JEE Main 2023 30th January Morning Shift Question Paper with Solutions

The magnetic moments associated with two closely wound circular coils $\mathrm{A}$ and $\mathrm{B}$ of radius $\mathrm{r}_{\mathrm{A}}=10$ $\mathrm{cm}$ and $\mathrm{r}_{\mathrm{B}}=20 \mathrm{~cm}$ respectively are equal if : (Where $\mathrm{N}_{\mathrm{A}}, \mathrm{I}_{\mathrm{A}}$ and $\mathrm{N}_{\mathrm{B}}, \mathrm{I}_{\mathrm{B}}$ are number of turn and current of $\mathrm{A}$ and $\mathrm{B}$ respectively)

The figure represents the momentum time ($\mathrm{p}-\mathrm{t}$) curve for a particle moving along an axis under the influence of the force. Identify the regions on the graph where the magnitude of the force is maximum and minimum respectively?

If $\left(t_{3}-t_{2}\right) < t_{1}$

A point source of light is placed at the centre of curvature of a hemispherical surface. The source emits a power of $24 \mathrm{~W}$. The radius of curvature of hemisphere is $10 \mathrm{~cm}$ and the inner surface is completely reflecting. The force on the hemisphere due to the light falling on it is ____________ $\times~10^{-8} \mathrm{~N}$.

A thin uniform rod of length $2 \mathrm{~m}$, cross sectional area '$A$' and density '$\mathrm{d}$' is rotated about an axis passing through the centre and perpendicular to its length with angular velocity $\omega$. If value of $\omega$ in terms of its rotational kinetic energy $E$ is $\sqrt{\frac{\alpha E}{A d}}$ then value of $\alpha$ is ______________.

In an experiment for estimating the value of focal length of converging mirror, image of an object placed at $40 \mathrm{~cm}$ from the pole of the mirror is formed at distance $120 \mathrm{~cm}$ from the pole of the mirror. These distances are measured with a modified scale in which there are 20 small divisions in $1 \mathrm{~cm}$. The value of error in measurement of focal length of the mirror is $\frac{1}{\mathrm{~K}} \mathrm{~cm}$. The value of $\mathrm{K}$ is __________.

In a screw gauge, there are 100 divisions on the circular scale and the main scale moves by $0.5 \mathrm{~mm}$ on a complete rotation of the circular scale. The zero of circular scale lies 6 divisions below the line of graduation when two studs are brought in contact with each other. When a wire is placed between the studs, 4 linear scale divisions are clearly visible while $46^{\text {th }}$ division the circular scale coincide with the reference line. The diameter of the wire is ______________ $\times 10^{-2} \mathrm{~mm}$.

In Young's double slit experiment, two slits $S_{1}$ and $S_{2}$ are '$d$' distance apart and the separation from slits to screen is $\mathrm{D}$ (as shown in figure). Now if two transparent slabs of equal thickness $0.1 \mathrm{~mm}$ but refractive index $1.51$ and $1.55$ are introduced in the path of beam $(\lambda=4000$ $\mathop A\limits^o$) from $\mathrm{S}_{1}$ and $\mathrm{S}_{2}$ respectively. The central bright fringe spot will shift by ___________ number of fringes.

Electric field in a certain region is given by $\overrightarrow{\mathrm{E}}=\left(\frac{\mathrm{A}}{x^{2}} \hat{i}+\frac{\mathrm{B}}{y^{3}} \hat{j}\right) \text {. The } \mathrm{SI} \text { unit of } \mathrm{A} \text { and } \mathrm{B}$ are :

Match Column-I with Column-II :

	Column-I ($x$-t graphs)		Column-II ($v$-t graphs)
A.		I.
B.		II.
C.		III.
D.		IV.

Choose the correct answer from the options given below:

A capacitor of capacitance $900 \mu \mathrm{F}$ is charged by a $100 \mathrm{~V}$ battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as $x \times 10^{-} { }^{2} \mathrm{~J}$. The value of $x$ is _____________.

A massless square loop, of wire of resistance $10 \Omega$, supporting a mass of $1 \mathrm{~g}$, hangs vertically with one of its sides in a uniform magnetic field of $10^{3} \mathrm{G}$, directed outwards in the shaded region. A dc voltage $\mathrm{V}$ is applied to the loop. For what value of $\mathrm{V}$, the magnetic force will exactly balance the weight of the supporting mass of $1 \mathrm{~g}$ ?

(If sides of the loop $=10 \mathrm{~cm}, \mathrm{~g}=10 \mathrm{~ms}^{-2}$)

The general displacement of a simple harmonic oscillator is $x = A\sin \omega t$. Let T be its time period. The slope of its potential energy (U) - time (t) curve will be maximum when $t = {T \over \beta }$. The value of $\beta$ is ______________.

A sinusoidal carrier voltage is amplitude modulated. The resultant amplitude modulated wave has maximum and minimum amplitude of $120 \mathrm{~V}$ and $80 \mathrm{~V}$ respectively. The amplitude of each sideband is :

A small object at rest, absorbs a light pulse of power $20 \mathrm{~mW}$ and duration $300 \mathrm{~ns}$. Assuming speed of light as $3 \times 10^{8} \mathrm{~m} / \mathrm{s}$, the momentum of the object becomes equal to :

In the following circuit, the magnitude of current I₁, is ___________ A.

The pressure $(\mathrm{P})$ and temperature ($\mathrm{T})$ relationship of an ideal gas obeys the equation $\mathrm{PT}^{2}=$ constant. The volume expansion coefficient of the gas will be :

Speed of an electron in Bohr's $7^{\text {th }}$ orbit for Hydrogen atom is $3.6 \times 10^{6} \mathrm{~m} / \mathrm{s}$. The corresponding speed of the electron in $3^{\text {rd }}$ orbit, in $\mathrm{m} / \mathrm{s}$ is :

Choose the correct relationship between Poisson ratio $(\sigma)$, bulk modulus (K) and modulus of rigidity $(\eta)$ of a given solid object :

A horse rider covers half the distance with $5 \mathrm{~m} / \mathrm{s}$ speed. The remaining part of the distance was travelled with speed $10 \mathrm{~m} / \mathrm{s}$ for half the time and with speed $15 \mathrm{~m} / \mathrm{s}$ for other half of the time. The mean speed of the rider averaged over the whole time of motion is $\frac{x}{7} \mathrm{~m} / \mathrm{s}$. The value of $x$ is ___________.

A ball of mass $200 \mathrm{~g}$ rests on a vertical post of height $20 \mathrm{~m}$. A bullet of mass $10 \mathrm{~g}$, travelling in horizontal direction, hits the centre of the ball. After collision both travels independently. The ball hits the ground at a distance $30 \mathrm{~m}$ and the bullet at a distance of $120 \mathrm{~m}$ from the foot of the post. The value of initial velocity of the bullet will be (if $g=10 \mathrm{~m} / \mathrm{s}^{2}$) :

The height of liquid column raised in a capillary tube of certain radius when dipped in liquid A vertically is, $5 \mathrm{~cm}$. If the tube is dipped in a similar manner in another liquid $\mathrm{B}$ of surface tension and density double the values of liquid $\mathrm{A}$, the height of liquid column raised in liquid $\mathrm{B}$ would be __________ m.

In a series LR circuit with $\mathrm{X_L=R}$, power factor P₁. If a capacitor of capacitance C with $\mathrm{X_C=X_L}$ is added to the circuit the power factor becomes P₂. The ratio of P₁ to P₂ will be :

As per the given figure, if $\frac{\mathrm{dI}}{\mathrm{dt}}=-1 \mathrm{~A} / s$ then the value of $\mathrm{V}_{\mathrm{AB}}$ at this instant will be ____________ $\mathrm{V}$.

If the gravitational field in the space is given as $\left(-\frac{K}{r^{2}}\right)$. Taking the reference point to be at $\mathrm{r}=2 \mathrm{~cm}$ with gravitational potential $\mathrm{V}=10 \mathrm{~J} / \mathrm{kg}$. Find the gravitational potential at $\mathrm{r}=3 \mathrm{~cm}$ in SI unit (Given, that $\mathrm{K}=6 \mathrm{~Jcm} / \mathrm{kg}$)

The output waveform of the given logical circuit for the following inputs A and B as shown below, is :

Heat is given to an ideal gas in an isothermal process.

A. Internal energy of the gas will decrease.

B. Internal energy of the gas will increase.

C. Internal energy of the gas will not change.

D. The gas will do positive work.

E. The gas will do negative work.

Choose the correct answer from the options given below :

The charge flowing in a conductor changes with time as $\mathrm{Q}(\mathrm{t})=\alpha \mathrm{t}-\beta \mathrm{t}^{2}+\gamma \mathrm{t}^{3}$. Where $\alpha, \beta$ and $\gamma$ are constants. Minimum value of current is :

As per the given figure, a small ball P slides down the quadrant of a circle and hits the other ball Q of equal mass which is initially at rest. Neglecting the effect of friction and assume the collision to be elastic, the velocity of ball Q after collision will be :

(g = 10 m/s²)

A person has been using spectacles of power $-1.0$ dioptre for distant vision and a separate reading glass of power $2.0$ dioptres. What is the least distance of distinct vision for this person :

Two isolated metallic solid spheres of radii $\mathrm{R}$ and $2 \mathrm{R}$ are charged such that both have same charge density $\sigma$. The spheres are then connected by a thin conducting wire. If the new charge density of the bigger sphere is $\sigma^{\prime}$. The ratio $\frac{\sigma^{\prime}}{\sigma}$ is :

Formation of photochemical smog involves the following reaction in which $\mathrm{A}, \mathrm{B}$ and $\mathrm{C}$ are respectively.

$$\begin{aligned} & \text { i. } \mathrm{NO}_{2} \stackrel{\mathrm{h} v}{\longrightarrow} \mathrm{A}+\mathrm{B} \\ & \text { ii. } \mathrm{B}+\mathrm{O}_{2} \rightarrow \mathrm{C} \\ & \text { iii. } \mathrm{A}+\mathrm{C} \rightarrow \mathrm{NO}_{2}+\mathrm{O}_{2} \end{aligned}$$

Choose the correct answer from the options given below :

When 2 litre of ideal gas expands isothermally into vacuum to a total volume of 6 litre, the change in internal energy is ____________ J. (Nearest integer)

For $\mathrm{OF}_{2}$ molecule consider the following :

A. Number of lone pairs on oxygen is 2 .

B. FOF angle is less than $104.5^{\circ}$.

C. Oxidation state of $\mathrm{O}$ is $-2$.

D. Molecule is bent '$\mathrm{V}$' shaped.

E. Molecular geometry is linear.

correct options are:

Lithium aluminium hydride can be prepared from the reaction of :

A $300 \mathrm{~mL}$ bottle of soft drink has $0.2 ~\mathrm{M}~ \mathrm{CO}_{2}$ dissolved in it. Assuming $\mathrm{CO}_{2}$ behaves as an ideal gas, the volume of the dissolved $\mathrm{CO}_{2}$ at $\mathrm{STP}$ is ____________ $\mathrm{mL}$. (Nearest integer)

Given : At STP, molar volume of an ideal gas is $22.7 \mathrm{~L} \mathrm{~mol}^{-1}$

In the wet tests for identification of various cations by precipitation, which transition element cation doesn't belong to group IV in qualitative inorganic analysis?

The alkaline earth metal sulphate(s) which are readily soluble in water is/are :

A. $\mathrm{BeSO}_{4}$

B. $\mathrm{MgSO}_{4}$

C. $\mathrm{CaSO}_{4}$

D. $\mathrm{SrSO}_{4}$

E. $\mathrm{BaSO}_{4}$

Choose the correct answer from the options given below :

In the extraction of copper, its sulphide ore is heated in a reverberatory furnace after mixing with silica to:

During the qualitative analysis of $\mathrm{SO}_{3}^{2-}$ using dilute $\mathrm{H}_{2} \mathrm{SO}_{4}, \mathrm{SO}_{2}$ gas is evolved which turns $\mathrm{K}_{2} \mathrm{Cr}_{2} \mathrm{O}_{7}$ solution (acidified with dilute $\mathrm{H}_{2} \mathrm{SO}_{4}$) :

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

Assertion (A) : Ketoses give Seliwanoff's test faster than Aldoses.

Reason (R) : Ketoses undergo $\beta$-elimination followed by formation of furfural.

In the light of the above statements, choose the correct answer from the options given below :

Some amount of dichloromethane $\left(\mathrm{CH}_{2} \mathrm{Cl}_{2}\right)$ is added to $671.141 \mathrm{~mL}$ of chloroform $\left(\mathrm{CHCl}_{3}\right)$ to prepare $2.6 \times 10^{-3} \mathrm{M}$ solution of $\mathrm{CH}_{2} \mathrm{Cl}_{2}(\mathrm{DCM})$. The concentration of $\mathrm{DCM}$ is ___________ ppm (by mass).

Given :

atomic mass : C = 12

H = 1

Cl = 35.5

density of $\mathrm{CHCl}_{3}=1.49 \mathrm{~g} \mathrm{~cm}^{-3}$