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For the logic circuit shown, the output waveform at \( Y \) is:

Given below are two statements:
Statement-I: If heat is added to a system, its temperature must increase.
Statement-II: If positive work is done by a system in a thermodynamic process, its volume must increase. In the light of the above statements, choose the correct answer from the options given below.

Certain galvanometers have a fixed core made of non-magnetic metallic material. The function of this metallic material is:

Given below are two statements:
Statement-I: If \( E \) be the total energy of a satellite moving around the earth, then its potential energy will be \( \dfrac{E}{2} \).
Statement-II: The kinetic energy of a satellite revolving in an orbit is equal to the half the magnitude of total energy \( E \).
In the light of the above statements, choose the most appropriate answer from the options given below.

The engine of a train moving with speed \( 10 \, \text{ms}^{-1} \) towards a platform sounds a whistle at frequency \( 400 \, \text{Hz} \). The frequency heard by a passenger inside the train is:
(Neglect air speed. Speed of sound in air \( = 330 \, \text{ms}^{-1} \))

At any instant the velocity of a particle of mass \( 500 \, \text{g} \) is \( (2t\hat{i} + 3t^{2}\hat{j}) \, \text{ms}^{-1} \). If the force acting on the particle at \( t = 1 \, \text{s} \) is \( (\hat{i} + x\hat{j}) \, \text{N} \). Then the value of \( x \) will be:

A cylindrical wire of mass \( (0.4 \pm 0.01) \, \text{g} \) has length \( (8 \pm 0.04) \, \text{cm} \) and radius \( (6 \pm 0.03) \, \text{mm} \). The maximum error in its density will be:

Graphical variation of electric field due to a uniformly charged insulating solid sphere of radius \( R \), with distance \( r \) from the centre \( O \) is represented by:

An aluminium rod with Young’s modulus \( Y = 7.0 \times 10^{10} \, \text{N}/\text{m}^{2} \) undergoes elastic strain of \( 0.04\% \). The energy per unit volume stored in the rod in SI unit is:

In a reflecting telescope, a secondary mirror is used to:

Two forces having magnitude \( A \) and \( \dfrac{A}{2} \) are perpendicular to each other. The magnitude of their resultant is:

A charge particle moving in magnetic field \( B \), has the components of velocity along \( B \) as well as perpendicular to \( B \). The path of the charge particle will be:

In this figure the resistance of the coil of galvanometer \( G \) is \( 2 \Omega \). The emf of the cell is \( 4 \, \text{V} \). The ratio of potential difference across \( C_1 \) and \( C_2 \) is:

Proton \( (P) \) and electron \( (e) \) will have same de-Broglie wavelength when the ratio of their momentum is (assume, \( m_p = 1849\, m_e \) ):

The weight of a body on the earth is \( 400 \, \text{N} \). Then weight of the body when taken to a depth half of the radius of the earth will be:

Dimension of \( \dfrac{1}{\mu_0 \, \epsilon_0} \) should be equal to:

A TV transmitting antenna is \( 98 \, \text{m} \) high and the receiving antenna is at the ground level. If the radius of the earth is \( 6400 \, \text{km} \), the surface area covered by the transmitting antenna is approximately.

An air bubble of volume \( 1 \, \text{cm}^3 \) rises from the bottom of a lake \( 40 \, \text{m} \) deep to the surface at a temperature of \( 12^\circ \text{C} \). The atmospheric pressure is \( 1 \times 10^5 \, \text{Pa} \), the density of water is \( 1000 \, \text{kg}/\text{m}^3 \) and \( g = 10 \, \text{m}/\text{s}^2 \). There is no difference of the temperature of water at the depth of \( 40 \, \text{m} \) and on the surface. The volume of air bubble when it reaches the surface will be:

Two particles A and B are thrown with initial velocities of \( 40 \, \text{m/s} \) and \( 60 \, \text{m/s} \) at angles \( 30^\circ \) and \( 60^\circ \) with the horizontal respectively. The ratio of their ranges respectively is:
\( (g = 10 \, \text{m/s}^2) \)

For a nucleus \( {}^{A}_{Z}X \) having mass number \( A \) and atomic number \( Z \).
A. The surface energy per nucleon \( (b_s) = -a_1 A^{2/3} \)
B. The Coulomb contribution to the binding energy \( b_c = -a_2 \dfrac{Z(Z-1)}{A^{4/3}} \)
C. The volume energy \( b_v = a_3 A \)
D. Decrease in the bonding energy is proportional to surface area
E. While estimating the surface energy, it is assumed that each nucleon interacts with \( 12 \) nucleons. \( (a_1, a_2 \text{ and } a_3 \text{ are constants}) \)
Choose the most appropriate answer from the options given below:

The magnetic intensity at the centre of a long current carrying solenoid is found to be \( 1.6 \times 10^3 \, \text{A m}^{-1} \). If the number of turns is \( 8 \) per cm, then the current flowing through the solenoid is ________ \( \text{A} \).

An oscillating LC circuit consists of a \( 75 \, \text{mH} \) inductor and a \( 1.2 \, \mu \text{F} \) capacitor. If the maximum charge to the capacitor is \( 2.7 \, \mu \text{C} \). The maximum current in the circuit will be ______ \( \text{mA} \).

An electric dipole of dipole moment is \( 6.0 \times 10^{-6} \, \text{C m} \) placed in a uniform electric field of \( 1.5 \times 10^{3} \, \text{N C}^{-1} \) in such a way that dipole moment is along electric field. The work done in rotating dipole by \( 180^\circ \) in this field will be ______ \( \text{mJ} \).

A nucleus with mass number \( 242 \) and binding energy per nucleon as \( 7.6 \, \text{MeV} \) breaks into two fragment each with mass number \( 121 \). If each fragment nucleus has binding energy per nucleon as \( 8.1 \, \text{MeV} \), the total gain in binding energy is ______ \( \text{MeV} \).

An air bubble of diameter \( 6 \, \text{mm} \) rises steadily through a solution of density \( 1750 \, \text{kg} / \text{m}^3 \) at the rate of \( 0.35 \, \text{cm}/\text{s} \). The co-efficient of viscosity of the solution (neglect density of air) is ________ \( \text{Pas} \).
(Given, \( g = 10 \, \text{m}\,\text{s}^{-2} \) )

The momentum of a body is increased by \( 50\% \). The percentage increase in the kinetic energy of the body is ________ \( \% \).

A current of \( 2 \, \text{A} \) flows through a wire of cross-sectional area \( 25.0 \, \text{mm}^{2} \). The number of free electrons in a cube meter are \( 2.0 \times 10^{28} \). The drift velocity of the electrons is ________ \( \times 10^{-6} \, \text{m}\,\text{s}^{-1} \).
(Given, charge on electron \( = 1.6 \times 10^{-19} \, \text{C} \))

An organ pipe \( 40 \, \text{cm} \) long is open at both ends. The speed of sound in air is \( 360 \, \text{m}\,\text{s}^{-1} \). The frequency of the second harmonic is ________ \( \text{Hz} \).

Two vertical parallel mirrors A and B are separated by \( 10 \, \text{cm} \). A point object O is placed at a distance of \( 2 \, \text{cm} \) from mirror A. The distance of the second nearest image behind mirror A from the mirror A is ________ \( \text{cm} \).

The moment of inertia of a semicircular ring about an axis, passing through the center and perpendicular to the plane of ring, is \( \dfrac{1}{x} MR^{2} \), where \( R \) is the radius and \( M \) is the mass of the semicircular ring. The value of \( x \) will be ________.

JEE Main 2023 8th April Morning Shift

Physics Chemistry Mathematics

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Dimension of \( \dfrac{1}{\mu_0 \, \epsilon_0} \) should be equal to: