JEE Main 2023 · 10 Apr 2023 · Shift 2

Q1.A person travels x distance with velocity ${\mathrm{v}}_1$ and then x distance with velocity ${\mathrm{v}}_2$ in the same direction. The average velocity of the person is v , then the relation between $\mathrm{v},{\mathrm{v}}_1$ and ${\mathrm{v}}_2$ will be :

Q2.The half-life of a radioactive substance is T. The time taken, for disintegrating $\frac{7}{8}$ th part of its original mass will be :

Q3.A gas mixture consists of 2 moles of oxygen and 4 moles of neon at temperature T. Neglecting all vibrational modes, the total internal energy of the system will be :

Q4.In an experiment with Vernier callipers of least count 0.1 mm , when two jaws are joined together the zero of Vernier scale lies right to the zero of the main scale and $6^{\text{th }}$ division of Vernier scale coincides with the main scale division. While measuring the diame …

Q5.Given below are two statements:

Statement I: For diamagnetic substance $-1\le \chi <0$, where $\chi$ is the magneticsusceptibility.

Statement II: Diamagnetic substances when placed in an external magnetic field, tend to move from stronger to weaker part of the field.

In t …

Q6.The distance between two plates of a capacitor is d and its capacitance is ${\mathrm{C}}_1$, when air is the medium between the plates. If a metal sheet of thickness $\frac{2\mathrm{d}}{3}$ and of same area as plate is introduced between the plates, the capacitance of the c …

Q7.Given below are two statements:

Statement I: Rotation of the earth shows effect on the value of acceleration due to gravity (g).

Statement II: The effect of rotation of the earth on the value of ' $g$ ' at the equator is minimum and that at the pole is maximum.

In the light …

Q8.The time period of a satellite, revolving above earth's surface at a height equal to $R$ will be (Given $\mathrm{g}={\pi }^2\mathrm{m}/{\mathrm{s}}^2,\mathrm{R}=$ radius of earth)

Q9.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: An electric fan continues to rotate for some time after the current is switched off.
Reason R: Fan continuous to rotate due to inertia of motion.
In the light of abo …

Q10.The amplitude of magnetic field in an electromagnetic wave propagating along y -axis is $6.0\times 10^{-7}\mathrm{T}$. The maximum value of electric field in the electromagnetic wave is:

Q11.A gas is compressed adiabatically, which one of the following statement is NOT true.

Q12.The ratio of intensities at two points P and Q on the screen in a Young's double slit experiment where phase difference between two wave of same amplitude are $\pi /3$ and $\pi /2$, respectively are

Q13.The variation of stopping potential (${\mathrm{V}}_0$) as a function of the frequency ($v$) of the incident light for a metal is shown in figure. The work function of the surface is

Q14.For a periodic motion represented by the equation
$\mathrm{Y}=\sin \omega \mathrm{t}+\cos \omega \mathrm{t}$
The amplitude of the motion is

Q15.In a metallic conductor, under the effect of applied electric field, the free electrons of the conductor

Q16.Young's moduli of the material of wires A and B are in the ratio of $1:4$, while its area of cross sections are in the ratio of $1:3$. If the same amount of load is applied to both the wires, the amount of elongation produced in the wires $A$ and $B$ will be in the rati …

Q17.Two projectiles are projected at $30^{\circ }$ and $60^{\circ }$ with the horizontal with the same speed. The ratio of the maximum height attained by the two projectiles respectively is:

Q18.A message signal of frequency 3 kHz is used to modulate a carrier signal of frequency 1.5 MHz . The bandwidth of the amplitude modulated wave is

Q19.If each diode has a forward bias resistance of $25\Omega$ in the below circuit,

Which of the following options is correct:

Q20.A bar magnet is released from rest along the axis of a very long vertical copper tube. After some time the magnet will

Q21.A square loop of side 2.0 cm is placed inside a long solenoid that has 50 turns per centimetre and carries a sinusoidally varying current of amplitude 2.5 A and angular frequency $700\mathrm{rad}{\mathrm{s}}^{-1}$. The central axes of the loop and solenoid coincide. The amplitu …

Q22.A rectangular block of mass 5 kg attached to a horizontal spiral spring executes simple harmonic motion of amplitude 1 m and time period 3.14 s . The maximum force exerted by spring on block is ____ N.

Q23.If $917\mathring{A}$ be the lowest wavelength of Lyman series then the lowest wavelength of Balmer series will be ____ Å.

Q24.Figure below shows a liquid being pushed out of the tube by a piston having area of cross section $2.0{\mathrm{cm}}^2$. The area of cross section at the outlet is $10{\mathrm{mm}}^2$. If the piston is pushed at a speed of $4\mathrm{cm}{\mathrm{s}}^{-1}$, the speed of …

Q25.A straight wire carrying a current of 14 A is bent into a semicircular arc of radius 2.2 cm as shown in the figure. The magnetic field produced by the current at the centre (O) of the arc is ______ $\times 10^{-4}$ T

Q26.A point object, 'O' is placed in front of two thin symmetrical coaxial convex lenses ${\mathrm{L}}_1$ and ${\mathrm{L}}_2$ with focal length 24 cm and 9 cm respectively. The distance between two lenses is 10 cm and the object is placed 6 cm away from lens ${\mathrm{L}}_1$ as show …

Q27.A rectangular parallelopiped is measured as 1 cm $\times$ 1 cm $\times$ 100 cm. If its specific resistance is $3\times 10^{-7}\Omega$ m, then the resistance between its two opposite rectangular faces will be ______ $\times 10^{-7}\Omega$.

Q28.A force of $-\mathrm{P}\hat{\mathrm{k}}$ acts on the origin of the coordinate system. The torque about the point $(2,-3)$ is $\mathrm{P}(\mathrm{a}\hat{\mathrm{i}}+\mathrm{b}\hat{\mathrm{j}})$, the ratio of $\frac{\mathrm{a}}{\mathrm{b}}$ is $\frac{\mathrm{x}}{2}$. The value o …

Q29.If the maximum load carried by an elevator is 1400 kg (600 kg - Passenger + 800 kg - elevator), which is moving up with a uniform speed of $3{\mathrm{ms}}^{-1}$ and the frictional force acting on it is 2000 N, then the maximum power used by the motor is ______ $\mathrm{kW}$ ( …

Q30.An electron revolves around an infinite cylindrical wire having uniform linear charge density $2\times 10^{-8}{\mathrm{Cm}}^{-1}$ in circular path under the influence of attractive electrostatic field as shown in the figure. The velocity of electron with which it is revolving is …

Q1.Incorrect method of preparation for alcohols from the following is:

Q2.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: The energy required to form ${\mathrm{Mg}}^{2+}$ from Mg is much higher than that required to produce ${\mathrm{Mg}}^{+}$.
Reason R: ${\mathrm{Mg}}^{2+}$ is small ion and …

Q3.In Carius tube, an organic compound 'X' is treated with sodium peroxide to form a mineral acid 'Y'. The solution of ${\mathrm{BaCl}}_2$ is added to 'Y' to form a precipitate 'Z'. 'Z' is used for the quantitative estimation of an extra element. 'X' could be:

Q4.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: 3.1500 g of hydrated oxalic acid dissolved in water to make 250.0 mL solution will result in 0.1 M oxalic acid solution.
Reason R: Molar mass of hydrated oxalic acid …

Q5.Buna-S can be represented as:

Q6.In the reaction give below:

The product 'X' is:

Q7.Ferric chloride is applied to stop bleeding because:

Q8.The reaction used for preparation of soap from fat is:

Q9.The decreasing order of hydride affinity for following carbocations is:
A. (see structure)
B. (see structure)
C. (see structure)
D. (see structure)
Choose the correct answer from the options given below:

Q10.The correct relationship between unit cell edge length 'a' and radius of sphere 'r' for face-centred and body centred cubic structures respectively are:

Q11.Number of water molecules in washing soda and soda ash respectively are:

Q12.The delicate balance of ${\mathrm{CO}}_2$ and ${\mathrm{O}}_2$ is NOT disturbed by:

Q13.The correct order of the number of unpaired electrons in the given complexes is
A. ${\left[\mathrm{Fe}(\mathrm{CN}{)}_6\right]}^{3-}$
B. ${\left[{\mathrm{FeF}}_6\right]}^{3-}$
C. ${\left[{\mathrm{CoF}}_6\right]}^{3-}$
D. ${\left[\mathrm{Cr}(\text{oxalate}{)}_3\right]}^{3-}$
E. …

Q14.The correct order for acidity of the following hydroxyl compound is:
A. ${\mathrm{CH}}_3\mathrm{OH}$
B. ${\left({\mathrm{CH}}_3\right)}_3\mathrm{COH}$
C. (see structure)
D. (see structure)
E. (see structure)

Choose the correct answer from the options given below:

Q15.The major product 'P' formed in the given reaction is:

Q16.Match List I with List II

List I: Complex
List II: Crystal Field splitting energy (${\Delta }_0$)

Choose the correct answer from the options given below:

Q17.Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.
Assertion A: Physical properties of isotopes of hydrogen are different.
Reason R: Mass difference between isotopes of hydrogen is very large.
In the light of the above statements …

Q18.Match List-I with List-II.

List-I: Substance
List-II: Property

Choose the correct answer from the options given below:
List-I:
(A) 16 g of ${\mathrm{CH}}_4(\mathrm{g})$
(B) 1 g of ${\mathrm{H}}_2(\mathrm{g})$
(C) 1 mole of ${\mathrm{N}}_2(\mathrm{g})$ …

Q19.The correct order of metallic character is:

Q20.Gibbs energy vs T plot for the formation of oxides is given below:

For the given diagram, the correct statement is-

Q21.$\mathrm{A}(\mathrm{g})\rightleftharpoons 2\mathrm{B}(\mathrm{g})+\mathrm{C}(\mathrm{g})$

For the given reaction, if the initial pressure is 450 mm Hg and the pressure at time t is 720 mm Hg at a constant temperature T and constant volume V. The fraction of …

Q22.In alkaline medium, the reduction of permanganate anion involves a gain of ______ electrons.

Q23.The number of endothermic process/es from the following is ______
A. ${\mathrm{I}}_2(\mathrm{g})\to 2\mathrm{I}(\mathrm{g})$
B. $\mathrm{HCl}(\mathrm{g})\to \mathrm{H}(\mathrm{g})+\mathrm{Cl}(\mathrm{g})$
C. …

Q24.The number of molecules from the following which contain only two lone pair of electrons is
${\mathrm{H}}_2\mathrm{O},{\mathrm{N}}_2,\mathrm{CO},{\mathrm{XeF}}_4,{\mathrm{NH}}_3,\mathrm{NO},{\mathrm{CO}}_2,{\mathrm{F}}_2$

Q25.The difference in the oxidation state of Xe between the oxidised product of Xe formed on complete hydrolysis of ${\mathrm{XeF}}_4$ and ${\mathrm{XeF}}_4$ is ______

Q26.An aqueous solution of volume $300{\mathrm{cm}}^3$ contains 0.63 g of protein. The osmotic pressure of the solution at 300 K is 1.29 mbar. The molar mass of the protein is ______ $\mathrm{g}{\mathrm{mol}}^{-1}$

Given: $\mathrm{R}=0.083\mathrm{L}$ bar …

Q27.For a metal ion, the calculated magnetic moment is 4.90 BM. This metal ion has ______ number of unpaired electrons.

Q28.The electron in the ${\mathrm{n}}^{\text{th}}$ orbit of ${\mathrm{Li}}^{2+}$ is excited to ($\mathrm{n}+1$) orbit using the radiation of energy $1.47\times 10^{-17}\mathrm{J}$ (as shown in the diagram). The value of $n$ is ______.

Given …

Q29.The specific conductance of 0.0025 M acetic acid is $5\times 10^{-5}\mathrm{S}{\mathrm{cm}}^{-1}$ at a certain temperature. The dissociation constant of acetic acid is ______ × $10^{-7}$. (Nearest integer)

Consider limiting molar conductivity of …

Q30.The number of incorrect statement/s from the following is ______

A. The successive half lives of zero order reactions decreases with time.

B. A substance appearing as reactant in the chemical equation may not affect the rate of reaction

C. Order and molecularity of a chemical …

Q1.Let $f$ be a continuous function satisfying ${\int }_0^{{\mathrm{t}}^2}\left(\mathrm{f}(\mathrm{x})+{\mathrm{x}}^2\right)\mathrm{dx}=\frac{4}{3}{\mathrm{t}}^3,\forall \mathrm{t}>0$. Then $\mathrm{f}\left(\frac{{\pi }^2}{4}\right)$ is equal to :

Q2.Eight persons are to be transported from city A to city B in three cars of different makes. If each car can accommodate at most three persons, then the number of ways, in which they can be transported, is:

Q3.For, $\alpha ,\beta ,\gamma ,\delta \in \mathbb{N}$, if …

Q4.Let the image of the point $\mathrm{P}(1,2,6)$ in the plane passing through the points $\mathrm{A}(1,2,0),\mathrm{B}(1,4,1)$ and $\mathrm{C}(0,5,1)$ be $\mathrm{Q}(\alpha ,\beta ,\gamma )$. Then $\left({\alpha }^2+{\beta }^2+{\gamma }^2\right)$ is equal to :

Q5.Let $\mathrm{A}=\{2,3,4\}$ and $\mathrm{B}=\{8,9,12\}$. Then the number of elements in the relation …

Q6.If $A=\frac{1}{5!6!7!}\left[\begin{array}{ccc}5!& 6!& 7!\\ 6!& 7!& 8!\\ 7!& 8!& 9!\end{array}\right]$, then $|\mathrm{adj}(\mathrm{adj}(2A))|$ is equal to :

Q7.Let A be the point $(1,2)$ and B be any point on the curve $x^2+y^2=16$. If the centre of the locus of the point P , which divides the line segment AB in the ratio $3:2$ is the point $\mathrm{C}(\alpha ,\beta )$, then the length of the line segment AC is

Q8.Let a die be rolled n times. Let the probability of getting odd numbers seven times be equal to the probability of getting odd numbers nine times. If the probability of getting even numbers twice is $\frac{\mathrm{k}}{2^{15}}$, then k is equal to :

Q9.Let $g(x)=f(x)+f(1-x)$ and $f^{\prime \prime }(x)>0,x\in (0,1)$.
If $g$ is decreasing in the interval $(0,\alpha )$ and increasing in the interval $(\alpha ,1)$, then …

Q10.Let a circle of radius 4 be concentric to the ellipse $15x^2+19y^2=285$. Then the common tangents are inclined to the minor axis of the ellipse at the angle.

Q11.Let $\vec{a}=2\hat{i}+7\hat{j}-\hat{k},\vec{b}=3\hat{i}+5\hat{k}$ and $\vec{c}=\hat{i}-\hat{j}+2\hat{k}$. Let $\vec{d}$ be a vector which is perpendicular to both $\vec{a}$ and $\vec{b}$, and $\vec{c}\cdot \vec{d}=12$. Then …

Q12.If ${\mathrm{S}}_{\mathrm{n}}=4+11+21+34+50+\dots$. to n terms, then $\frac{1}{60}\left({\mathrm{S}}_{29}-{\mathrm{S}}_9\right)$ is equal to

Q13.If the points P and Q are respectively the circumcentre and the orthocentre of a $△\mathrm{ABC}$, then $\overrightarrow{\mathrm{PA}}+\overrightarrow{\mathrm{PB}}+\overrightarrow{\mathrm{PC}}$ is equal to

Q14.The statement $\sim [\mathrm{p}\vee (\sim (\mathrm{p}\wedge \mathrm{q}))]$ is equivalent to

Q15.Let $\mathrm{S}=\left\{\mathrm{x}\in \left(-\frac{\pi }{2},\frac{\pi }{2}\right):9^{1-{\tan }^2\mathrm{x}}+9^{{\tan }^2\mathrm{x}}=10\right\}$ and $\beta ={\sum }_{\mathrm{x}\in \mathrm{s}}{\tan }^2\left(\frac{\mathrm{x}}{3}\right)$, then $\frac{1}{6}(\beta -14{)}^2$ is equa …

Q16.If the coefficients of $x$ and $x^2$ in $(1+x{)}^p(1-x{)}^q$ are 4 and -5 respectively, then $2p+3q$ is equal to

Q17.Let the line $\frac{x}{1}=\frac{6-y}{2}=\frac{z+8}{5}$ intersect the lines $\frac{x-5}{4}=\frac{y-7}{3}=\frac{z+2}{1}$ and $\frac{x+3}{6}=\frac{3-y}{3}=\frac{z-6}{1}$ at the points A and B respectively. Then the distance of the mid-point of the line segment AB from the plan …

Q18.Let $S=\{z=x+iy:\frac{2z-3i}{4z+2i}$ is a real number $\}$.

Then which of the following is NOT correct?

Q19.Let the number $(22{)}^{2022}+(2022{)}^{22}$ leave the remainder $\alpha$ when divided by 3 and $\beta$ when divided by 7. Then $({\alpha }^2+{\beta }^2)$ is equal to

Q20.Let $\mu$ be the mean and $\sigma$ be the standard deviation of the distribution

\begin{tabular}{|l|l|l|l|l|l|l|}
\hline ${\mathrm{x}}_{\mathrm{i}}$ & 0 & 1 & 2 & 3 & 4 & 5 \\
\hline ${\mathrm{f}}_{\mathrm{i}}$ & $\mathrm{k}+2$ & 2 k & ${\mathrm{k}}^2-1$ & ${\mathrm{k}}^2-1$ & …

Q21.Let the equations of two adjacent sides of a parallelogram ABCD be $2\mathrm{x}-3\mathrm{y}=-23$ and $5\mathrm{x}+4\mathrm{y}=23$. If the equation of its one diagonal AC is $3\mathrm{x}+7\mathrm{y}=23$ and the distance of A from the other diagonal is d , then …

Q22.Let S be the set of values of $\lambda$, for which the system of equations
$6\lambda \mathrm{x}-3\mathrm{y}+3\mathrm{z}=4{\lambda }^2$,
$2\mathrm{x}+6\lambda \mathrm{y}+4\mathrm{z}=1$,
$3x+2y+3\lambda z=\lambda$ has no solution. Then …

Q23.Let the foot of perpendicular from the point $\mathrm{A}(4,3,1)$ on the plane $P:x-y+2z+3=0$ be $N$. If $B(5,\alpha ,\beta ),\alpha ,\beta \in \mathbb{Z}$ is a point on plane P such that the area of the triangle ABN in $3\sqrt{2}$, then …

Q24.Let quadratic curve passing through the point $(-1,0)$ and touching the line $\mathrm{y}=\mathrm{x}$ at $(1,1)$ be $\mathrm{y}=\mathrm{f}(\mathrm{x})$. Then the x -intercept of the normal to the curve at the point $(\alpha ,\alpha +1)$ in the first quadrant is

Q25.Let the tangent at any point P on a curve passing through the points $(1,1)$ and $\left(\frac{1}{10},100\right)$, intersect positive x-axis and y-axis at the points A and B respectively. If $\mathrm{PA}:\mathrm{PB}=1:\mathrm{k}$ and $\mathrm{y}=\mathrm{y}(\mathrm{x})$ …

Q26.Suppose ${\mathrm{a}}_1,{\mathrm{a}}_2,2,{\mathrm{a}}_3,{\mathrm{a}}_4$ be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is $\frac{49}{2}$, t …

Q27.If the domain of the function $f(x)={\sec }^{-1}\left(\frac{2x}{5x+3}\right)$ is $[\alpha ,\beta )\cup (\gamma ,\delta ]$, then $|3\alpha +10(\beta +\gamma )+21\delta |$ is equal to ______.

Q28.The sum of all the four-digit numbers that can be formed using all the digits $2,1,2,3$ is equal to ______.

Q29.In the figure, ${\theta }_1+{\theta }_2=\frac{\pi }{2}$ and $\sqrt{3}(\mathrm{BE})=4(\mathrm{AB})$. If the area of $△\mathrm{CAB}$ is $2\sqrt{3}-3$ unit ${}^2$, when $\frac{{\theta }_2}{{\theta }_1}$ is the largest, then the perimeter (in unit) of …

Q30.If the area of the region $\left\{(x,y):\left|x^2-2\right|\le y\le x\right\}$ is A, then $6\mathrm{A}+16\sqrt{2}$ is equal to ______.