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Conductivity of a photodiode starts changing only if the wavelength of incident light is less than \( 660 \, \text{nm} \). The band gap of photodiode is found to be \( \left(\dfrac{X}{8}\right) \, \text{eV} \). The value of \( X \) is:
(Given, \( h = 6.6 \times 10^{-34} \, \text{J s}, \, e = 1.6 \times 10^{-19} \, \text{C} \) )

32.

A diatomic gas \( (\gamma = 1.4) \) does \( 200 \, \text{J} \) of work when it is expanded isobarically. The heat given to the gas in the process is:

33.

In an ammeter, \( 5\% \) of the main current passes through the galvanometer. If resistance of the galvanometer is \( G \), the resistance of ammeter will be:

34.

A galvanometer (\( G \)) of \( 2\,\Omega \) resistance is connected in the given circuit. The ratio of charge stored in \( C_{1} \) and \( C_{2} \) is:

35.

From the statements given below:
(A) The angular momentum of an electron in \( n^{\text{th}} \) orbit is an integral multiple of \( \hbar \).
(B) Nuclear forces do not obey inverse square law.
(C) Nuclear forces are spin dependent.
(D) Nuclear forces are central and charge independent.
(E) Stability of nucleus is inversely proportional to the value of packing fraction.
Choose the correct answer from the options given below:

36.

A body of mass \( 4 \, \text{kg} \) experiences two forces \( \vec{F}_1 = 5\hat{i} + 8\hat{j} + 7\hat{k} \) and \( \vec{F}_2 = 3\hat{i} - 4\hat{j} - 3\hat{k} \). The acceleration acting on the body is:

37.

A disc of radius \( R \) and mass \( M \) is rolling horizontally without slipping with speed \( v \). It then moves up an inclined smooth surface as shown in figure. The maximum height that the disc can go up the incline is:

38.

In a metre-bridge when a resistance in the left gap is \( 2\,\Omega \) and unknown resistance in the right gap, the balance length is found to be \( 40 \, \text{cm} \). On shunting the unknown resistance with \( 2\,\Omega \), the balance length changes by:

39.

A cricket player catches a ball of mass \( 120 \, \text{g} \) moving with \( 25 \, \text{m/s} \) speed. If the catching process is completed in \( 0.1 \, \text{s} \) then the magnitude of force exerted by the ball on the hand of player will be:
(in SI unit):

40.

If frequency of electromagnetic wave is \( 60 \, \text{MHz} \) and it travels in air along \( z \) direction then the corresponding electric and magnetic field vectors will be mutually perpendicular to each other and the wavelength of the wave (in \( \text{m} \)) is:

41.

\( C_1 \) and \( C_2 \) are two hollow concentric cubes enclosing charges \( 2Q \) and \( 3Q \) respectively as shown in figure. The ratio of electric flux passing through \( C_1 \) and \( C_2 \) is:

42.

Train A is moving along two parallel rail tracks towards north with speed \( 72 \, \text{km/h} \) and train B is moving towards south with speed \( 108 \, \text{km/h} \). Velocity of train B with respect to A and velocity of ground with respect to B are (in \( \text{m s}^{-1} \) ) :

43.

A microwave of wavelength \( 2.0 \, \text{cm} \) falls normally on a slit of width \( 4.0 \, \text{cm} \). The angular spread of the central maxima of the diffraction pattern obtained on a screen \( 1.5 \, \text{m} \) away from the slit, will be:

44.

A light planet is revolving around a massive star in a circular orbit of radius \( R \) with a period of revolution \( T \). If the force of attraction between planet and star is proportional to \( R^{-3/2} \) then chose the correct option:

45.

If the root mean square velocity of hydrogen molecule at a given temperature and pressure is \( 2 \, \text{km/s} \), the root mean square velocity of oxygen at the same condition in km/s is:

46.

A big drop is formed by coalescing \( 1000 \) small droplets of water. The surface energy will become:

47.

To measure the temperature coefficient of resistivity \( \alpha \) of a semiconductor, an electrical arrangement shown in the figure is prepared. The arm BC is made up of the semiconductor.The experiment is being conducted at \( 25^\circ \) and resistance of the semiconductor arm is \( 3\,\text{m}\Omega \). Arm BC is cooled at a constant rate of \( 2^\circ\text{C}/\text{s} \). If the galvanometer G shows no deflection after \( 10\,\text{s} \), then \( \alpha \) is:

48.

Match List-I with List-II.

List-I (Number)	List-II (Significant figure)
(A) \( 1001 \)	(I) \( 3 \)
(B) \( 010.1 \)	(II) \( 4 \)
(C) \( 100.100 \)	(III) \( 5 \)
(D) \( 0.0010010 \)	(IV) \( 6 \)

Choose the correct answer from the options given below:

49.

Monochromatic light of frequency \( 6 \times 10^{14}\,\text{Hz} \) is produced by a laser. The power emitted is \( 2 \times 10^{-3}\,\text{W} \). How many photons per second on an average, are emitted by the source?

50.

A transformer has an efficiency of \( 80\% \) and works at \( 10\,\text{V} \) and \( 4\,\text{kW} \). If the secondary voltage is \( 240\,\text{V} \), then the current in the secondary coil is:

51.

In an electrical circuit drawn below the amount of charge stored in the capacitor is ______ \( \mu\text{C} \).

52.

A particle initially at rest starts moving from reference point \( x = 0 \) along x-axis, with velocity \( v \) that varies as \( v = 4\sqrt{x}\,\text{m/s} \). The acceleration of the particle is _______ \( \text{m s}^{-2} \).

53.

A mass \( m \) is suspended from a spring of negligible mass and the system oscillates with a frequency \( f_1 \). The frequency of oscillations if a mass \( 9m \) is suspended from the same spring is \( f_2 \). The value of \( \dfrac{f_1}{f_2} \) is ____________.

54.

One end of a metal wire is fixed to a ceiling and a load of \( 2 \, \text{kg} \) hands from the other end. A similar wire is attached to the bottom of the load and anther load of \( 1 \, \text{kg} \) hangs from this lower wire. Then the ratio of longitudinal strain of upper wire to that of the lower wire will be ________.
[Area of cross section of wire \( = 0.005 \, \text{cm}^2 \); \( Y = 2 \times 10^{11} \, \text{N m}^{-2} \) and \( g = 10 \, \text{m s}^{-2} \)]

55.

A coil of \( 200 \) turns and area \( 0.20 \, \text{m}^2 \) is rotated at half a revolution per second and is placed in uniform magnetic field of \( 0.01 \, \text{T} \) perpendicular to axis of rotation of the coil. The maximum voltage generated in the coil is \( \dfrac{2\pi}{\beta} \) volt. The value of \( \beta \) is __________.

56.

A moving coil galvanometer has \( 100 \) turns and each has an area of \( 2.0 \, \text{cm}^2 \). The magnetic field produced by the magnet is \( 0.01 \, \text{T} \) and the deflection in the coil is \( 0.05 \) radian when a current of \( 10 \, \text{mA} \) is passed through it. The torsional constant of the suspension wire is \( x \times 10^{-5} \, \text{N·m/rad} \). The value of \( x \) is __________.

57.

A uniform rod AB of mass \( 2 \, \text{kg} \) and length \( 30 \, \text{cm} \) at rest on a smooth horizontal surface. An impulse of force \( 0.2 \, \text{Ns} \) is applied to end B. The time taken by the rod to turn through at right angles will be \( \dfrac{\pi}{x} \, \text{s} \), where \( x = \) __________.

58.

A particular hydrogen-like ion emits the radiation of frequency \( 3 \times 10^{15} \, \text{Hz} \) when it makes transition from \( n=2 \) to \( n=1 \). The frequency of radiation emitted in transition from \( n=3 \) to \( n=1 \) is \( \dfrac{x}{9} \times 10^{15} \, \text{Hz} \), when \( x = \) ____________.

59.

In Yong’s double slit experiment, monochromatic light of wavelength \( 5000 \, \mathring{A}\) is used. The slits are \( 1.0 \, \text{mm} \) apart and screen is placed at \( 1.0 \, \text{m} \) away from slits. The distance from the centre of the screen where intensity becomes half of the maximum intensity for the first time is __________ \( \times 10^{-6} \, \text{m} \).

60.

Suppose a uniformly charged wall provides a uniform electric field of \( 2 \times 10^{4} \, \text{N/C} \) normally. A charged particle of mass \( 2 \, \text{g} \) being suspended through a silk thread of length \( 20 \, \text{cm} \) and remain stayed at a distance of \( 10 \, \text{cm} \) from the wall. Then the charge on the particle will be \( \dfrac{1}{\sqrt{x}} \, \mu \text{C} \) where \( x = \_\_\_\_\_\_\_\_\_\_ \). [use \( g = 10 \, \text{m/s}^{2} \) ]

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