1.
From a disc of radius R and mass M, a circular hole of diameter R, whose rim passes through the centre is cut. What is the moment of inertia of the remaining part of the disc about a perpendicular axis, passing through the centre?

2.
The magnetic susceptibility is negative for :

3.
A siren emitting a sound of frequency 800 Hz moves away from an observer towards a cliff at a speed of 15m/s. Then, the frequency of sound that the observer hears in the echo reflected from the cliff is:

(Take velocity of sound in air=330m/s)

4.
In a diffraction pattern due to a single slit of width 'a', the first minimum is observed at an angle 30° when light of wavelength 5000Å is incident on the slit. The first secondary maximum is observed at an angle of-

5.
Out of the following options which one can be used to produce a propagating electromagnetic wave?

6.
At what height from the surface of earth the gravitation potential and the value of g are (-5.4 x 10) J kg-² and 6.0 ms-² respectively?

(Take the radius of earth as 6400km)

7.
A refrigerator works between 4°C and 30°C. It is required to remove 600 calories of heat every second in order to keep the temperature of the refrigerated space constant. The power required is:

(Take 1 cal=4.2 Joules)

8.
An air column, closed at one end and open at the other, resonates with a tuning fork when the smallest length of the column is 50 cm. The next larger length of the column resonating with the same tuning fork is:

9.
A black body is at a temperature of 5760 K. The energy of radiation emitted by the body at wavelength 250 nm is U1, at wavelength 500 nm is U2 and that at 1000 nm is U3. Wien's constant, b=2.88 x 10⁶ nmK. Which of the following is correct?

10.
Coefficient of linear expansion of brass and steel rods are a1 and a2. Lengths of brass and steel rods are l1 and l2 respectively. If (l2-l1) is maintained same at all temperatures, which one of the following relations holds good?

11.
A disk and a sphere of same radius but different masses roll off on two inclined planes of the same altitude and length. Which one of the two objects gets to the bottom of the plane first?

12.
The angle of incidence for a ray of light at a refracting surface of a prism is 45°. The angle of prism is 60°. If the ray suffers minimum deviation through the prism, the angle of minimum deviation and refractive index of the material of the prism respectively, are:

13.
The molecules of a given mass of a gas have r.m.s. velocity of 200 ms-¹ at 27°C and (1.0x105)Nm-² pressure. When the temperature and pressure of the gas are respectively, 127°C and (0.05x10⁵) Nm-², the r.m.s. velocity of its molecules in ms-¹ is:

14.
When an α particle of mass 'm' moving with velocity v bombards on a heavy nucleus of charge "Ze", its distance of closest approach from the nucleus depends on m as:

15.
A particle moves so that its position vector is given by r=cosωtx̂+sinωtŷ,where ω is a constant.Which of the following is true ?

16.
What is the minimum velocity with which a body of mass m must enter a vertical loop of radius R so that it can complete the loop?

17.
A potentiometer wire is 100 cm long and a constant potential difference is maintained across it. Two cells are connected in series first to support one another and then in opposite direction. The balance points are obtained at 50 cm and 10 cm from the positive end of the wire in the two cases. The ratio of emf's is :

18.
A astronomical telescope has objective and eyepiece of focal lengths 40 cm and 4 cm respectively. To view an object 200 cm away from the objective, the lenses must be separated by a distance:

19.
To get output 1 for the following circuit, the correct choice for the input is-

20.
A piece of ice falls from a height h so that it melts completely. Only one-quarter of the heat produced is absorbed by the ice and all energy of ice gets converted into heat during its fall. The value of h is:

[Latent heat of ice is 3.4 x 10⁵ J/kg and g = 10 N/kg]

21.
The ratio of escape velocity at earth (Ve) to the escape velocity at a planet (Vp) whose radius and mean density are twice as that of earth is :

22.
If the magnitude of sum of two vectors is equal to the magnitude of difference of the two vectors, the angle between these vectors is :

23.
Given the value of Rydberg constant is 10⁷m-¹, the wave number of the last line of the Balmer series in hydrogen spectrum will be:

24.
An inductor 20 mH, a capacitor 50µF and a resistor 40Ω are connected in series across a source of emf V= 10 sin 340 t. The power loss in A.C. circuit is :

25.
A long solenoid has 1000 turns. When a current of 4A flows through it, the magnetic flux linked with each turn of the solenoid is 4 x 10-³ Wb. The self inductance of the solenoid is:

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26.
In the spectrum of hydrogen, the ratio of the longest wavelength in the Lyman series to the longest wavelength in the Balmer series is:

27.
The energy of the em waves is of the order of 15 kev. To which part of the spectrum does it belong?

28.
An electron moves on a straight line path XY as shown. The abcd is a coil adjacent to the path of the electron. What will be the direction of current, if any current is induced in the coil?

29.
The Young's modulus of steel is twice that of brass .Two wires of same length and of same area of cross section, one of steel and another of brass are suspended from the same roof. If we want the lower ends of the wires to be at the same level, then the weights added to the steel and brass wires must be in the ratio of:

30.
A particle is executing a simple harmonic motion. Its maximum acceleration is α and maximum velocity is β . Then, its time period of vibration will be:

31.
A source of sound S emitting waves of frequency 100 Hz and an observer O are located at some distance from each other. The source is moving with a speed of 19.4 ms-¹ at an angle of 60° with the source observer line as shown in the figure. The observer is at rest. The apparent frequency observed by the observer (velocity of sound in air 330 ms-¹) is:

32.
An automobile moves on a road with a speed of 54 km/h The radius of its wheels is 0.45 m and the moment of inertia of the wheel about its axis of rotation is 3 kgm². If the vehicle is brought to rest in 15s, the magnitude of average torque transmitted by its brakes to wheel is:

33.
Two vessels separately contain two ideal gases A and B at the same temperature, the pressure of A being twice that of B. Under such conditions, the density of A is found to be 1.5 times the density of B. The ratio of molecular weight of A and B is:

34.
A string is stretched between fixed points separated by 75.0 cm. It is observed to have resonant frequencies of 420 Hz and 315 Hz. There are no other resonant frequencies between these two. The lowest resonant frequencies for this string is:

35.
At the first minimum adjacent to the central maximum of a single-slit diffraction pattern the phase difference between the Huygen's wavelet from the edge of the slit and the wavelet from the mid point of the slit is:

36.
A nucleus of uranium decays at rest into nuclei of Thorium and Helium. Then

37.
Light of wavelength 500 nm is incident on a metal with work function 2.28 eV. The de Broglie wavelength of the emitted electron is :

38.
A plank with a box on it at one end is gradually raised about the other end. As the angle of inclination with the horizontal reaches 30°, the box starts to slip and slides 4.0 m down the plank in 4.0s The coefficients of static and kinetic friction between the box and the plank will be, respectively.

39.
Two stones of masses m and 2m are whirled in horizontal circles, the heavier one in a radius r/2 and the lighter one in radius r. The tangential speed of lighter stone is n times that of the value of heavier stone when they experience same centripetal forces. The value of n is:

40.
An ideal gas is compressed to half its initial volume by means of several processes. Which of the process results in the maximum work done on the gas ?

41.
A circuit contains an ammeter, a battery of 30 V and a resistance 40.8 ohm all connected in series. If the ammeter has a coil of resistance 480 ohm and a shunt of 20 ohm, the reading in the ammeter will be:

42.
Water rises to height 'h' in capillary tube. If the length of capillary tube above the surface of water is made less than 'h', then-

43.
The value of coefficient of volume expansion of glycerin is 5 x 10-⁴K .The fractional change in the density of glycerin for a rise of 40°C in its temperature, is:

44.
A beam of light consisting of red, green and blue colours is incident on a right angled prism. The refractive index of the material of the prism for the above red, green and blue wavelengths are 1.39, 1.44 and 1.47 respectively.The prism will-

2 out of 2