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Question 1 of 45
1. Question
Planck’s constant (h), speed of light in vacuum (c) and Newton’s gravitational constant (G) are three fundamental constants. Which of the following combinations of these has the dimension of length?
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Question 2 of 45
2. Question
Two cars P and Q start from a point at the same time in a straight line and their positions are represented by x_{P}(t) = at + bt^{2} and x_{Q}(t) = ft – t^{2}. At what time do the cars have the same velocity?
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Question 3 of 45
3. Question
In the given figure, a = 15 m/s^{2} represents the total acceleration of a particle moving in the clockwise direction in a circle of radius R = 2.5 m at a given instant of time. The speed of the particle is
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Question 4 of 45
4. Question
A rigid ball of mass m strikes a rigid wall at 60° and gets reflected without loss of speed as shown in the figure below. The value of impulse imparted by the wall on the ball will be
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Question 5 of 45
5. Question
A bullet of mass 10 g moving horizontally, with a velocity of 400 ms^{−1} strikes a wooden block of mass 2 kg which is suspended by a light inextensible string of length 5 m. As a result, the centre of gravity of the block is found to rise a vertical distance of 10 cm. The speed of the bullet after it emerges out horizontally from the block will be
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Question 6 of 45
6. Question
Two identical balls A and B having velocities of 0.5 m/s and −0.3 m/s respectively collide elastically in one dimension. The velocities of B and A after the collision respectively will be
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Question 7 of 45
7. Question
A particle moves from a point when a force of is applied. How much work has been done by the force?
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Question 8 of 45
8. Question
Two rotating bodes A and B of masses m and 2m with moments of inertia I_{A} and I_{B}(I_{B} > I_{A}) have equal kinetic energy of rotation. If L_{A} and L_{B} be their angular momenta respectively, then
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Question 9 of 45
9. Question
A solid sphere of mass m and radius R is rotating about its diameter. A solid cylinder of the same mass and same radius is also rotating about its geometrical axis with an angular speed twice that of the sphere. The ratio of their kinetic energies of rotation E_{sphere}/E_{cylinder}) will be
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Question 10 of 45
10. Question
A light rod of length l has two masses m_{1} and m_{2} attached to its two ends. The moment of inertia of the system about an axis perpendicular to the rod and passing through the centre of mass is
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Question 11 of 45
11. Question
Starting from the centre of the earth having radius R, the variation of g (acceleration due to gravity) is shown by
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Question 12 of 45
12. Question
A satellite of mass m is orbiting the earth (of radius R) at a height h from its surface. The total energy of the satellite in terms of g_{0}, the value of acceleration due to gravity at the earth’s surface, is
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Question 13 of 45
13. Question
A rectangular film of liquid is extended from (4 cm × 2 cm) to (5 cm × 4 cm). If the work done is 3 × 10^{−4} J, the value of the surface tension of the liquid is
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Question 14 of 45
14. Question
Three liquids of densities ρ_{1}, ρ_{2} and ρ_{3} (with ρ_{1} > ρ_{2} > ρ_{3}), having the same value of surface tension T, rise to the same height in three identical capillaries. .The angles of contact θ_{1}, θ_{2} and θ_{3} obey
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Question 15 of 45
15. Question
Two identical bodies are made of a material for which the heat capacity increases with temperature. One of these is at 100℃, while the other one is at 0℃. If the two bodies are brought into contact, then, assuming no heat loss, the final common temperature is
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Question 16 of 45
16. Question
A body cools from a temperature 3T to 2T in 10 minutes. The room temperature is T. Assume that Newton’s law of cooling is applicable. The temperature of the body at the end of next 10 minutes will be
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Question 17 of 45
17. Question
One mole of an ideal monatomic gas undergoes a process described by the equation PV^{3} = constant. The heat capacity of the gas during this process is
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Question 18 of 45
18. Question
The temperature inside a refrigerator is t_{2}℃ and the room temperature is t_{1}℃. The amount of heat delivered to the room for each joule of electrical energy consumed ideally will be
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Question 19 of 45
19. Question
A given sample of an ideal gas occupies a volume V at a pressure P and absolute temperature T. The mass of each molecule of the gas is m. Which of the following gives the density of the gas?
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Question 20 of 45
20. Question
A body of mass m is attached to the lower end of a spring whose upper end is fixed. The spring has negligible mass. When the mass m is slightly pulled down and released, it oscillates with a time period of 3 s. When the mass m is increased by 1 kg, the time period of oscillations becomes 5 s. The value of m in kg is
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Question 21 of 45
21. Question
The second overtone of an open organ pipe has the same frequency as the first overtone of a closed pipe L metre long. The length of the open pipe will be
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Question 22 of 45
22. Question
Three sound waves of equal amplitudes have frequencies (n – 1), n, (n + 1). They superimpose to give beats. The number of beats produced per second will be
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Question 23 of 45
23. Question
An electric dipole is placed at an angle of 30° with an electric field intensity 2 × 10^{5} N/C. It experiences a torque equal to 4 N m. The charge on the dipole, if the dipole length is 2 cm, is
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Question 24 of 45
24. Question
A parallelplate capacitor of area A, p late separation d and capacitance C is filled with four dielectric materials having dielectric constants k_{1}, k_{2}, k_{3} and k_{4} as shown in the figure below. If a single dielectric material is to be used to have the same capacitance C in this capacitor, then its dielectric constant k is given by
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Question 25 of 45
25. Question
The potential difference (V_{A} – V_{B}) between the points A and B in the given figure is
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Question 26 of 45
26. Question
A filament bulb (500 W, 100 V) is to be used in a 230 V main supply. When a resistance R is connected in series, it works perfectly and the bulb consumes 500 W. The value of R is
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Question 27 of 45
27. Question
A long wire carrying a steady current is bent into a circular loop of one turn. The magnetic field at the centre of the loop is B. It is then bent into a circular coil of n turns. The magnetic field at the centre of this coil of n turns will be
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Question 28 of 45
28. Question
A bar magnet is hung by a thin cotton thread in a uniform horizontal magnetic field and is in equilibrium state. The energy required to rotate it by 60° is W. Now the torque required to keep the magnet in this new position is
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Question 29 of 45
29. Question
An electron is moving in a circular path under the influence of a transverse magnetic field of 3.57 × 10^{−2} T. If the value of e/m is 1.76 × 10^{11} C/kg, the frequency of revolution of the electron is
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Question 30 of 45
30. Question
Which of the following combinations should be selected for better tuning of an LCR circuit used for communication?
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Question 31 of 45
31. Question
A uniform magnetic field is restricted within a region of radius r. The magnetic field changes with time at a rate Loop 1 of radius R > r encloses the region r and loop 2 of radius R is outside the region of magnetic field as shown in the figure below. Then the e.m.f. generated is
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Question 32 of 45
32. Question
The potential differences across the resistance, capacitance and inductance are 80 V, 40 V and 100 V respectively in an LCR circuit. The power factor of this circuit is
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Question 33 of 45
33. Question
A 100 Ω resistance and a capacitor of 100 Ω reactance are connected in series across a 220 V source. When the capacitor is 50% charged, the peak value of the displacement current is
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Question 34 of 45
34. Question
Two identical glass (μ_{g} = 3/2) equiconvex lenses of focal length f each are kept in contact. The space between the two lenses is filled with water (μ_{w} = 4/3). The focal length of the combination is
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Question 35 of 45
35. Question
An air bubble in a glass slab with refractive index 1.5 (near normal incidence) is 5 cm deep when viewed from one surface and 3 cm deep when viewed from the opposite face. The thickness (in cm) of the slab is
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Question 36 of 45
36. Question
The interference pattern is obtained with two coherent light sources of intensity ration n. In the interference pattern, the ratio will be
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Question 37 of 45
37. Question
A person can see clearly objects only when they lie between 50 cm and 400 cm from his eyes. In order to increase the maximum distance of distinct vision to infinity, the type and power of the correcting lens, the person has to use, will be
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Question 38 of 45
38. Question
A linear aperture whose width is 0.02 cm is placed immediately in front of a lens of focal length 60 cm. The aperture is illuminated normally by a parallel beam of wavelength 5 × 10^{−5} cm. The distance of the first dark band of the diffraction pattern from the centre of the screen is
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Question 39 of 45
39. Question
Electrons of mass m with deBroglie wavelength λ fall on the target in an Xray tube. The cutoff wavelength (λ_{0}) of the emitted Xray is
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Question 40 of 45
40. Question
Photons with energy 5 eV are incident on a cathode C in a photoelectric cell. The maximum energy of emitted photoelectrons is 2 eV. When photons of energy 6 eV are incident on C, no photoelectrons will reach the anode A, if the stopping potential of A relative to C is
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Question 41 of 45
41. Question
If an electron in a hydrogen atom jumps from the 3^{rd} orbit to the 2^{nd} orbit, it emits a photon of wavelength λ. When it jumps from the 4^{th} orbit to the 3^{rd} orbit, the corresponding wavelength of the photon will be
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Question 42 of 45
42. Question
The halflife of a radioactive substance is 30 minutes. The time (in minutes) taken between 40% decay and 85% decay of the same radioactive substance is
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Question 43 of 45
43. Question
For CE transistor amplifier, the audio signal voltage across the collector resistance of 2 kΩ is 4 V. If the current amplification factor of the transistor is 100 and the base resistance is 1 kΩ, then the input signal voltage is
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Question 44 of 45
44. Question
The given circuit has two ideal diodes connected as shown in the figure below. The current flowing through the resistance R_{1} will be
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Question 45 of 45
45. Question
What is the output Y in the following circuit, when all the three inputs A, B, C are first o and then 1?
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