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Question 1 of 30
1. Question
A rectangular loop has a sliding connector PQ of length ℓ and resistance R Ω and it is moving with a speed v as shown. The setup is placed in a uniform magnetic field going into the plane of the paper. The three currents I₁, I₂ and I are
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Question 2 of 30
2. Question
Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t₁ is the time taken for the energy stored in the capacitor to reduce to half its initial value and t₂ is the time taken for the charge to reduce to onefourth its initial value. Then the ratio t₁/t₂ will be
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Question 3 of 30
3. Question
Directions: Questions number 3 – 4 contains Statement1 and Statement2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement1: Two particles moving in the same direction do not lose all their energy in a completely inelastic collision.
Statement2: Principle of conservation of momentum holds true for all kinds of collisions.
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Question 4 of 30
4. Question
Statement1: When ultraviolet light is incident on a photocell, its stopping potential is V₀ and the maximum kinetic energy of the photoelectrons is K_{max}. When the ultraviolet light is replaced by Xrays, both V₀ and K_{max} increase.
Statement2: Photoelectrons are emitted with speeds ranging from zero to a maximum value because of the range of frequencies present in the incident light.
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Question 5 of 30
5. Question
A ball is made of a material of density ρ where ρ_{oil} < ρ< ρ_{water} with ρ_{oil} and ρ_{water}representing the densities of oil and water, respectively. The oil and water are immiscible. If the above ball is in equilibrium in a mixture of this oil and water, which of the following pictures represents its equilibrium position?
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Question 6 of 30
6. Question
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Question 7 of 30
7. Question
Two long parallel wires are at a distance 2d apart. They carry steady equal current flowing out of the plane of the paper as shown. The variation of the magnetic field along the line XX’ is given by
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Question 8 of 30
8. Question
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Question 9 of 30
9. Question
The figure shows the position – time (x – t) graph of onedimensional motion of a body of mass 0.4 kg. The magnitude of each impulse is
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Question 10 of 30
10. Question
Directions: Questions number 10 – 11 are based on the following paragraph.
A nucleus of mass M + ∆m is at rest and decays into two daughter nuclei of equal mass M/2 each. Speed of light is c.
The binding energy per nucleon for the parent nucleus is E₁ and that for the daughter nuclei is E₂. Then
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Question 11 of 30
11. Question
The speed of daughter nuclei is
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Question 12 of 30
12. Question
A radioactive nucleus (initial mass number A and atomic number Z) emits 3 αparticles and 2 positrons. The ratio of number of neutrons to that of protons in the final nucleus will be
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Question 13 of 30
13. Question
A thin semicircular ring of radius r has a positive charge q distributed uniformly over it. The net field at the centre O is
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Question 14 of 30
14. Question
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Question 15 of 30
15. Question
A diatomic ideal gas is used in a Car engine as the working substance. If during the adiabatic expansion part of the cycle, volume of the gas increases from V to 32V the efficiency of the engine is
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Question 16 of 30
16. Question
If a source of power 4 kW produces 10²⁰ photons/second, the radiation belong to a part of the spectrum called
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Question 17 of 30
17. Question
The respective number of significant figures for the numbers 23.023, 0.0003 and 2.1 × 10⁻³ are
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Question 18 of 30
18. Question
In a series LCR circuit R = 200 Ω and the voltage and the frequency of the main supply is 220 V and 50 Hz respectively. On taking out the capacitance from the circuit the current lags behind the voltage by 30°. On taking out the inductor from the circuit the current leads the voltage by 30⁰. The power dissipated in the LCR circuit is
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Question 19 of 30
19. Question
Let there be a spherically symmetric charge distribution with charge density varying as up to r = R, and ρ(r) = 0 for r > R, where r is the distance from the origin. The electric field at a distance r(r < R) from the origin is given by
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Question 20 of 30
20. Question
The potential energy function for the force between two atoms in a diatomic molecule is approximately given by , where a and b are constants and x is the distance between the atoms. If the dissociation energy of the molecule is D = [U(x = ∞) – U_{at equilibrium}], D is
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Question 21 of 30
21. Question
Two identical charged spheres are suspended by strings of equal lengths. The strings make an angle of 30° with each other. When suspended in a liquid of density 0.8 g cm⁻³, the angle remains the same. If density of the material of the sphere is 16 g cm⁻³, the dielectric constant of the liquid is
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Question 22 of 30
22. Question
Two conductors have the same resistance at 0°C but their temperature coefficients of resistance are α₁ and α₂. The respective temperature coefficients of their series and parallel combinations are nearly
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Question 23 of 30
23. Question
A point P moves in counterclockwise direction on a circular path as shown in the figure. The movement of ‘P’ is such that it sweeps out a length s = t³ + 5, where s is in metres and t is in seconds. The radius of the path is 20 m. The acceleration of ‘P’ when t = 2 s is nearly
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Question 24 of 30
24. Question
Two fixed frictionless inclined plane making an angle 30° and 60° with the vertical are shown in the figure. Two block A and B are placed on the two planes. What is the relative vertical acceleration of A with respect to B?
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Question 25 of 30
25. Question
For a particle in uniform circular motion the acceleration at a point P(R,θ) on the circle of radius R is (here θ is measured from the x–axis)
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Question 26 of 30
26. Question
Directions: Questions number 26 – 28 are based on the following paragraph.
An initially parallel cylindrical beam travels in a medium of refractive index μ(I) = μ₀+ μ₂I , where μ₀ and μ₂ are positive constants and I is the intensity of the light beam. The intensity of the beam is decreasing with increasing radius.
As the beam enters the medium, it will
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Question 27 of 30
27. Question
The initial shape of the wave front of the beam is
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Question 28 of 30
28. Question
The speed of light in the medium is
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Question 29 of 30
29. Question
A small particle of mass m is projected at an angle θ with the xaxis with an initial velocity v₀ in the xy plane as shown in the figure. At a time , the angular momentum of the particle is
Where and are unit vectors along x, y and z–axis respectively.
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Question 30 of 30
30. Question
The equation of a wave on a string of linear mass density 0.04 kg m⁻¹ is given by
. The tension in the string isCorrectIncorrect