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Physics

An object is placed at a distance of \( 12 \, \text{cm} \) in front of a plane mirror. The virtual and erect image is formed by the mirror. Now the mirror is moved by \( 4 \, \text{cm} \) towards the stationary object. The distance by which the position of image would be shifted, will be:

Two satellites of masses \( m \) and \( 3m \) revolve around the earth in circular orbits of radii \( r \) and \( 3r \) respectively. The ratio of orbital speeds of the satellites respectively is:

Consider two containers A and B containing monoatomic gases at the same Pressure (\( P \)), Volume (\( V \)) and Temperature (\( T \)). The gas in A is compressed isothermally to \( \dfrac{1}{8} \) of its original volume while the gas in B is compressed adiabatically to \( \dfrac{1}{8} \) of its original volume. The ratio of final pressure of gas in B to that of gas in A is:

Match List I with List II:

List I	List II
(A) \( 3 \) Translational degrees of freedom	(I) Monoatomic gases
(B) \( 3 \) Translational, \( 2 \) rotational degrees of freedoms	(II) Polyatomic gases
(C) \( 3 \) Translational, \( 2 \) rotational and \( 1 \) vibrational degrees of freedom	(III) Rigid diatomic gases
(D) \( 3 \) Translational, \( 3 \) rotational and more than one vibrational degrees of freedom	(IV) Nonrigid diatomic gases

Choose the correct answer from the options given below:

The equivalent resistance of the circuit shown below between points a and b is:

A physical quantity \( P \) is given as \( P = \dfrac{a^{2} b^{3}}{c \sqrt{d}} \)
The percentage error in the measurement of \( a \), \( b \), \( c \) and \( d \) are \( 1\% \), \( 2\% \), \( 3\% \) and \( 4\% \) respectively. The percentage error in the measurement of quantity \( P \) will be:

Given below are two statements:
Statement I : If the number of turns in the coil of a moving coil galvanometer is doubled then the current sensitivity becomes double.
Statement II : Increasing current sensitivity of a moving coil galvanometer by only increasing the number of turns in the coil will also increase its voltage sensitivity in the same ratio
In the light of the above statements, choose the correct answer from the options given below:

Assuming the earth to be a sphere of uniform mass density, the weight of a body at a depth \( d = \dfrac{R}{2} \) from the surface of earth, if its weight on the surface of earth is \( 200 \, \text{N} \), will be: (Given \( R \) = radius of earth)

A Zener diode of power ration \( 1.6 \, \text{W} \) is to be used as voltage regulator. If the Zener diode has a breakdown of \( 8 \, \text{V} \) and it has to regulate voltage fluctuating between \( 3 \, \text{V} \) and \( 10 \, \text{V} \). The value of resistance \( R_8 \) for safe operation of diode will be:

10.

The angular momentum for the electron in Bohr’s orbit is \( L \). If the electron in assumed to revolve in second orbit of hydrogen atom, then the change in angular momentum will be:

11.

The energy of an electromagnetic wave contained in a small volume oscillates with:

12.

Given below are two statements:
Statement I : Maximum power is dissipated in a circuit containing an inductor, a capacitor and a resistor connected in series with an AC source, when resonance occurs
Statement II : Maximum power is dissipated in a circuit containing pure resistor due to zero phase difference between current and voltage.
In the light of the above statement, choose the correct answer from the potions given below:

13.

A particle of mass \( m \) moving with velocity \( v \) collides with a stationary particle of mass \( 2m \). After collision, they stick together and continue to move together with velocity.

14.

The de Broglie wavelength of a molecule in a gas at room temperature \( (300 \, \text{K}) \) is \( \lambda_1 \). If the temperature of the gas is increased to \( 600 \, \text{K} \), then the de Broglie wavelength of the same gas molecule becomes.

15.

Given below are two statements:
Statement I : Pressure in a reservoir of water is same at all points at the same level of water.
Statement II: The pressure applied to enclosed water is transmitted in all directions equally.
In the light of the above statements, choose the correct answer from the options given below:

16.

A carrier wave of amplitude \( 15 \, \text{V} \) is modulated by a sinusoidal base band signal of amplitude \( 3 \, \text{V} \). The ratio of maximum amplitude to minimum amplitude in an amplitude modulated wave is:

17.

The position-time graphs for two students A and B returning from the school to their homes are shown in figure:

(A) A lives closer to the school (B) B lives closer to the school (C) A takes lesser time to reach home (D) A travles faster than B (E) B travel faster than A
Choose the correct answer from the options given below:

18.

The equivalent capacitance of the combination shown is:

19.

The range of the projectile projected at an angle of \( 15^\circ \) with horizontal is \( 50 \, \text{m} \). If the projectile is projected with same velocity at an angle of \( 45^\circ \) with horizontal, then its range will be:

20.

A particle executes S.H.M. of amplitude \( A \) along \( x \)-axis. At \( t = 0 \), the position of the particle is \( x=\dfrac{A}{2} \) and it moves along positive \( x \)-axis. The displacement of particle in time \( t \) is \( x = A \sin(\omega t + \delta) \), then the value \( \delta \) will be:

21.

If the earth suddenly shrinks to \( \dfrac{1}{64} \) th of its original volume with its mass remaining the same, the period of rotation of earth becomes \( \dfrac{24}{x} \, \text{h} \). The value of \( x \) is ________.

22.

A transverse harmonic wave on a string is given by \( y(x,t)=5\sin(6t+0.003x) \) where \( x \) and \( y \) are in \( \text{cm} \) and \( t \) in sec. The wave velocity is __________ \( \text{m s}^{-1} \).

23.

The current required to be passed trough a solenoid of \( 15 \, \text{cm} \) length and \( 60 \) turns in order to demagnetise a bar magnet of magnetic intensity \( 2.4 \times 10^{3} \, \text{A m}^{-1} \) is __________ \( \text{A} \).

24.

The decay constant for a radioactive nuclide is \( 1.5\times 10^{-5} \, \text{s}^{-1} \). Atomic weight of the substance is \( 60 \, \text{g mole}^{-1} \), \( (N_A=6\times 10^{23}) \). The activity of \( 1.0 \, \mu \text{g} \) of the substance is __________ \( \times 10^{10} \, \text{Bq} \).

25.

Three concentric spherical metallic shells X, Y and Z of radius \( a \), \( b \) and \( c \) respectively \([ a < b < c ]\) have surface charge densities \( \sigma \), \( -\sigma \) and \( \sigma \), respectively. The shells X and Z are at same potential. If the radii of X and Y are \( 2 \, \text{cm} \) and \( 3 \, \text{cm} \), respectively. The radius of shell Z is ________ \( \text{cm} \).

26.

A \( 1 \, \text{m} \) long metal rod XY completes the circuit as shown in figure. The plane of the circuit is perpendicular to the magnetic field of flux density \( 0.15 \, \text{T} \). If the resistance of the circuit is \( 5 \, \Omega \), the force needed to move the rod in direction, as indicated, with a constant speed of \( 4 \, \text{m/s} \) will be ______ \( 10^{-3} \, \text{N} \).

27.

Two wires each of radius \( 0.2 \, \text{cm} \) and negligible mass, one made of steel and the other made of brass are loaded as shown in the figure. The elongation of the steel wire is ______ \( \times 10^{-6} \, \text{m} \). [Young’s modulus for steel \( = 2 \times 10^{11} \, \text{N m}^{-2} \) and \( g = 10 \, \text{m s}^{-2} \)]

28.

Unpolarised light of intensity \( 32 \, \text{W m}^{-2} \) passes through the combination of three polaroids such that the pass axis of the last polaroid is perpendicular to that of the pass axis of first polaroid. If intensity of emerging light is \( 3 \, \text{W m}^{-2} \), then the angle between pass axis of fist two polaroids is ________ \( ^\circ \).

29.

A closed circular tube of average radius \( 15 \, \text{cm} \), whose inner walls are rough, is kept in vertical plane. A block of mass \( 1 \, \text{kg} \) just fit inside the tube. The speed of block is \( 22 \, \text{m/s} \), when it is introduced at the top of tube. After completing five oscillations, the block stops at the bottom region of tube. The work done by the tube on the block is ________ \( \text{J} \). (Given \( g = 10 \, \text{m/s}^2 \)).

30.

\( 10 \) resistors each of resistance \( 10 \, \Omega \) can be connected in such as to get maximum and minimum equivalent resistance. The ratio of maximum and minimum equivalent resistance will be _______.

JEE Main 2023 10th April Morning Shift

Physics Chemistry Mathematics

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