JEE Main 2023 · 11 Apr 2023 · Shift 2

Q1.Eight equal drops of water are falling through air with a steady speed of $10\mathrm{cm}/\mathrm{s}$. If the drops coalesce, the new velocity is:-

Q2.A car P travelling at $20{\mathrm{ms}}^{-1}$ sounds its horn at a frequency of 400 Hz. Another car Q is travelling behind the first car in the same direction with a velocity $40{\mathrm{ms}}^{-1}$. The frequency heard by the passenger of the car Q is approximately [Take, velo …

Q3.A plane electromagnetic wave of frequency 20 MHz propagates in free space along x-direction. At a particular space and time, $\overrightarrow{\mathrm{E}}=6.6\hat{\mathrm{j}}\mathrm{V}/\mathrm{m}$. What is $\overrightarrow{\mathrm{B}}$ at this point?

Q4.A capacitor of capacitance C is charged to a potential V. The flux of the electric field through a closed surface enclosing the positive plate of the capacitor is:

Q5.If force (F), velocity (V) and time (T) are considered as fundamental physical quantity, then dimensional formula of density will be:

Q6.In satellite communication, the uplink frequency band used is:

Q7.If V is the gravitational potential due to sphere of uniform density on it's surface, then it's value at the center of sphere will be:-

Q8.A body of mass 500 g moves along x-axis such that it's velocity varies with displacement x according to the relation $\mathrm{v}=10\sqrt{\mathrm{x}}\mathrm{m}/\mathrm{s}$ the force acting on the body is:-

Q9.A projectile is projected at $30^{\circ }$ from horizontal with initial velocity $40{\mathrm{ms}}^{-1}$. The velocity of the projectile at $\mathrm{t}=2\mathrm{s}$ from the start will be:
(Given $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$)

Q10.When one light ray is reflected from a plane mirror with $30^{\circ }$ angle of reflection, the angle of deviation of the ray after reflection is:

Q11.A spaceship of mass $2\times 10^4\mathrm{kg}$ is launched into a circular orbit close to the earth surface. The additional velocity to be imparted to the spaceship in the orbit to overcome the gravitational pull will be (if $\mathrm{g}=10\mathrm{m}/{\mathrm{s}}^2$ an …

Q12.The ratio of the de-Broglie wavelengths of proton and electron having same kinetic energy:
(Assume ${\mathrm{m}}_{\mathrm{p}}={\mathrm{m}}_{\mathrm{e}}\times 1849$)

Q13.The thermodynamic process, in which internal energy of the system remains constant is

Q14.The energy of ${\mathrm{He}}^{+}$ ion in its first excited state is. (The ground state energy for the Hydrogen atom is -13.6 eV ):

Q15.The logic operations performed by the given digital circuit is equivalent to:

Q16.The root mean square speed of molecules of nitrogen gas at $27^{\circ }\mathrm{C}$ is approximately:
(Given mass of a nitrogen molecule $=4.6\times 10^{-26}\mathrm{kg}$ and take Boltzmann constant ${\mathrm{k}}_{\mathrm{B}}=1.4\times 10^{-23}{\mathrm{JK}}^{-1}$ )

Q17.The current flowing through ${\mathrm{R}}_2$ is:

Q18.Given below are two statements : one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: A bar magnet dropped through a metallic cylindrical pipe takes more time to come down compared to a non-magnetic bar with same geometry and mass.

Reason R: For th …

Q19.An electron is allowed to move with constant velocity along the axis of current carrying straight solenoid.
A. The electron will experience magnetic force along the axis of the solenoid.
B. The electron will not experience magnetic force.
C. The electron will continue to move alo …

Q20.In the given circuit,
${\mathrm{C}}_1=2\mu \mathrm{F},{\mathrm{C}}_2=0.2\mu \mathrm{F},{\mathrm{C}}_3=2\mu \mathrm{F},{\mathrm{C}}_4=4\mu \mathrm{F}$, ${\mathrm{C}}_5=2\mu \mathrm{F},{\mathrm{C}}_6=2\mu \mathrm{F}$, the charge stored on capacitor ${\mathrm{C}}_4$ …

Q21.A circular plate is rotating in horizontal plane, about an axis passing through its center and perpendicular to the plate, with an angular velocity $\omega$. A person sits at the center having two dumbbells in his hands. When he stretches out his hands, the moment of inertia of t …

Q22.A nucleus disintegrates into two nuclear parts, in such a way that ratio of their nuclear sizes is $1:2^{1/3}$. Their respective speed have a ratio of $n:1$. The value of n is $\_\_\_\_$

Q23.Two identical cells each of emf 1.5 V are connected in series across a $10\Omega$ resistance. An ideal voltmeter connected across $10\Omega$ resistance reads 1.5 V . The internal resistance of each cell is
$\_\_\_\_$ $\Omega$.

Q24.A block of mass 5 kg starting from rest pulled up on a smooth incline plane making an angle of $30^{\circ }$ with horizontal with an affective acceleration of 1 ${\mathrm{ms}}^{-2}$. The power delivered by the pulling force at $\mathrm{t}=10\mathrm{s}$ from the start is $\_\_\_\_$ …

Q25.A coil has an inductance of 2 H and resistance of $4\Omega$. A 10 V is applied across the coil. The energy stored in the magnetic field after the current has built up to its equilibrium value will be $\_\_\_\_$ $\times 10^{-2}$ J

Q26.A metallic cube of side 15 cm moving along y-axis at a uniform velocity of $2{\mathrm{ms}}^{-1}$. In a region of uniform magnetic field of magnitude 0.5 T directed along z-axis. In equilibrium the potential difference between the faces of higher and lower potential developed beca …

Q27.A wire of density $8\times 10^3{kg/m}^3$ is stretched between two clamps 0.5 m apart. The extension developed in the wire is $3.2\times 10^{-4}\mathrm{m}$. If $Y=8\times 10^{10}{N/m}^2$, the fundamental frequency of vibration in the wire will be …

Q28.The surface tension of soap solution is $3.5\times 10^{-2}{\mathrm{Nm}}^{-1}$. The amount of work done required to increase the radius of soap bubble from 10 cm to 20 cm is $\_\_\_\_$ $\times 10^{-4}\mathrm{J}$.

Q29.As shown in the figure, a plane mirror is fixed at a height of 50 cm from the bottom of tank containing water $\left(\mu =\frac{4}{3}\right)$. The height of water in the tank is 8 cm. A small bulb is placed at the bottom of the water tank. The distance of image of the bulb formed …

Q1.Which hydride among the following is less stable?

Q2.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : (see structure) can be subjected to Wolff-Kishner reduction to give (see structure)

Reason R : Wolff-Kishner reduction is used to convert (see structure) into (se …

Q3.The major product formed in the following reaction is:
(see reaction scheme)
(A) (see structure)
(B) (see structure)
(C) (see structure)
(D) (see structure)

Choose the correct answer from the options given below :

Q4.Which of the following compounds is an example of Freon?

Q5.For a chemical reaction $\mathrm{A}+\mathrm{B}\to$ Product, the order is 1 with respect to A and B .
| 0.4 …

Q6.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : $[\mathrm{CoCl}({\mathrm{NH}}_3{)}_5{]}^{2+}$ absorbs at lower wavelength of light with respect to …

Q7.Given below are two statements, one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A : A solution of the product obtained by heating a mole of glycine with a mole of chlorine in presence of red phosphorous generates chiral carbon atom.

Reason R : A …

Q8.Compound ' B ' is
(see reaction scheme)

Choose the correct answer from the options given below :

Q9.Given below are two statements :

Statements I : Ethene at 333 to 343 K and 6-7 atm pressure in the presence of ${\mathrm{AlEt}}_3$ and ${\mathrm{TiCl}}_4$ undergoes addition polymerization to give LDP.

Statement II : Caprolactam at 533-543 K in ${\mathrm{H}}_2\mathrm{O}$ throu …

Q10.Which one of the following pairs is an example of polar molecular solids?

Q11.One mole of ${\mathrm{P}}_4$ reacts with 8 moles of ${\mathrm{SOCl}}_2$ to give 4 moles of A , $x$ mole of ${\mathrm{SO}}_2$ and 2 moles of B. A, B and $x$ respectively are

Q12.Compound from the following that will not produce precipitate on reaction with ${\mathrm{AgNO}}_3$ is :

Q13.A solution is prepared by adding 2g of " X " of 1 mole of water. Mass percent of " X " in the solution is :

Q14.Given below are two statements :

Statement-I : In the metallurgy process, sulphide ore is converted to oxide before reduction.

Statement-II : Oxide ores in general are easier to reduce.

In the light of the above statements, choose the most appropriate answer from the options g …

Q15.Alkali metal from the following with least melting point is :

Q16.What weight of glucose must be dissolved in 100 g of water to lower the vapour pressure by 0.20 mm Hg ?
(Assume dilute solution is being formed)
Given : Vapour pressure of pure water is 54.2 mm Hg at room temperature. Molar mass of glucose is …

Q17.The magnetic moment is measured in Bohr Magneton (BM).
Spin only magnetic moment of Fe in ${\left[\mathrm{Fe}{\left({\mathrm{H}}_2\mathrm{O}\right)}_6\right]}^{3+}$ and ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$ complexes respectively is :

Q18.Match List I with List II.

\begin{tabular}{|l|l|l|l|}
\hline \multicolumn{2}{|c|}{ List I } & \multicolumn{2}{c|}{ List II } \\
Complex & \multicolumn{2}{|c|}{ Colour } \\
\hline A. & $\mathrm{Mg}\left({\mathrm{NH}}_4\right){\mathrm{PO}}_4$ & I. & Brown \\
\hline B. & …

Q19.If ${\mathrm{Ni}}^{2+}$ is replaced by ${\mathrm{Pt}}^{2+}$ in the complex ${\left[{\mathrm{NiCl}}_2{\mathrm{Br}}_2\right]}^{2-}$, which of the following properties are expected to get changed?
A. Geometry
B. Geometrical isomerism
C. Optical isomerism
D. Magnetic properties

Q20.Number of compounds from the following which will not produce orange red precipitate with Benedict solution is ______

Glucose, maltose, sucrose, ribose, 2-deoxyribose, amylose, lactose.

Q21.4.5 moles each of hydrogen and iodine is heated in a sealed ten litre vessel. At equilibrium, 3 moles of HI were found. The equilibrium constant for ${\mathrm{H}}_2(\mathrm{g})+{\mathrm{I}}_2(\mathrm{g})\rightleftharpoons 2\mathrm{HI}(\mathrm{g})$ is ______

Q22.The number of correct statements about modern adsorption theory of heterogeneous catalysis from the following is ______
A. The catalyst is diffused over the surface of reactants.
B. Reactants are adsorbed on the surface of the catalyst.
C. Occurrence of chemical reaction on the c …

Q23.The number of correct statements from the following ______
A. For 1s orbital, the probability density is maximum at the nucleus.
B. For 2 s orbital, the probability density first increases to maximum and then decreases sharply to zero.
C. Boundary surface diagrams of the orbitals …

Q24.The number of possible isomeric products formed when 3-chloro-1-butene reacts with HCl through carbocation formation is ______

Q25.$\mathrm{Mg}{\left({\mathrm{NO}}_3\right)}_2\cdot {\mathrm{XH}}_2\mathrm{O}$ and $\mathrm{Ba}{\left({\mathrm{NO}}_3\right)}_2\cdot {\mathrm{YH}}_2\mathrm{O}$, represent formula of the crystalline forms of nitrate salts. Sum of X and Y is ____

Q26.The total number of intensive properties from the following is ____
Volume, Molar heat capacity, Molarity, ${\mathrm{E}}^{\theta }$ cell, Gibbs free energy change, Molar mass, Mole

Q27.The maximum number of lone pairs of electrons on the central atom from the following species is ____
${\mathrm{ClO}}_3^{-}$, ${\mathrm{XeF}}_4$, ${\mathrm{SF}}_4$ and ${\mathrm{I}}_3^{-}$

Q28.The volume of hydrogen liberated at STP by treating 2.4 g of magnesium with excess of hydrochloric acid is ____ $\times 10^{-2}$ L.

Given: Molar volume of gas is 22.4 L at STP.
Molar mass of magnesium is $24{\mathrm{g}\mathrm{mol}}^{-1}$.

Q29.The number of correct statements from the following is :
(A) ${\mathrm{E}}_{\text{cell}}$ is an intensive parameter.
(B) A negative ${\mathrm{E}}^{\Theta }$ means that the redox couple is a stronger reducing agent than the ${\mathrm{H}}^{+}/{\mathrm{H}}_2$ couple.
(C) The amount of el …

Q30.$\mathrm{C}{\mathrm{H}}_3-\mathrm{C}{\mathrm{H}}_2-\underset{|}{\underset{OH}{\mathrm{CH}}}-\mathrm{C}{\mathrm{H}}_3\underset{\text{(iii) }{\mathrm{D}}_2\mathrm{O}}{\overset{\text{(i) NaI, }{\mathrm{H}}_3\mathrm{P}{\mathrm{O}}_4;\text{(ii) Mg, dry ether}}{\to }}[X]$

Product $[X]$ formed in the above reaction is:

Q1.If $\left|\begin{array}{ccc}\mathrm{x}+1& \mathrm{x}& \mathrm{x}\\ \mathrm{x}& \mathrm{x}+\lambda & \mathrm{x}\\ \mathrm{x}& \mathrm{x}& \mathrm{x}+{\lambda }^2\end{array}\right|=\frac{9}{8}(103\mathrm{x}+81)$, then $\lambda$, $\frac{\lambda }{3}$ are the roots of the …

Q2.Let the line passing through the points, $\mathrm{P}(2,-1,2)$ and $\mathrm{Q}(5,3,4)$ meet the plane $\mathrm{x}-\mathrm{y}+\mathrm{z}=4$ at the point R. Then the distance of the point R from the plane $\mathrm{x}+2\mathrm{y}+3\mathrm{z}+2=0$ measured parallel to the li …

Q3.If the $1011^{\text{th}}$ term from the beginning in the binomial expansion of ${\left(\frac{4\mathrm{x}}{5}-\frac{5}{2\mathrm{x}}\right)}^{2022}$ is 1024 times the $1011^{\text{th}}$ term from the end, then $|\mathrm{x}|$ is equal to

Q4.Let the function $\mathrm{f}:[0,2]\to \mathrm{R}$ be defined as …

Q5.Let $y=y(x)$ be the solution of the differential equations $\frac{dy}{dx}+\frac{5}{x\left(x^5+1\right)}y=\frac{{\left(x^5+1\right)}^2}{x^7},x>0$. If $y(1)=2$, then $y(2)$ is equal to

Q6.If four distinct points with position vectors $\vec{a},\vec{b},\vec{c}$ and $\overrightarrow{\mathrm{d}}$ are coplanar; then $[\overrightarrow{\mathrm{a}}\overrightarrow{\mathrm{b}}\overrightarrow{\mathrm{c}}]$ is equal to

Q7.If $\mathrm{f}:\mathbb{R}\to \mathbb{R}$ be a continuous function satisfying
${\int }_0^{\pi /2}f(\sin 2x)\cdot \sin xdx+\alpha {\int }_0^{\pi /4}f(\cos 2x)\cdot \cos xdx=0$, then $\alpha$ is equal to

Q8.If the system of linear equations
$7x+11y+\alpha z=13$
$5x+4y+7z=\beta$
$175x+194y+57z=361$
has infinitely many solutions, then $\alpha +\beta +2$ is equal to

Q9.The domain of the function
$\mathrm{f}(\mathrm{x})=\frac{1}{\sqrt{[\mathrm{x}{]}^2-3[\mathrm{x}]-10}}$ is (where $[\mathrm{x}]$ denotes the greatest integer less than or equal to x)

Q10.Let P be the plane passing through the points (5, 3, 0), (13, 3, -2) and (1, 6, 2). For $\alpha \in \mathrm{N}$, if the distances of the points $\mathrm{A}(3,4,\alpha )$ and $\mathrm{B}(2,\alpha ,a)$ from the plane P are 2 and 3 respectively, then the positive value of …

Q11.The converse of the statement $((\sim p)\wedge q)\Rightarrow r$ is

Q12.The angle of elevation of the top P of a tower from the feet of one person standing due South of the tower is $45^{\circ }$ and from the feet of another person standing due west of the tower is $30^{\circ }$. If the height of the tower is 5 meters, then the distance (in meters) …

Q13.Let a, b, c and d be positive real numbers such that $a+b+c+d=11$. If the maximum value of $a^5{b}^3{c}^{2}d$ is $3750\beta$, then the value of $\beta$ is

Q14.If the radius of the largest circle with centre $(2,0)$ inscribed in the ellipse $x^2+4y^2=36$ is $r$, then $12r^2$ is equal to

Q15.Let the mean of 6 observation 1, 2, 4, 5, x and y be 5 and their variance be 10. Then their mean deviation about the mean is equal to

Q16.The sum of the coefficients of three consecutive terms in the binomial expansion of $(1+x{)}^{n+2}$, which are in the ratio $1:3:5$, is equal to

Q17.If the letters of the word MATHS are permuted and all possible words so formed are arranged as in a dictionary with serial numbers, then the serial number of the word THAMS is

Q18.For $a\in \mathbb{C}$, let $A=\{z\in \mathbb{C}:\mathrm{Re}(a+\bar{z})>\mathrm{Im}(\bar{a}+z)\}$ and $B=\{z\in \mathbb{C}:\mathrm{Re}(a+\bar{z})<\mathrm{Im}(\bar{a}+z)\}$. Then among the two statements:
(S1): If …

Q19.Let $A=\{1,3,4,6,9\}$ and $B=\{2,4,5,8,10\}$. Let R be a relation defined on $A\times B$ such that $R=\{((a_1,b_1),(a_2,b_2)):a_1\le b_2$ and $b_1\le a_2\}$. Then the number of elements in the set R is

Q20.Let $f$ and $g$ be two functions defined by
$f(x)=\{\begin{array}{ll}x+1,& x<0\\ |x-1|,& x\ge 0\end{array}$ and $g(x)=\{\begin{array}{ll}x+1,& x<0\\ 1,& x\ge 0\end{array}$.
Then $(g\circ f)(x)$ is

Q21.The number of points, where the curve $f(x)=e^{8x}-e^{6x}-3e^{4x}-e^{2x}+1$, $x\in \mathbb{R}$ cuts $x$-axis, is equal to

Q22.Let the probability of getting head for a biased coin be $\frac{1}{4}$. It is tossed repeatedly until a head appears. Let N be the number of tosses required. If the probability that the equation $64x^2+5Nx+1=0$ has no real root is $\frac{p}{q}$, where $p$ and $q$ are …

Q23.Let $\vec{a}=\hat{i}+2\hat{j}+3\hat{k}$ and $\vec{b}=\hat{i}+\hat{j}-\hat{k}$. If $\vec{c}$ is a vector such that $\vec{a}\cdot \vec{c}=11$, $\vec{b}\cdot (\vec{a}\times \vec{c})=27$ and $\vec{b}\cdot \vec{c}=-\sqrt{3}|\vec{b}|$, then …

Q24.Let $S=\left\{z\in \mathbb{C}-\{i,2i\}:\frac{z^2+8iz-15}{z^2-3iz-2}\in \mathbb{R}\right\}$. If $\alpha -\frac{13}{11}i\in S$, $\alpha \in \mathbb{R}-\{0\}$, then $242{\alpha }^2$ is equal to

Q25.For $\mathrm{k}\in \mathbb{N}$, if the sum of the series
$1+\frac{4}{\mathrm{k}}+\frac{8}{{\mathrm{k}}^2}+\frac{13}{{\mathrm{k}}^3}+\frac{19}{{\mathrm{k}}^4}+\dots$ is 10, then the value of k is

Q26.Let $\mathrm{A}=\{1,2,3,4,5\}$ and $\mathrm{B}=\{1,2,3,4,5,6\}$. Then the number of functions $\mathrm{f}:\mathrm{A}\to \mathrm{B}$ satisfying $\mathrm{f}(1)+\mathrm{f}(2)=\mathrm{f}(4)-1$ is equal to

Q27.Let the tangent to the parabola ${\mathrm{y}}^2=12\mathrm{x}$ at the point $(3,\alpha )$ be perpendicular to the line $2\mathrm{x}+2\mathrm{y}=3$. Then the square of distance of the point $(6,-4)$ from the normal to the hyperbola …

Q28.Let the line $\ell :\mathrm{x}=\frac{1-\mathrm{y}}{-2}=\frac{\mathrm{z}-3}{\lambda },\lambda \in \mathbb{R}$ meet the plane $\mathrm{P}:\mathrm{x}+2\mathrm{y}+3\mathrm{z}=4$ at the point $(\alpha ,\beta ,\gamma )$. If the angle between the line $\ell$ and the plane P is …

Q29.If the line ${\ell }_1:3\mathrm{y}-2\mathrm{x}=3$ is the angular bisector of the lines ${\ell }_2:x-y+1=0$ and ${\ell }_3:\alpha x+\beta y+17=0$, then ${\alpha }^2+{\beta }^2-\alpha -\beta$ is equal to

Q30.If A is the area in the first quadrant enclosed by the curve $\mathrm{C}:2{\mathrm{x}}^2-\mathrm{y}+1=0$, the tangent to C at the point (1,3) and the line $\mathrm{x}+\mathrm{y}=1$, then the value of 60A is