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Question 1 of 30
1. Question
If electronic charge e, electron mass m, speed of light in vacuum c and Planck’s constant h are taken as fundamental quantities, the permeability of vacuum μ_{0} can be expressed in units of :
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Question 2 of 30
2. Question
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Question 3 of 30
3. Question
A large number (n) of identical beads, each of mass m and radius r are strung on a thin smooth rigid horizontal rod of length L (L >> r) and are at rest at random positions. The rod is mounted between two rigid supports (see figure). If one of the beads is now given a speed v, the average force experienced by each support after a long time is (assume all collisions are elastic):
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Question 4 of 30
4. Question
A particle is moving in a circle of radius r under the action of a force F =αr^{2} which is directed towards centre of the circle. Total mechanical energy kinetic energy + potential energy) of the particle is (take potential energy = 0 for r = 0):
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Question 5 of 30
5. Question
A uniform thin rod AB of length L has linear mass density where x is measured from A. If the CM of the rod lies at a distance of from A, then a and b are related as :
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Question 6 of 30
6. Question
A particle of mass 2 kg is on a smooth horizontal table and moves in a circular path of radius 0.6 m. The height of the table from the ground is 0.8 m. If the angular speed of the particle is 12 rad s^{− 1}, the magnitude of its angular momentum about a point on the ground right under the centre of the circle is:
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Question 7 of 30
7. Question
Which of the following most closely depicts the correct variation of the gravitation potential V(r) due to a large planet of radius R and uniform mass density? (figures are not drawn to scale)
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Question 8 of 30
8. Question
A cylindrical block of wood (density = 650 kg m^{−3}), of base area 30 cm^{2} and height 54 cm, floats in a liquid of density 900 kg m^{–3}. The block is depressed slightly and then released. The time period of the resulting oscillations of the block would be equal to that of a simple pendulum of length (nearly) :
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Question 9 of 30
9. Question
A beaker contains a fluid of density ρ kg / m^{3}, specific heat S J / kgºC and viscosity η. The beaker is filled upto height h. To estimate the rate of heat transfer per unit area by convection when beaker is put on a hot plate, a student proposes that it should depend on η, when ∆θ (in ºC) is the difference in the temperature between the bottom and top of the fluid. In that situation the correct option for (Q / A) is :
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Question 10 of 30
10. Question
An experiment takes 10 minutes to raise the temperature of water in a container from 0ºC to 100ºC and another 55 minutes to convert it totally into steam by a heater supplying heat at a uniform rate. Neglecting the specific heat of the container and taking specific heat of water to be 1 cal / g ºC, the heat of vapourization according to this experiment will come out to be :
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Question 11 of 30
11. Question
Using equipartition of energy, the specific heat (in J kg ^{–1} K^{– 1} ) of aluminium at room temperature can be estimated to be (atomic weight of aluminium = 27)
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Question 12 of 30
12. Question
A pendulum with time period of 1s is losing energy due to damping. At certain time its energy is 45 J. If after completing 15 oscillations, its energy has become 15 J, its damping constant (in s ^{– 1}) is :
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Question 13 of 30
13. Question
A source of sound emits sound waves at frequency f_{0. }It is moving towards an observer with fixed speed υ _{s }(υ _{s}<υ, where υ is the speed of sound in air). If the observer were to move towards the source with speed υ _{0}, one of the following two graphs (A and B) will given the correct variation of the frequency f heard by the observer as υ _{0} is changed.
The variation of f with υ_{0} is given correctly by :
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Question 14 of 30
14. Question
A wire, of length L (=20 cm), is bent into a semicircular arc. If the two equal halves, of the arc, were each to be uniformly charged with charges + Q, [Q = 10^{3 }ε_{0 }Coulomb where ε_{0} is the permittivity (in SI units) of free space] the net electric field at the centre O of the semicircular arc would be :
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Question 15 of 30
15. Question
An electrical field exists in a region of space. If the potential at the origin is taken to be zero then the potential at x= 2 m, y = 2 m is :
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Question 16 of 30
16. Question
In figure is shown a system of four capacitors connected across a 10 V battery. Charge that will flow from switch S when it is closed is :
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Question 17 of 30
17. Question
In the electric network shown, when no current flows through the 4 resistor in the arm EB, the potential difference between the points A and D will be :
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Question 18 of 30
18. Question
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Question 19 of 30
19. Question
Two long straight parallel wires, carrying (adjustable) current I_{1} and I_{2}, are kept at a distance d apart. If the force ‘F’ between the two wires is taken as ‘positive’ when the wires repel each other and ‘negative’ when the wires attract each other, the graph showing the dependence of ‘F’, on the product I_{1 }I_{2}, would be :
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Question 20 of 30
20. Question
A wire carrying current I is tied between points P and Q and is in the shape of a circular arch of radius R due to a uniform magnetic field B (perpendicular to the plane of the paper, shown by xxx) in the vicinity of the wire. If the wire subtends an angle 2θ_{0} at the centre of the circle (of which it forms an arch) then the tension in the wire is :
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Question 21 of 30
21. Question
A short bar magnet is placed in the magnetic meridian of the earth with north pole pointing north. Neutral points are found at a distance of 30 cm from the magnet on the East – West line, drawn through the middle point of the magnet. The magnetic moment of the magnet in Am^{2} is close to :
(Given in SI units and B_{H }= Horizontal component of earth’s magnetic field = 3.6 × 10^{–5 } Tesla.)
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Question 22 of 30
22. Question
For the LCR circuit, shown here, the current is observed to lead the applied voltage. An additional capacitor C’, when joined with the capacitor C present in the circuit, makes the power factor of the circuit unity. The capacitor C’, must have been connected in :
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Question 23 of 30
23. Question
For plane electromagnetic waves propagating in the z direction, which one of the following combination gives the correct possible direction for field respectively?
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Question 24 of 30
24. Question
A thin convex lens of focal length ‘f’ is put on a plane mirror as shown in the figure. When an object is kept at a distance ‘a’ from the lens – mirror combination, its image is formed at a distance in front of the combination. The value of ‘a’ is :
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Question 25 of 30
25. Question
In a Young’s double slit experiment with light of wavelength λ the separation of slits is d and distance of screen is D such that D >> d >> λ. If the fringe width is β, the distance from point of maximum intensity to the point where intensity falls to half of maximum intensity on either side is:
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Question 26 of 30
26. Question
Unpolarized light of intensity I_{0} is incident on surface of a block of glass at Brewster’s angle. In that case, which one of the following statements is true?
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Question 27 of 30
27. Question
The deBroglie wavelength associated with the electron in the n = 4 level is :
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Question 28 of 30
28. Question
Let N_{β} be the number of β particles emitted by 1 gram of Na^{24} radioactive nuclei (half life = 15 hrs) in 7.5 hours, N_{β} is close to (Avogadro number = 6.023 × 10^{23}/g. mole) :
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Question 29 of 30
29. Question
A 2V battery is connected across AB as shown in the figure. The value of the current supplied by the battery when in one case battery’s positive terminal is connected to A and in other case when positive terminal of battery is connected to B will respectively be :
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Question 30 of 30
30. Question
The AC voltage across a resistance can be measured using a :
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