JEE Main 2023 · 13 Apr 2023 · Shift 2

Q1.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : The binding energy per nucleon is practically independent of the atomic number for nuclei of mass number in the range 30 to 170.
Reason R : Nuclear force is short r …

Q2.The output from a NAND gate having inputs A and B given below will be.

Q3.In the network shown below, the charge accumulated in the capacitor in steady state will be :

Q4.Given below are two statements :
Statement I: For a planet, if the ratio of mass of the planet to its radius increases, the escape velocity from the planet also increases.
Statement II: Escape velocity is independent of the radius of the planet.
In the light of above statements, …

Q5.A particle executes SHM of amplitude A. The distance from the mean position when its's kinetic energy becomes equal to its potential energy is :

Q6.A passenger sitting in a train A moving at $90\mathrm{km}/\mathrm{h}$ observes another train B moving in the opposite direction for 8 s . If the velocity of the train B is $54\mathrm{km}/\mathrm{h}$, then length of train B is :

Q7.The initial pressure and volume of an ideal gas are ${\mathrm{P}}_0$ and ${\mathrm{V}}_0$. The final pressure of the gas when the gas is suddenly compressed to volume $\frac{{\mathrm{V}}_0}{4}$ will be : (Given $\gamma =$ ratio of specific heats at constant pressure and at …

Q8.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A : A spherical body of radius $(5\pm 0.1)$ mm having a particular density is falling through a liquid of constant density. The percentage error in the calculation of …

Q9.In an electromagnetic wave, at an instant and at a particular position, the electric field is along the negative z -axis and magnetic field is along the positive x -axis. Then the direction of propagation of electromagnetic wave is:

Q10.The distance travelled by an object in time $t$ is given by $s=(2\cdot 5)t^2$. The instantaneous speed of the object at $\mathrm{t}=5\mathrm{s}$ will be :

Q11.An electron is moving along the positive x -axis. If the uniform magnetic field is applied parallel to the negative z -axis. then
A. The electron will experience magnetic force along positive y -axis
B. The electron will experience magnetic force along negative y -axis
C. The ele …

Q12.Two planets A and B of radii R and 1.5 R have densities $\rho$ and $\rho /2$ respectively. The ratio of acceleration due to gravity at the surface of B to A is :

Q13.Given below are two statements:

Statement I: An AC circuit undergoes electrical resonance if it contains either a capacitor or an inductor.
Statement II : An AC circuit containing a pure capacitor or a pure inductor consumes high power due to its non-zero power factor.

In the l …

Q14.A vehicle of mass 200 kg is moving along a levelled curved road of radius 70 m with angular velocity of $0.2\mathrm{rad}/\mathrm{s}$. The centripetal force acting on the vehicle is :

Q15.To radiate EM signal of wavelength $\lambda$ with high efficiency, the antennas should have a minimum size equal to :

Q16.Given below are two statements:

Statement I : Out of microwaves, infrared rays and ultraviolet rays, ultraviolet rays are the most effective for the emission of electrons from a metallic surface.

Statement II : Above the threshold frequency, the maximum kinetic energy of photoe …

Q17.A $10\mu \mathrm{C}$ charge is divided into two parts and placed at 1 cm distance so that the repulsive force between them is maximum. The charges of the two parts are :

Q18.In the equation $\left[X+\frac{a}{Y^2}\right][Y-b]=\mathrm{R}T,X$ is pressure, $Y$ is volume, R is universal gas constant and $T$ is temperature. The physical quantity equivalent to the ratio $\frac{a}{b}$ is :

Q19.In a Young's double slits experiment, the ratio of amplitude of light coming from slits is $2:1$. The ratio of the maximum to minimum intensity in the interference pattern is :

Q20.The mean free path of molecules of a certain gas at STP is 1500 d , where d is the diameter of the gas molecules. While maintaining the standard pressure, the mean free path of the molecules at 373 K is approximately :

Q21.A bi convex lens of focal length 10 cm is cut in two identical parts along a plane perpendicular to the principal axis. The power of each lens after cut is ______ D.

Q22.An atom absorbs a photon of wavelength 500 nm and emits another photon of wavelength 600 nm . The net energy absorbed by the atom in this process is $\mathrm{n}\times 10^{-4}\mathrm{eV}$. The value of n is ______.
[Assume the atom to be stationary during the absorption and emis …

Q23.Three point charges $\mathrm{q},-2\mathrm{q}$ and 2 q are placed on x -axis at a distance $x=0,x=\frac{3}{4}R$ and $x=R$ respectively from origin as shown. If $\mathrm{q}=2\times 10^{-6}\mathrm{C}$ and $\mathrm{R}=2\mathrm{cm}$, the magnitude of net force experienced by th …

Q24.In the circuit shown, the energy stored in the capacitor is $n\mu J$. The value of $n$ is ______.

Q25.An insulated copper wire of 100 turns is wrapped around a wooden cylindrical core of the cross-sectional area $24{\mathrm{cm}}^2$. The two ends of the wire are connected to a resistor. The total resistance in the circuit is $12\Omega$. If an externally applied uniform magnetic …

Q26.In an experiment with sonometer when a mass of 180 g is attached to the string, it vibrates with fundamental frequency of 30 Hz. When a mass m is attached, the string vibrates with fundamental frequency of 50 Hz. The value of m is $\_\_\_\_$ g.

Q27.A light rope is wound around a hollow cylinder of mass 5 kg and radius 70 cm. The rope is pulled with a force of 52.5 N. The angular acceleration of the cylinder will be $\_\_\_\_$ rad s${}^{-2}$.

Q28.A car accelerates from rest to $u\mathrm{m}/\mathrm{s}$. The energy spent in this process is E J. The energy required to accelerate the car from $u\mathrm{m}/\mathrm{s}$ to $2u\mathrm{m}/\mathrm{s}$ is nE J. The value of $n$ is $\_\_\_\_$.

Q29.Two plates A and B have thermal conductivities $84{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ and $126{\mathrm{Wm}}^{-1}{\mathrm{K}}^{-1}$ respectively. They have same surface area and same thickness. They are placed in contact along their surfaces. If the temperatures of the outer surfaces …

Q30.A straight wire AB of mass 40 g and length 50 cm is suspended by a pair of flexible leads in uniform magnetic field of magnitude 0.40 T as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is $\_\_\_\_$ A. (Take …

Q1.In the wet tests for detection of various cations by precipitation, ${\mathrm{Ba}}^{2+}$ cations are detected by obtaining precipitate of

Q2.The naturally occurring amino acid that contains only one basic functional group in its chemical structure is

Q3.Given below are two statements related to Ellingham diagram:
Statement-I : Ellingham diagrams can be constructed for formation of oxides, sulfides and halides of metals.
Statement-II : It consists of plots of ${\Delta }_{\mathrm{f}}{\mathrm{H}}^0$ vs T for formation of oxides of el …

Q4.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : The diameter of colloidal particles in solution should not be much smaller than wavelength of light to show Tyndall effect.
Reason R : The light scatters in all dir …

Q5.The total number of stereoisomers for the complex ${\left[\mathrm{Cr}(\mathrm{ox}{)}_2\mathrm{ClBr}\right]}^{3-}$ (where ox $=$ oxalate) is:

Q6.Better method for preparation of ${\mathrm{BeF}}_2$, among the following is

Q7.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A : Isotopes of hydrogen have almost same chemical properties, but difference in their rates of reaction.
Reason R : Isotopes of hydrogen have different enthalpy of bon …

Q8.Given below are two statements:
Statement I: Tropolone is an aromatic compound and has $8\pi$ electrons.
Statement II: $\pi$ electrons of $>\mathrm{C}=\mathrm{O}$ group in tropolone is involved in aromaticity.
In the light of the above statements, choose the correct answer …

Q9.Compound A from the following reaction sequence is:

Q10.The major product for the following reaction is:

$\mathrm{C}{\mathrm{H}}_2=\mathrm{CH}-\mathrm{CN}$ (acrylonitrile) $+$ $\mathrm{HO}-\mathrm{C}{\mathrm{H}}_2\mathrm{C}{\mathrm{H}}_2-\mathrm{SH}$ (2-mercaptoethanol) $⟶$ ?

Q11.Which of the following are the Green house gases?
A. Water vapour
B. Ozone
C. ${\mathrm{I}}_2$
D. Molecular hydrogen
Choose the most appropriate answer from the options given

Q12.Given below are two statements:

Statement I: ${\mathrm{SO}}_2$ and ${\mathrm{H}}_2\mathrm{O}$ both possess V-shaped structure.
Statement II: The bond angle of ${\mathrm{SO}}_2$ is less than that of ${\mathrm{H}}_2\mathrm{O}$.
In the light of the above statements, choose the most …

Q13.The correct group of halide ions which can be oxidised by oxygen in acidic medium is

Q14.What happens when methane undergoes combustion in systems A and B respectively?

Q15.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Order of acidic nature of the following compounds is A>B>C.

Reason R: Fluoro is a stronger electron withdrawing group than Chloro group.
In the light of the above s …

Q16.Identify the correct order of standard enthalpy of formation of sodium halides.

Q17.Match List I with List II

1-Bromopropane is reacted with reagents in List I to give product in List II

Q18.The covalency and oxidation state respectively of boron in $[{\mathrm{BF}}_4{]}^{-}$, are

Q19.Which of the following complexes will exhibit maximum attraction to an applied magnetic field?

Q20.0.400 g of an organic compound (X) gave 0.376 g of AgBr in Carius method for estimation of bromine. % of bromine in the compound (X) is ______.
(Given: Molar mass $\mathrm{AgBr}=188{\mathrm{g}\mathrm{mol}}^{-1}$, $\mathrm{Br}=80{\mathrm{g}\mathrm{mol}}^{-1}$)

Q21.1 g of a carbonate $({\mathrm{M}}_2{\mathrm{CO}}_3)$ on treatment with excess HCl produces 0.01 mol of ${\mathrm{CO}}_2$. The molar mass of ${\mathrm{M}}_2{\mathrm{CO}}_3$ is ______ ${\mathrm{g}\mathrm{mol}}^{-1}$. (Nearest integer)

Q22.See the following chemical reaction:
${\mathrm{Cr}}_2{\mathrm{O}}_7^{2-}+X{\mathrm{H}}^{+}+6{\mathrm{Fe}}^{2+}\to Y{\mathrm{Cr}}^{3+}+6{\mathrm{Fe}}^{3+}+Z{\mathrm{H}}_2\mathrm{O}$
The sum of X, Y and Z is ______.

Q23.If the formula of Borax is ${\mathrm{Na}}_2{\mathrm{B}}_4{\mathrm{O}}_x(\mathrm{OH}{)}_y\cdot z{\mathrm{H}}_2\mathrm{O}$, then $x+y+z=$ ______.

Q24.At 298 K, the standard reduction potential for ${\mathrm{Cu}}^{2+}/\mathrm{Cu}$ electrode is 0.34 V.

Given: ${\mathrm{K}}_{\mathrm{sp}}\mathrm{Cu}(\mathrm{OH}{)}_2=1\times 10^{-20}$
Take $\frac{2.303\mathrm{RT}}{\mathrm{F}}=0.059\mathrm{V}$
The reduction potential at …

Q25.20 mL of 0.1 M NaOH is added to 50 mL of 0.1 M acetic acid solution. The pH of the resulting solution is ____ $\times 10^{-2}$ (Nearest integer)

Given: $\mathrm{pKa}({\mathrm{CH}}_3\mathrm{COOH})=4.76$
$\log 2=0.30$
$\log 3=0.48$

Q26.$\mathrm{A}(\mathrm{g})\to 2\mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$ is a first order reaction. The initial pressure of the system was found to be 800 mm Hg which increased to 1600 mm Hg after 10 min. The total pressure of the system after 30 min will be ____ m …

Q27.The orbital angular momentum of an electron in 3s orbital is $\frac{\mathrm{xh}}{2\pi }$. The value of x is ____.

Q28.Sodium metal crystallizes in a body centred cubic lattice with unit cell edge length of $4\mathring{A}$. The radius of sodium atom is ____ $\times 10^{-1}\mathring{A}$ (Nearest integer)

Q29.Sea water contains $29.25\%\mathrm{NaCl}$ and $19\%{\mathrm{MgCl}}_2$ by weight of solution. The normal boiling point of the sea water is ____ ${}^{\circ }\mathrm{C}$ (Nearest integer)

Assume $100\%$ ionization for both NaCl and ${\mathrm{MgCl}}_2$
Given: …

Q1.If the system of equations
$2x+y-z=5$
$2x-5y+\lambda z=\mu$
$x+2y-5z=7$
has infinitely many solutions, then $(\lambda +\mu {)}^2+(\lambda -\mu {)}^2$ is equal to

Q2.The coefficient of $x^5$ in the expansion of ${\left(2x^3-\frac{1}{3x^2}\right)}^5$ is

Q3.The plane, passing through the points $(0,-1,2)$ and $(-1,2,1)$ and parallel to the line passing through $(5,1,-7)$ and $(1,-1,-1)$, also passes through the point

Q4.Let $\alpha ,\beta$ be the roots of the equation $x^2-\sqrt{2}x+2=0$. Then ${\alpha }^{14}+{\beta }^{14}$ is equal to

Q5.Let $a_1,a_2,a_3,\dots$ be a G.P. of increasing positive numbers. Let the sum of its $6^{\text{th}}$ and $8^{\text{th}}$ terms be 2 and the product of its $3^{\text{rd}}$ and $5^{\text{th}}$ terms be $\frac{1}{9}$. Then $6(a_2+a_4)(a_4+a_6)$ is equal to

Q6.Let $(\alpha ,\beta )$ be the centroid of the triangle formed by the lines $15x-y=82$, $6x-5y=-4$ and $9x+4y=17$. Then $\alpha +2\beta$ and $2\alpha -\beta$ are the roots of the equation

Q7.Let $|\vec{a}|=2$, $|\vec{b}|=3$ and the angle between the vectors $\vec{a}$ and $\vec{b}$ be $\frac{\pi }{4}$. Then $|(\vec{a}+2\vec{b})\times (2\vec{a}-3\vec{b}){|}^2$ is equal to

Q8.Let N be the foot of perpendicular from the point P $(1,-2,3)$ on the line passing through the points $(4,5,8)$ and $(1,-7,5)$. Then the distance of N from the plane $2x-2y+z+5=0$ is

Q9.If ${\lim }_{x\to 0}\frac{e^{ax}-\cos (bx)-\frac{cx{e}^{-cx}}{2}}{1-\cos (2x)}=17$, then $5a^2+b^2$ is equal to

Q10.Let the centre of a circle C be $(\alpha ,\beta )$ and its radius $r<8$. Let $3x+4y=24$ and $3x-4y=32$ be two tangents and $4x+3y=1$ be a normal to C. Then $(\alpha -\beta +r)$ is equal to

Q11.All words, with or without meaning, are made using all the letters of the word MONDAY. These words are written as in a dictionary with serial numbers. The serial number of the word MONDAY is

Q12.The range of $f(x)=4{\sin }^{-1}\left(\frac{x^2}{x^2+1}\right)$ is

Q13.The statement $(p\wedge (\sim q))\vee ((\sim p)\wedge q)\vee ((\sim p)\wedge (\sim q))$ is equivalent to

Q14.The random variable $X$ follows binomial distribution $B(n,p)$ for which the difference of the mean and the variance is 1. If $2P(X=2)=3P(X=1)$, then $n^{2}P(X>1)$ is equal to

Q15.Let for $A=\left[\begin{array}{ccc}1& 2& 3\\ a& 3& 1\\ 1& 1& 2\end{array}\right]$, $|A|=2$. If $|2\mathrm{adj}(2\mathrm{adj}(2A))|=32^n$, then $3n+\alpha$ is equal to

Q16.Let $S=\left\{Z\in C:\bar{Z}=i\left(Z^2+\mathrm{Re}(\bar{Z})\right)\right\}$. Then ${\sum }_{z\in S}|z{|}^2$ is equal to

Q17.The area of the region $\left\{(x,y):x^2\le y\le \left|x^2-4\right|,y\ge 1\right\}$ is

Q18.Let for a triangle ABC,
$\overrightarrow{AB}=-2\hat{i}+\hat{j}+3\hat{k}$
$\overrightarrow{CB}=\alpha \hat{i}+\beta \hat{j}+\gamma \hat{k}$
$\overrightarrow{CA}=4\hat{i}+3\hat{j}+\delta \hat{k}$
If $\delta >0$ and the area of the triangle ABC is $5\sqrt{6}$, then …

Q19.The line, that is coplanar to the line $\frac{x+3}{-3}=\frac{y-1}{1}=\frac{z-5}{5}$, is

Q20.The value of $\frac{e^{-\frac{\pi }{4}}+{\int }_0^{\frac{\pi }{4}}{e}^{-x}{\tan }^{50}xdx}{{\int }_0^{\frac{\pi }{4}}{e}^{-x}\left({\tan }^{49}x+{\tan }^{51}x\right)dx}$ is

Q21.The mean and standard deviation of the marks of 10 students were found to be 50 and 12 respectively. Later, it was observed that two marks 20 and 25 were wrongly read as 45 and 50 respectively. Then the correct variance is ______.

Q22.Let $\mathrm{A}=\{-4,-3,-2,0,1,3,4\}$ and $\mathrm{R}=\{(\mathrm{a},\mathrm{b})\in \mathrm{A}\times \mathrm{A}:\mathrm{b}=|\mathrm{a}|$ or ${\mathrm{b}}^2=\mathrm{a}+1\}$ be a relation on A. Then the minimum number of elements, that must be added to the relation $R$ s …

Q23.Let $\mathrm{f}(\mathrm{x})={\sum }_{\mathrm{k}=1}^{10}{\mathrm{kx}}^{\mathrm{k}},\mathrm{x}\in \mathrm{R}$. If $2f(2)+f^{\prime }(2)=119(2{)}^{\mathrm{n}}+1$ then n is equal to ______.

Q24.Total numbers of 3-digit numbers that are divisible by 6 and can be formed by using the digits 1, 2, 3, 4, 5 with repetition, is ______.

Q25.Let $[\alpha ]$ denote the greatest integer $\le \alpha$. Then $[\sqrt{1}]+[\sqrt{2}]+[\sqrt{3}]+\dots +[\sqrt{120}]$ is equal to ______.

Q26.For $x\in (-1,1]$, the number of solutions of the equation ${\sin }^{-1}x=2{\tan }^{-1}x$ is equal to ______.

Q27.If $y=y(x)$ is the solution of the differential equation $\frac{dy}{dx}+\frac{4x}{\left(x^2-1\right)}y=\frac{x+2}{{\left(x^2-1\right)}^{\frac{5}{2}}},x>1$ such that $\mathrm{y}(2)=\frac{2}{9}{\log }_{\mathrm{e}}(2+\sqrt{3})$ and …

Q28.The foci of a hyperbola are $(\pm 2,0)$ and its eccentricity is $\frac{3}{2}$. A tangent, perpendicular to the line $2x+3y=6$, is drawn at a point in the first quadrant on the hyperbola. If the intercepts made by the tangent on the x- and y-axes are a and b respectively, th …

Q29.Let $f_n={\int }_0^{\frac{\pi }{2}}\left({\sum }_{k=1}^n{\sin }^{k-1}x\right)\left({\sum }_{k=1}^n(2k-1){\sin }^{k-1}x\right)\cos xdx$, $n\in \mathbb{N}$. Then $f_{21}-f_{20}$ is equal to ______.

Q30.The remainder, when $7^{103}$ is divided by 17 is ______.