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Physics

A radio active material is reduced to \( {1}/{8} \) of its original amount in \( 3 \, \text{days} \). If \( 8 \times 10^{-3} \, \text{kg} \) of the material is left after \( 5 \, \text{days} \) the initial amount of the material is:

The equivalent resistance between \( A \) and \( B \) as shown in figure is:

For particle \( P \) revolving round the centre \( O \) with radius of circular path \( r \) and angular velocity \( \omega \), as shown in below figure, the projection of \( OP \) on the \( x \)-axis at time \( t \) is:

The acceleration due to gravity at height \( h \) above the earth if \( h << R \) (Radius of earth) is given by:

The trajectory of projectile, projected from the ground is given by \( y = x - \dfrac{x^2}{20} \). Where \( x \) and \( y \) are measured meter. The maximum height attained by the projectile will be:

The orbital angular momentum of a satellite is \( L \), when it is revolving in a circular orbit at height \( h \) from earth surface. If the distance of satellite from the earth centre is increased by eight times to its initial value, then the new angular momentum will be:

Match List I with List II

List I	List II
A Torque	I. \( ML^{-2}T^{-2} \)
B Stress	II. \( ML^{2}T^{-2} \)
C Pressure gradient	III. \( ML^{-1}T^{-1} \)
D Coefficient of viscosity	IV. \( ML^{-1}T^{-2} \)

Choose the correct answer from the options given below:

The waves emitted when a metal target is bombarded with high energy electrons are:

For a given transistor amplifier circuit in CE configuration \( V_{CC} = 1 \, \text{V} \), \( R_{C} = 1 \, \text{k}\Omega \), \( R_{b} = 100 \, \text{k}\Omega \) and \( \beta = 100 \). Value of base current \( I_{b} \) is:

10.

The power radiated from a linear antenna of length \( l \) is proportional to: (Given, \( \lambda \) \(=\) Wavelength of wave)

11.

Work done by a Carnot engine operating between temperatures \( 127^\circ \text{C} \) and \( 27^\circ \text{C} \) is \( 2 \, \text{kJ} \). The amount of heat transferred to the engine by the reservoir is:

12.

Electric potential at a point ‘P’ due to a point charge of \( 5 \times 10^{-9} \, \text{C} \) is \( 50 \, \text{V} \). The distance of ‘P’ from the point charge is:
(Assume, \( \dfrac{1}{4\pi \varepsilon_{0}} = 9 \times 10^{+9} \, \text{N m}^{2} \text{C}^{-2} \) )

13.

A hydraulic automobile lift is designed to lift vehicles of mass \( 5000 \, \text{kg} \). The area of cross section of the cylinder carrying the load is \( 250 \, \text{cm}^2 \). The maximum pressure the smaller piston would have to bear is: [Assume \( g = 10 \, \text{m/s}^2 \)]

14.

Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R
Assertion A: Electromagnets are made of soft iron.
Reason R: Soft iron has high permeability and low retentivity.
In the light of above, statements, choose the most appropriate answer from the options given below:

15.

A bullet of mass \( 0.1 \, \text{kg} \) moving horizontally with speed \( 400 \, \text{m s}^{-1} \) hits a wooden block of mass \( 3.9 \, \text{kg} \) kept on a horizontal rough surface. The bullet gets embedded into the block and moves \( 20 \, \text{m} \) before coming to rest. The coefficient of friction between the block and the surface is _____.
(Given \( g = 10 \, \text{m/s}^2 \))

16.

The temperature at which the kinetic energy of oxygen molecules becomes double then its value at \( 27^\circ \text{C} \) is:

17.

The width of fringe is \( 2 \, \text{mm} \) on the screen in a double slits experiment for the light of wavelength of \( 400 \, \text{nm} \). The width of the fringe for the light of wavelength \( 600 \, \text{nm} \) will be:

18.

Given below are two statements:
Statement I: Area under velocity-time graph gives the distance travelled by the body in a given time.
Statement II: Area under acceleration- time graph is equal to the change in velocity-in the given time.
In the light of given statements, choose the correct answer from the options given below:

19.

In photo electric effect
A. The photocurrent is proportional to the intensity of the incident radiation.
B. Maximum Kinetic energy with which photoelectrons are emitted depends on the intensity of incident light.
C. Max. K.E. with which photoelectrons are emitted depends on the frequency of incident light.
D. The emission of photoelectrons requires a minimum threshold intensity of incident radiation.
E. Max. K.E. of the photoelectrons is independent of the frequency of the incident light
Choose the correct answer from the options given below:

20.

An emf of \( 0.08 \, \text{V} \) is induced in a metal rod of length \( 10 \, \text{cm} \) held normal to a uniform magnetic field of \( 0.4 \, \text{T} \), when moves with a velocity of:

21.

The number density of free electrons in copper is nearly \( 8 \times 10^{28} \, \text{m}^{-3} \). A copper wire has its area of cross section \( = 2 \times 10^{-6} \, \text{m}^2 \) and is carrying a current of \( 3.2 \, \text{A} \). A drift speed of the electrons is ______ \( \times 10^{-6} \, \text{ms}^{-1} \).

22.

A hollow spherical ball of uniform density rolls up a curved surface with an initial velocity \( 3 \, \text{m/s} \) (as shown in figure). Maximum height with respect to the initial position covered by it will be ______ \( \text{cm} \) (take, \( g = 10 \, \text{m/s}^2 \)).

23.

Two transparent media having refractive indices \( 1.0 \) and \( 1.5 \) are separated by a spherical refracting surface of radius of curvature \( 30 \, \text{cm} \). The centre of curvature of surface is towards denser medium and a point object is placed on the principle axis in rarer medium at a distance of \( 15 \, \text{cm} \) from the pole of the surface. The distance of image from the pole of the surface is ______ \( \text{cm} \).

24.

A steel rod of length \( 1 \, \text{m} \) and cross sectional area \( 10^{-4} \, \text{m}^{2} \) is heated from \( 0^\circ \text{C} \) to \( 200^\circ \text{C} \) without being allowed to extend or bend. The compressive tension produced in the rod is \( \_\_\_\_\_\_\_\_\_ \times 10^{4} \, \text{N} \)
(Given Young’s modulus of steel \( = 2 \times 10^{11} \, \text{N m}^{-2} \), coefficient of linear expansion \( = 10^{-5} \, \text{K}^{-1} \))

25.

The ratio of magnetic field at the centre of a current carrying coil of radius \( r \) to the magnetic field at distance \( r \) from the centre of coil on its axis is \( \sqrt{x} : 1 \). The value of \( x \) is ________________.

26.

A body of mass \( 5 \, \text{kg} \) is moving with a momentum of \( 10 \, \text{kg m s}^{-1} \). Now a force of \( 2 \, \text{N} \) acts on the body in the direction of its motion for \( 5 \, \text{s} \). The increase in the Kinetic energy of the body is __________ \( \text{J} \).

27.

The ratio of wavelength of spectral line \( H_{\alpha} \) and \( H_{\beta} \) in the Balmer series is \( \dfrac{x}{20} \). The value of \( x \) is ________.

28.

A \( 600 \, \text{pF} \) capacitor is charged by \( 200 \, \text{V} \) supply. It is then disconnected from the supply and is connected to another uncharged \( 600 \, \text{pF} \) capacitor. Electrostatic energy lost in the process is __________ \( \mu \text{J} \).

29.

A guitar string of length \( 90 \, \text{cm} \) vibrates with a fundamental frequency of \( 120 \, \text{Hz} \). The length of the string producing a fundamental frequency of \( 180 \, \text{Hz} \) will be __________ \( \text{cm} \).

30.

A series combination of resistor of resistance \( 100 \, \Omega \), inductor of inductance \( 1 \, \text{H} \) and capacitor of capacitance \( 6.25 \, \mu \text{F} \) if connected to an ac source. The quality factor of the circuit will be ________.

JEE Main 2023 8th April Evening Shift

Physics Chemistry Mathematics

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