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A real gas within a colored chamber at \( 27^\circ\text{C} \) undergoes the cyclic process as shown in figure. The gas obeys \( PV^{3}=RT \) equation for the path \( A \) to \( B \). The net work done in the complete cycle is (assuming \( R=8 \,\text{J/mol K} \)):

32.

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of \( 2:1 \). After disintegration they will move:

33.

A hydrogen atom in ground state is given an energy of \( 10.2\,\text{eV} \). How many spectral lines will be emitted due to transition of electrons?

34.

The effective resistance between \( A \) and \( B \), if resistance of each resistor is \( R \), will be

35.

A square loop of side \(15 \, \text{cm}\) being moved towards right at a constant speed of \(2 \, \text{cm/s}\) as shown in figure. The front edge enters the \(50 \, \text{cm}\) wide magnetic field at \(t = 0\). The value of induced emf in the loop at \(t = 10 \, \text{s}\) will be:

36.

In the truth table of the above circuit the value of \(X\) and \(Y\) are:

37.

A spherical call of radius \(1 \times 10^{-4} \, \text{m}\) and density \(10^{5} \, \text{kg/m}^{3}\) falls freely under gravity through a distance \(h\) before entering a tank of water. If after entering in water the velocity of the ball does not change, then the value of \(h\) is approximately:
(The coefficient of viscosity of water is \(9.8 \times 10^{-6} \, \text{N s/m}^{2}\))

38.

The de-Broglie wavelength associated with a particle of mass \(m\) and energy \(E\) is \( \dfrac{h}{\sqrt{2 m E}} \). The dimensional formula for Planck's constant is:

39.

A \(1 \, \text{kg}\) mass is suspended from the ceiling by a rope of length \(4 \, \text{m}\). A horizontal force \(F\) is applied at the mid point of the rope so that the rope makes an angle of \(45^\circ\) with respect to the vertical axis as shown in figure. The magnitude of \(F\) is:
(Assume that the system is in equilibrium and \(g = 10 \, \text{m/s}^{2}\))

40.

The energy released in the fusion of \( 2 \, \text{kg} \) of hydrogen deep in the sun is \( E_H \) and the energy released in the fission of \( 2 \, \text{kg} \) \( {}^{235}\!U \) is \( E_U \). The ratio \( \dfrac{E_H}{E_U} \) is approximately:
(Consider the fusion reaction as \( 4\,{}^{1}_{1}\!H + 2e^{-} \rightarrow {}^{4}_{2}\!He + 2\nu + 6\gamma + 26.7 \, \text{MeV} \) , energy released in the fission reaction of \( {}^{235}\!U \) is \( 200 \, \text{MeV} \) per fission nucleus and \( N_A = 6.023 \times 10^{23} \))

41.

The following figure represents two biconvex lenses \( L_1 \) and \( L_2 \) having focal length \( 10 \, \text{cm} \) and \( 15 \, \text{cm} \) respectively. The distance between \( L_1 \) and \( L_2 \) is:

42.

Two cars are travelling towards each other at speed of \( 20 \, \text{m s}^{-1} \) each. When the cars are \( 300 \, \text{m} \) apart, both the drivers apply brakes and the cars retard at the rate of \( 2 \, \text{m s}^{-2} \). The distance between them when they come to rest is:

43.

Five charges \( +q \), \( +5q \), \( -2q \), \( +3q \) and \( -4q \) are situated as shown in the figure. The electric flux due to this configuration through the surface \( S \) is:

44.

The magnetic field in a plane electromagnetic wave is \( B_{y} = (3.5 \times 10^{-7}) \sin (1.5 \times 10^{3} x + 0.5 \times 10^{11} t) \, \text{T} \). The corresponding electric field will be

45.

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

46.

UV light of \( 4.13 \, \text{eV} \) is incident on a photosensitive metal surface having work function \( 3.13 \, \text{eV} \). The maximum kinetic energy of ejected photoelectrons will be:

47.

A satellite of \( 10^3 \, \text{kg} \) mass is revolving in circular orbit of radius \( 2R \). If \( \frac{10^4 R}{6} \, \text{J} \) energy is supplied to the satellite, it would revolve in a new circular orbit of radius: (use \( g = 10 \, \text{m/s}^2 \), \( R \) = radius of earth)

48.

The temperature of a gas is \( -78^\circ \text{C} \) and the average translational kinetic energy of its molecules is \( K \). The temperature at which the average translational kinetic energy of the molecules of the same gas becomes \( 2K \) is:

49.

The I–V characteristics of an electronic device shown in the figure. The device is:

50.

A proton and deuteron \( (q = +e, \, m = 2.0u) \) having same kinetic energies enter a region of uniform magnetic field \( \vec{B} \), moving perpendicular to \( \vec{B} \). The ratio of the radius \( r_d, \) of deuteron path to the radius \( r_p \) of the proton path is:

51.

A straight magnetic strip has a magnetic moment of \( 44 \, \text{Am}^2 \). If the strip is bent in a semicircular shape, its magnetic moment will be ____ \( \text{Am}^2 \).
\( \left( \text{given } \pi = \frac{22}{7} \right) \)

52.

The resultant of two vectors \( \vec{A} \) and \( \vec{B} \) is perpendicular to \( \vec{A} \) and its magnitude is half that of \( \vec{B} \). The angle between vectors \( \vec{A} \) and \( \vec{B} \) is…..\( ^\circ \).

53.

A capacitor reactance \( 4\sqrt{3} \, \Omega \) and a resistor of resistance \( 4 \, \Omega \) are connected in series with an ac source of peak value \( 8\sqrt{2} \, V \). The power dissipation in the circuit is ......\( W \).

54.

At room temperature \( (27^\circ \text{C}) \), the resistance of a heating element is \( 50 \, \Omega \). The temperature coefficient of the material is \( 2.4 \times 10^{-4} \, ^\circ \text{C}^{-1} \). The temperature of the element, when its resistance is \( 62 \, \Omega \) is ......\( ^\circ \text{C} \).

55.

A force \( (3x^{2}+2x-5)\, \text{N} \) displaces a body from \( x = 2 \, \text{m} \) to \( x = 4 \, \text{m} \). Work done by this force is ......\( \text{J} \).

56.

A circular disc reaches from top to bottom of an inclined plane of length \( l\). When it slips down the plane, it takes \( t \, \text{s} \). When it rolls down the plane then it takes \( \left( \dfrac{\alpha}{2} \right)^{1/2} t \, \text{s} \), where \( \alpha \) is ........

57.

An electric field \( \vec{E} = (2x\hat{i}) \, \text{N} \, \text{C}^{-1} \) exists in space. A cube of side \( 2 \, \text{m} \) is placed in the space as per figure given below. The electric flux through the cube is ____ \( \text{N}\,\text{m}^{2}/\text{C} \).

58.

To determine the resistance \( (R) \) of a wire, a circuit is designed below. the V–I characteristic curve for this circuit is plotted for the voltmeter and the ammeter readings as shown in figure. The value of \( R \) is ..... \( \Omega \).

59.

Monochromatic light of wavelength \( 500 \, \text{nm} \) is used in Young's double slit experiment. An interference pattern is obtained on a screen. When one of the slits is covered with a very thin glass plate (refractive index \( = 1.5 \)), the central maximum is shifted to a position previously occupied by the \( 4{\text{th}} \) bright fringe. The thickness of the glass-plate is...... \( \mu\text{m} \).

60.

A particle of mass \( 0.50 \, \text{kg} \) executes simple harmonic motion under force \( F = -50 \, (\text{N m}^{-1}) \, x \).The time period of oscillation is \( \dfrac{x}{35} \, \text{s} \). The value of \( x \) is
(Given \( \pi = \dfrac{22}{7} \))

JEE Main 2024 9th April Evening Shift

Mathematics Physics Chemistry

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The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between the volume of the first and the second bubble is:

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