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Question 1 of 30
1. Question
A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of
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Question 2 of 30
2. Question
A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?
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Question 3 of 30
3. Question
A body of mass m = 10^{−2} kg is moving in a medium and experiences a frictional force F = −kv^{2}. Its initial speed is v_{0} = 10 ms^{−1}. If, after 10 s, its energy is the value of k will be
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Question 4 of 30
4. Question
A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 second will be
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Question 5 of 30
5. Question
The moment of inertia of a uniform cylinder of length ℓ and radius R about its perpendicular bisector is I. What is the ratio such that the moment of inertia is minimum ?
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Question 6 of 30
6. Question
A slender uniform rod of mass M and length l is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle θ with the vertical is
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Question 7 of 30
7. Question
The variation of acceleration due to gravity g with distance d from centre of the earth is best represented by (R = Earth’s radius) :
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Question 8 of 30
8. Question
A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75°C. T is given by :
(Given : room temperature = 30°C, specific heat of copper = 0.1 cal/gm°C)
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Question 9 of 30
9. Question
An external pressure P is applied on a cube at 0°C so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and α is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by :
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Question 10 of 30
10. Question
C_{p} and C_{v} are specific heats at constant pressure and constant volume respectively. It is observed that
C_{p} – C_{v} = a for hydrogen gas
C_{p} – C_{v} = b for nitrogen gas
The correct relation between a and b is :
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Question 11 of 30
11. Question
The temperature of an open room of volume 30 m^{3} increases from 17℃ to 27℃ due to the sunshine. The atmospheric pressure in the room remains 1 × 10^{5} Pa. If n_{i} and n_{f} are the number of molecules in the room before and after heating, then n_{f} – n_{i} will be
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Question 12 of 30
12. Question
A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energytime graph of the particle will look like :
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Question 13 of 30
13. Question
An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10 GHz. What is the frequency of the microwave measured by the observer? (speed of light = 3 × 108 ms^{–1})
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Question 14 of 30
14. Question
An electric dipole has a fixed dipole moment which makes angle θ with respect xaxis. When subjected to an electric field it experiences a torque When subjected to another electric field it experiences a torque . The angle θ is
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Question 15 of 30
15. Question
A capacitance of 2 μF is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 μF capacitors are available which can withstand a potential difference of not more than 300 V.
The minimum number of capacitors required to achieve this is
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Question 16 of 30
16. Question
In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be :
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Question 17 of 30
17. Question
In the above circuit the current in each resistance is
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Question 18 of 30
18. Question
A magnetic needle of magnetic moment 6.7 × 10^{−2} Am^{2} and moment of inertia 7.5 × 10^{−6} kg m^{2} is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillation is
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Question 19 of 30
19. Question
When a current of 5 mA is passed through a galvanometer having a coil of resistance 15 Ω, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 010 V is
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Question 20 of 30
20. Question
In a coil of resistance 100 Ω, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is
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Question 21 of 30
21. Question
An electron beam is accelerated by a potential difference V to hit a metallic target to produce Xrays. It produces continuous as well as characteristic Xrays. If λ_{min} is the smallest possible wavelength of Xray in the spectrum, the variation of log λ_{min} with log V is correctly represented in
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Question 22 of 30
22. Question
A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15 cm from a converging lens of magnitude of focal length 20 cm. A beam of parallel light falls on the diverging lens. The final image formed is
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Question 23 of 30
23. Question
In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is
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Question 24 of 30
24. Question
A particle A of mass m and initial velocity v collides with a particle B of mass which is at rest. The collision is head on, and elastic. The ratio of the deBroglie wavelengths λ_{A} to λ_{B} after the collision is
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Question 25 of 30
25. Question
Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = λ_{1}/λ_{2}, is given by
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Question 26 of 30
26. Question
A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the ratio of the number of B to that of A is 0.3. Then, t is given by
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Question 27 of 30
27. Question
In a common emitter amplifier circuit using an npn transistor, the phase difference between the input and the output voltages will be
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Question 28 of 30
28. Question
In amplitude modulation, sinusoidal carrier frequency used is denoted by ω_{c} and the signal frequency is denoted by ω_{m. }The bandwidth (∆ω_{m}) of the signal is such that ∆ω_{m} << ω_{c}. Which of the following frequencies is not contained in the modulated wave ?
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Question 29 of 30
29. Question
Which of the following statements is false?
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Question 30 of 30
30. Question
The following observations were taken for determining surface tension T of water by capillary method : diameter of capillary, D = 1.25 × 10^{−}^{2} m rise of water, h = 1.45 × 10^{−}^{2} m rise of water, h = 1.45 × 10^{−}^{2}
Using g = 9.80 m/s^{2} and the simplified relation the possible error in surface tension is closest to
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