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Question 1 of 30
1. Question
x and y displacements of a particle are given as x(t) = a sinωt and y(t) = a sin 2ωt. Its trajectory will look like :
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Question 2 of 30
2. Question
If a body moving in a circular path maintains constant speed of 10 ms^{–1}, then which of the following correctly describes relation between acceleration and radius?
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Question 3 of 30
3. Question
A block of mass m = 10 kg rests on a horizontal table. The coefficient of friction between the block and the table is 0.05. When hit by a bullet of mass 50 g moving with speed υ, that gets embedded in it, the block moves and come to stop after moving a distance of 2m on the table. If a freely falling object were to acquire speed after being dropped from height H, then neglecting energy losses and taking g = 10 ms^{–2}, the value of H is close to :
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Question 4 of 30
4. Question
A block of mass m = 0.1 kg is connected to a spring of unknown spring constant k. It is compressed to a distance x from rest. After approaching half the distance from equilibrium position, it hits another block and comes to rest momentarily, while the other block moves with a velocity 3ms^{–1}. the total initial energy of the spring is :
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Question 5 of 30
5. Question
A uniform solid cylindrical roller of mass ‘m’ is being pulled on a horizontal surface with force F parallel to the surface and applied at its centre. If the acceleration of the cylinder is ‘a’ and it is rolling without slipping then the value of ‘F’ is :
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Question 6 of 30
6. Question
Consider a thin uniform square sheet made of a right material. If its side is ‘a’, mass m and moment of inertia I about one of its diagonals, then :
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Question 7 of 30
7. Question
A very long (length L) cylindrical galaxy is made of uniformly distributed mass and has radius R (R << L). A star outside the galaxy is orbiting the galaxy in a plane perpendicular to the galaxy and passing through its centre. If the time period of star is T and its distance from the galaxy’s axis is r, then :
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Question 8 of 30
8. Question
If it takes 5 minutes to fill a 15 litre bucket from a water tap of diameter cm then the Reynolds number for the flow is (density of water = 10^{3} kg/m^{3} and viscosity of water = 10^{–3} Pa.s) close to :
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Question 9 of 30
9. Question
If two glass plates have water between them and are separated by very small distance (see figure), it is very difficult to pull them apart. It is because the water in between forms cylindrical surface on the side that gives rise to lower pressure in the water in comparison to atmosphere. If the radius of the cylindrical surface is R and surface tension of water is T then the pressure in water between the plates is lower by :
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Question 10 of 30
10. Question
An ideal gas goes through a reversible cycle a → b → c → d has the V – T diagram shown below. Process d → a and b → c are adiabatic.
The corresponding P – V diagram for the process is (all figures are schematic and not drawn to scale) :
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Question 11 of 30
11. Question
In an ideal gas at temperature t, the average force that a molecule applies on the walls of a closed container depends on T as T^{q}. A good estimate for q is
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Question 12 of 30
12. Question
A simple harmonic oscillator of angular frequency 2 rad s^{–1} is acted upon by an external force F = sin t N. If the oscillator is at rest in its equilibrium position at t = 0, its position at later times is proportional to :
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Question 13 of 30
13. Question
A bat moving at 10ms^{–1} towards a wall sends a sound signal of 8000 Hz towards it. On reflection it hears a sound of frequency f. The value of f in Hz is close to (speed of sound = 320 ms^{–1})
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Question 14 of 30
14. Question
A thin disc of radius b = 2a has concentric hole of radius ‘a’ in it (see figure). It carries uniform surface charge ‘σ’ on it. If the electric field on its axis at height ‘h’ (h << a) from its centre is given as ‘Ch’ then value of ‘C’ is :
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Question 15 of 30
15. Question
Shown in the figure are two point charges +Q and – Q inside the cavity of a spherical shell. The charges are kept near the surface of the cavity on opposite sides of the centre of the shell. If σ_{1} is the surface charge on the inner surface and Q_{1} net charge on it and σ_{2} the surface charge on the outer surface and Q_{2} net charge on it then :
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Question 16 of 30
16. Question
If the capacitance of a nanocapacitor is measured in terms of a unit ‘u’ made by combining the electronic charge ‘e’, Bohr radius ‘a_{0}’, Planck’s constant ‘h’ and speed of light ‘c’ then:
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Question 17 of 30
17. Question
Suppose the drift velocity υ_{d} in a material varied with the applied electric field E as υ_{d} α √E . Then V – l graph for a wire made of such a material is best given by :
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Question 18 of 30
18. Question
A 10V battery with internal resistance 1Ω and a 15V battery with internal resistance 0.6Ω are connected in parallel to a voltmeter (see figure). The reading in the voltmeter will be close to :
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Question 19 of 30
19. Question
A proton (mass m) accelerated by a potential difference V files through a uniform transverses magnetic field B. The field occupies a region of space by width ‘d’. If ‘α’ be the angle of deviation of proton from initial direction of motion (see figure,) the value of sin α will be :
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Question 20 of 30
20. Question
A 25 cm long solenoid has radius 2 cm and 500 total number of turns. It carries a current of 15 A. If it is equivalent to a magnet of the same size and magnetization (magnetic moment/volume), then is :
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Question 21 of 30
21. Question
When current in a coil changes from 5 A to 2 A in 0.1 s, average voltage of 50V is produced. The self – inductance of the coil is :
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Question 22 of 30
22. Question
In the circuits (a) and (b) switches S_{1} and S_{2} are closed at t = 0 and are kept closed for a long time. The variation of currents in the two circuits for t ≥ 0 are roughly shown by (figures are schematic and not drawn to scale :
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Question 23 of 30
23. Question
An electromagnetic wave travelling in the xdirection has frequency of 2 × 10^{14} Hz and electric field amplitude of 27 Vm^{–1}. From the options given below, which one describes the magnetic field for this wave ?
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Question 24 of 30
24. Question
You are asked to design a shaving mirror assuming that a person keeps it 10 cm from his face and views the magnified image of the face at the closest comfortable distance of 25 cm. The radius of curvature of the mirror would then be :
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Question 25 of 30
25. Question
A parallel beam of electrons travelling in xdirection falls on a slit of width d (see figure). If after passing the slit, an electron acquires momentum p_{y} in the ydirection then for a majority of electrons passing through the slit (h is Planck’s constant) :
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Question 26 of 30
26. Question
A telescope has an objective lens of focal length 150 cm and an eyepiece of focal length 5 cm. If a 50 m tall tower at a distance of 1 km is observed through this telescope in normal setting, the angle formed by the image of the tower is θ then θ is close to :
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Question 27 of 30
27. Question
deBroglie wavelength of an electron accelerated by a voltage of 50 V is close to (e = 1.6 × 10^{–19} C, m_{e} = 9.1 × 10^{–31} kg, h = 6.6 × 10^{–34} Js) :
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Question 28 of 30
28. Question
If one were to apply Bohr model to a particle of mass ‘m’ and charge ‘q’ moving in a plane under the influence of a magnetic field ‘B’, the energy of the charged particle in the nth level will be :
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Question 29 of 30
29. Question
In an unbiased np junction electrons diffuse from nregion to pregion because :
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Question 30 of 30
30. Question
Diameter of a steel ball is measured using a vernier callipers which has divisions of 0.1 cm on its main scale (MS) and 10 divisions of its vernier scale (VS) match 9 divisions on the main scale. Three such measurements for a ball are given as :
If the zero error is – 0.03 cm, then mean corrected diameter is :
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