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Physics

A block of mass \( m \) is placed on a surface having vertical cross section given by \( y=\dfrac{x^{2}}{4} \). If coefficient of friction is \( 0.5 \), the maximum height above the ground at which block can be placed without slipping is:

33.

If a nuclear fission reaction of an isotope of mass \( M \), three similar daughter nuclei of same mass are formed. The speed of a daughter nuclei in terms of mass defect \( \Delta M \) will be:

34.

A beam of unpolarized light of intensity \( I_{0} \) passed through a polaroid \( A \) and then through another polaroid \( B \) which is oriented so that its principal plane makes an angle of \( 45^{\circ} \) relative to that of \( A \). The intensity of emergent light is:

35.

If the total energy transferred to a surface in time \( t \) is \( 6.48\times10^{5}\, \text{J} \), then the magnitude of the total momentum delivered to this surface for complete absorption will be:

36.

A particle of charge \( '-q '\) and mass \(' m' \) moves in a circle of radius \( 'r '\) around an infinitely long line charge of linear charge density \(' +\lambda' \). Then time period will be given as:
(Consider \( k \) as Coulomb’s constant)

37.

If mass is written as \( m = k c^{P} G^{-1/2} h^{1/2} \) then the value of \( P \) will be: (Constants have their usual meaning with \( k \) a dimensionless constant).

38.

If \( 50 \) Vernier divisions are equal to \( 49 \) main scale division of a traveling microscope and one smallest reading of main scale is \( 0.5 \, \text{mm} \), the Vernier constant of traveling microscope is:

39.

In the given circuit, the voltage across load resistance \( (R_L) \) is:

40.

If three moles of monoatomic gas \( \left( \gamma = \dfrac{5}{3} \right) \) is mixed with two moles of a diatomic gas \( \left( \gamma = \dfrac{7}{5} \right) \), the value of adiabatic exponent \( \gamma \) for the mixture is:

41.

For the photoelectric effect, the maximum kinetic energy \( (E_k) \) of the photoelectrons is plotted against the frequency \( (v) \) of the incident photons as shown in figure. The slope of the graph gives

42.

Choose the correct statement for processes A & B shown in figure.

43.

Projectiles A and B are thrown at angles of \( 45^\circ \) and \( 60^\circ \) with vertical respectively from top of a \( 400 \, \text{m} \) high tower. If their range and times of flight are same, the ratio of their speeds of projection \( v_A : v_B \) is:
[Take \( g = 10 \, \text{m s}^{-2} \) ]

44.

A block of ice at \( -10^\circ \text{C} \) is slowly heated and converted to steam at \( 100^\circ \text{C} \). Which of the following curves represent the phenomenon qualitatively:

45.

Three block A, B and C are pulled on a horizontal smooth surface by a force of \( 80 \, \text{N} \) as shown in figure.
The tension \( T_1 \) and \( T_2 \) in the string are respectively:

46.

An electron revolving in \( n^{\text{th}} \) Bohr orbit has magnetic moment \( \mu_n \). If \( \mu_n\) \( \\\alpha n^x \), the value of \( x \) is:

47.

A block of mass \( 1 \, \text{kg} \) is pushed up a surface inclined to horizontal at an angle of \( 60^\circ \) by a force of \( 10 \, \text{N} \) parallel to the inclined surface as shown in figure. When the block is pushed up by \( 10 \, \text{m} \) along inclined surface, the work done against frictional force is:
[ \( g = 10 \, \text{m} /\, \text{s}^{-2} \) ]

48.

When a potential difference \( V \) is applied across a wire of resistance \( R \), it dissipate energy at a rate \( W \). If the wire is cut into two halve and these halve are connected mutually parallel across the same supply, the energy dissipation rate will become:

49.

Escape velocity of a body from earth is \\( 11.2 \\, \\text{km/s} \\). If the radius of a planet be one-third the radius of earth and mass be one-sixth that of earth, the escape velocity from the planet is:

50.

An alternating voltage \( V(t)=220\sin 100\pi t \) volt is applied to a purely resistive load of \( 50 \, \Omega \). The time taken for the current to rise from half of the peak value to the peak value is:

51.

Match List I with List II.

List-I	List-II
(A). Gauss’s law of magnetostatics	(I). \( \oint \vec{E}\cdot \vec d{a}=\dfrac{1}{\varepsilon_{0}}\int \rho \, dV \)
(B). Faraday’s law of electro magnetic induction	(II). \( \oint \vec{B}\cdot \vec d{a}=0 \)
(C). Ampere’s Law	(III). \( \oint \vec{E}\cdot \vec d{l}=\dfrac{-d}{dt}\int \vec{B}\cdot \vec d{a} \)
(D). Gaus’s law of electrostatics	(IV). \( \oint \vec{B}\cdot \vec d{l}=\mu_{0} I \)

Choose the correct answer from the options given below:

52.

In an experiment to measure the focal length \( (f) \) of a convex lens, the magnitude of object distance \( (x) \) and the image distance \( (y) \) are measured with reference to the focal point of the lens. The \( y\text{-}x \) plot is shown in figure. The focal length of the lens is ________ \( \text{cm} \).

53.

A simple pendulum is placed at a place where its distance from the earth’s surface is equal to the radius of the earth. If the length of the string is \( 4 \, \text{m}\), then the time period of small oscillation will be ________ \( \text{s} \).
\([ \text{take } g=\pi^{2} \, \text{m s}^{-2} ]\)

54.

A big drop is formed by coalescing \( 1000 \) small identical drops of water. If \( E_{1} \) be the total surface energy of \( 1000 \) small drops of water and \( E_{2} \) be the surface energy of single big drop of water, then \( E_{1}:E_{2} \) is \( x:1 \) where \( x=\_\_\_\_\_\_\_\_. \)

55.

Two resistance of \( 100\,\Omega \) and \( 200\,\Omega \) are connected in series with a battery of \( 4\,\text{V} \) and negligible internal resistance. A voltmeter is used to measure voltage across \( 100\,\Omega \) resistance, which give reading as \( 1\,\text{V} \). The resistance of voltmeter must be ______ \( \Omega \).

56.

A power transmission line feeds input power at \( 2.3\,\text{kV} \) to a step down transformer with its primary winding having \( 3000 \) turns. The output power is delivered at \( 230\,\text{V} \) by the transformer. The current in the primary of the transformer is \( 5\,\text{A} \) and it efficiency is \( 90\% \). The winding of transformer is made of copper. The output current of transformer is ______ \( \text{A} \).

57.

A point source is emitting sound waves of intensity \( 16 \times 10^{-8}\ \text{W}\ \text{m}^{-2} \) at the origin. The difference in intensity (magnitude only) at two points located at a distance of \( 2\,\text{m} \) and \( 4\,\text{m} \) from the origin respectively will be ______ \( \times 10^{-8}\ \text{W}\ \text{m}^{-2} \).

58.

Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of \( 37^\circ \) with each other. When suspended in a liquid of density \( 0.7\ \text{g}/\text{cm}^3 \), the angle remains same. If density of material of the sphere is \( 1.4\ \text{g}/\text{cm}^3 \), the dielectric constant of the liquid is ______ \( \left( \tan 37^\circ = \dfrac{3}{4} \right) \).

59.

The current of \( 5\,\text{A} \) flows in a square loop of side \( 1\,\text{m} \) is placed in air. The magnetic field at the centre of the loop is \( X\sqrt{2} \times 10^{-7}\ \text{T} \). The value of \( X \) is ______.

60.

Two discs of moment of inertia \( I_1 = 4 \,\mathrm{kg\,m^2} \) and \( I_2 = 2 \,\mathrm{kg\,m^2} \), about their central axes & normal to their planes, rotating with angular speeds \( 10 \,\mathrm{rad/s} \) & \( 4 \,\mathrm{rad/s} \) respectively are brought into contact face to face with their axes of rotation coincident. The loss in kinetic energy of the system in the process is ______ J.

JEE Main 2024 30th Jan Evening Shift

Mathematics Physics Chemistry

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