gives 330 g of ${\mathrm{CO}}_2$ and 270 g of water on complete combustion. The percentage of carbon and hydrogen, respectively are.

Q2.The energy of one mole of photons of radiation of wavelength 300 nm is
(Given : $\mathrm{h}=6.63\times 10^{-34}$ Js, ${\mathrm{N}}_{\mathrm{A}}=6.02\times 10^{23}$ mol${}^{-1}$, c $=3\times 10^8$ ms${}^{-1}$ )

Q3.The correct order of bond orders of ${\mathrm{C}}_2^{2-}$, ${\mathrm{N}}_2^{2-}$ and ${\mathrm{O}}_2^{2-}$ is, respectively.

Q4.At $25^{\circ }\mathrm{C}$ and 1 atm pressure, the enthalpies of combustion are as given below:
| …

Q5.For a first order reaction, the time required for completion of $90\%$ reaction is '$x$' times the half life of the reaction. The value of '$x$' is
(Given: $\ln 10=2.303$ and $\log 2=0.3010$ )

Q6.Metals generally melt at very high temperature. Amongst the following, the metal with the highest melting point will be

Q7.Which of the following chemical reactions represents Hall-Heroult Process?

Q8.In the industrial production of which of the following, molecular hydrogen is obtained as a byproduct?

Q9.Which one of the following compounds is used as a chemical in certain type of fire extinguishers?

Q10.${\mathrm{PCl}}_5$ is well known, but ${\mathrm{NCl}}_5$ is not. Because.

Q11.Transition metal complex with highest value of crystal field splitting ( ${\Delta }_0$ ) will be

Q12.Some gases are responsible for heating of atmosphere (green house effect). Identify from the following the gaseous species which does not cause it.

Q13.Arrange the following carbocations in decreasing order of stability.

Q14.Given below are two statements.

Statement I : The presence of weaker π-bonds make alkenes less stable than alkanes.

Statement II : The strength of the double bond is greater than that of carbon-carbon single bond.

In the light of the above statements, choose the correct answer …

Q15.Which of the following reagents/ reactions will convert 'A' to 'B'?

Q16.Hex-4-ene-2-ol on treatment with PCC gives 'A'. 'A' on reaction with sodium hypoiodite gives 'B', which on further heating with soda lime gives 'C'. The compound 'C' is

Q17.The conversion of propan-1-ol to n-butylamine involves the sequential addition of reagents. The correct sequential order of reagents is.

Q18.Which of the following is not an example of a condensation polymer?

Q19.The structure shown below is of which well-known drug molecule?

Q20.In the flame test of a mixture of salts, a green flame with blue centre was observed. Which one of the following cations may be present?

Q21.At 300 K, a sample of 3.0 g of gas A occupies the same volume as 0.2 g of hydrogen at 200 K at the same pressure. The molar mass of gas A is _____ g ${\mathrm{mol}}^{-1}$ (nearest integer) Assume that the behaviour of gases as ideal. (Given: The molar mass of hydrogen …

Q22.A company dissolves 'X' amount of ${\mathrm{CO}}_2$ at 298 K in 1 litre of water to prepare soda water
$\mathrm{X}=$ _____ $\times 10^{-3}\mathrm{g}$. (nearest integer)
(Given: partial pressure of ${\mathrm{CO}}_2$ at $298\mathrm{K}=0.835$ bar.

Henry's law constant …

Q23.${\mathrm{PCl}}_5$ dissociates as


5 moles of ${\mathrm{PCl}}_5$ are placed in a 200 litre vessel which contains 2 moles of ${\mathrm{N}}_2$ and is maintained a …

Q24.The resistance of conductivity cell containing 0.01 M KCl solution at 298 K is $1750\Omega$. If the conductivity of 0.01 M KCl solution at 298 K is $0.152\times 10^{-3}\mathrm{S}{\mathrm{cm}}^{-1}$, then the cell constant of the conductivity cell is _____ …

Q25.When 200 mL of 0.2 M acetic acid is shaken with 0.6 g of wood charcoal, the final concentration of acetic acid after adsorption is 0.1 M. The mass of acetic acid adsorbed per gram of carbon is _____ g.

Q26.(a) Baryte, (b) Galena, (c) Zinc blende and (d) Copper pyrites. How many of these minerals are sulphide based?

Q27.Manganese (VI) has ability to disproportionate in acidic solution. The difference in oxidation states of two ions it forms in acidic solution is ____

Q28.$0.2\text{g}$ of an organic compound was subjected to estimation of nitrogen by Dumas method in which volume of $\mathrm{N}{}_2$ evolved (at STP) was found to be 22.400 mL. The percentage of nitrogen in the compound is ____. [nearest integer]
(Given: Molar mass of $\mathrm{N}{}_2$ is …

Q29.Consider the above reaction. The number of $\pi$ electrons present in the product 'P' is ____.

Q30.In alanylglycylleucylalanylvaline, the number of peptide linkages is ____.

Q1.Let $x\ast y=x^2+y^3$ and $(x\ast 1)\ast 1=x\ast (1\ast 1)$.

Then a value of $2{\sin }^{-1}\left(\frac{x^4+x^2-2}{x^4+x^2+2}\right)$ is

Q2.The sum of all the real roots of the equation $(e^{2x}-4)(6e^{2x}-5e^x+1)=0$ is

Q3.Let the system of linear equations
$x+y+\alpha z=2$
$3x+y+z=4$
$x+2z=1$
have a unique solution $(x^{\ast },y^{\ast },z^{\ast })$. If $(\alpha ,x^{\ast })$, $(y^{\ast },\alpha )$ and $(x^{\ast },-y^{\ast })$ are collinear points, then the sum of absolute values of all possible values of …

Q4.Let $x,y>0$. If $x^3{y}^2=2^{15}$, then the least value of $3x+2y$ is

Q5.Let $f(x)=\{\begin{array}{ll}\max \{2x,3[|x|]\}& ,|x|<1\\ 1& ,\text{otherwise}\end{array}$
where $[t]$ denotes greatest integer $\le t$. If m is the number of points where $f$ is not continuous and n is the number of points where $f$ is not differentiable, then the ordered …

Q6.The value of the integral ${\int }_{-\pi /2}^{\pi /2}\frac{dx}{(1+e^x)({\sin }^{6}x+{\cos }^{6}x)}$ is equal to

Q7.${\lim }_{n\to \infty }\left(\frac{n^2}{(n^2+1)(n+1)}+\frac{n^2}{(n^2+4)(n+2)}+\frac{n^2}{(n^2+9)(n+3)}+\dots +\frac{n^2}{(n^2+n^2)(n+n)}\right)$ is equal to

Q8.A particle is moving in the $xy$-plane along a curve C passing through the point $(3,3)$. The tangent to the curve C at the point P meets the x-axis at Q. If the y-axis bisects the segment PQ, then C is a parabola with

Q9.Let the maximum area of the triangle that can be inscribed in the ellipse $\frac{x^2}{a^2}+\frac{y^2}{4}=1$, $a>2$, having one of its vertices at one end of the major axis of the ellipse and one of its sides parallel to the y-axis, be $6\sqrt{3}$. Then the eccentricit …

Q10.Let the area of the triangle with vertices $A(1,\alpha )$, $B(\alpha ,0)$ and $C(0,\alpha )$ be 4 sq. units. If the points $(\alpha ,-\alpha )$, $(-\alpha ,\alpha )$ and $({\alpha }^2,\beta )$ are collinear, then $\beta$ is equal to

Q11.The number of distinct real roots of the equation $x^7-7x-2=0$ is

Q12.A random variable $X$ has the following probability distribution:

The value of $P(1<X<4\mid X\le 2)$ is equal to:

Q13.The number of solutions of the equation $\cos \left(x+\frac{\pi }{3}\right)\cos \left(\frac{\pi }{3}-x\right)=\frac{1}{4}{\cos }^{2}2x,x\in [-3\pi ,3\pi ]$ is :

Q14.If the shortest distance between the lines $\frac{x-1}{2}=\frac{y-2}{3}=\frac{z-3}{\lambda }$ and $\frac{x-2}{1}=\frac{y-4}{4}=\frac{z-5}{5}$ is $\frac{1}{\sqrt{3}}$, then the sum of all possible values of $\lambda$ is :

Q15.Let the points on the plane P be equidistant from the points $(-4,2,1)$ and $(2,-2,3)$. Then the acute angle between the plane P and the plane $2x+y+3z=1$ is

Q16.Let $\hat{a}$ and $\hat{b}$ be two unit vectors such that $|(\hat{a}+\hat{b})+2(\hat{a}\times \hat{b})|=2$. If $\theta \in (0,\pi )$ is the angle between $\hat{a}$ and $\hat{b}$, then among the statements:
(S1) : $2|\hat{a}\times \hat{b}|=|\hat{a}-\hat{b}|$
(S2) : The projection …

Q17.If $y={\tan }^{-1}\left(\sec x^3-\tan x^3\right),\frac{\pi }{2}<x^3<\frac{3\pi }{2}$, then

Q18.Consider the following statements :
A : Rishi is a judge.
B : Rishi is honest.
C : Rishi is not arrogant.
The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is

Q19.The slope of normal at any point $(x,y),x>0,y>0$ on the curve $y=y(x)$ is given by $\frac{x^2}{xy-x^2{y}^2-1}$.
If the curve passes through the point $(1,1)$, then $e\cdot y(e)$ is equal to

Q20.Let ${\lambda }^{\ast }$ be the largest value of $\lambda$ for which the function $f_{\lambda }(x)=4\lambda x^3-36\lambda x^2+36x+48$ is increasing for all $x\in \mathbb{R}$. Then $f_{{\lambda }^{\ast }}(1)+f_{{\lambda }^{\ast }}(-1)$ is equal to :

Q21.Let $S=\{z\in \mathbb{C}:|z-3|\le 1$ and $z(4+3i)+\bar{z}(4-3i)\le 24\}$.
If $\alpha +i\beta$ is the point in S which is closest to $4i$, then $25(\alpha +\beta )$ is equal to ______.

Q22.Let $S=\left\{\left(\begin{array}{cc}-1& a\\ 0& b\end{array}\right);a,b\in \{1,2,3,\dots 100\}\right\}$ and let $T_n=\left\{A\in S:A^{n(n+1)}=I\right\}$. Then the number of elements in ${\bigcap }_{n=1}^{100}{T}_n$ is ______.

Q23.The number of 7-digit numbers which are multiples of 11 and are formed using all the digits $1,2,3,4,5,7$ and $9$ is ______.

Q24.The sum of all the elements of the set $\{\alpha \in \{1,2,\dots ,100\}:\mathrm{HCF}(\alpha ,24)=1\}$ is ______.

Q25.The remainder on dividing $1+3+3^2+3^3+\dots +3^{2021}$ by 50 is ____.

Q26.The area (in sq. units) of the region enclosed between the parabola $y^2=2x$ and the line $x+y=4$ is ____.

Q27.Let a circle $C:(x-h{)}^2+(y-k{)}^2=r^2,k>0$, touch the x-axis at $(1,0)$. If the line $x+y=0$ intersects the circle C at P and Q such that the length of the chord PQ is 2, then the value of $h+k+r$ is equal to ____.

Q28.In an examination, there are 10 true-false type questions. Out of 10, a student can guess the answer of 4 questions correctly with probability $\frac{3}{4}$ and the remaining 6 questions correctly with probability $\frac{1}{4}$.

If the probability that the student guesses the an …

Q29.Let the hyperbola $H:\frac{x^2}{a^2}-y^2=1$ and the ellipse $E:3x^2+4y^2=12$ be such that the length of latus rectum of H is equal to the length of latus rectum of E. If $e_H$ and $e_E$ are the eccentricities of H and E respectively, then the value of …

Q30.Let $P_1$ be a parabola with vertex $(3,2)$ and focus $(4,4)$ and $P_2$ be its mirror image with respect to the line $x+2y=6$. Then the directrix of $P_2$ is $x+2y=$ ____.