1. Which of the following units denotes the dimensions [ML²/Q²], where Q denotes the electric charge?
a) Wb/m²
b) Henry (H)
c) H/m²
d) Weber (Wb)

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2. Dimensions of $\frac{1}{\mu_{0} \epsilon_{0}}$, where symbols have their usual meaning, are
a) [L^-1T]
b) [L²T²]
c) [L²T^-2]
d) [LT^-1]

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1. A car, starting from rest, accelerates at the rate f through a distance s, then continues at constant speed for times t and then decelerates at the rate f/2 to come to rest. If the total distance travelled is 15 s, then
a) s = ft
b) s = $\frac{1}{6}ft^{2}$
c) s = $\frac{1}{2}ft^{2}$
d) s = $\frac{1}{4}ft^{2}$

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2. The velocity of a particle is v = v₀ + gt + ft². If its position is x = 0 at t = 0, then its displacement after unit time (t = 1) is
a) v₀ + 2g + 3f
b) $v_{0} + \frac{g}{2} + \frac{f}{3}$
c) v₀ + g + f
d) v₀ + $\frac{g}{2}$ + f

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1. A smooth block is released at rest in a 45⁰ incline and then slides a distance d. The time taken to slide is n times as much to slide on rough incline than on a smooth incline. The coefficient of friction is
a) μ_k = 1- $\frac{1}{n^{2}}$
b) μ_k = $\sqrt{1 - \frac{1}{n^{2}}}$
c) μ_s = 1 - $\frac{1}{n^{2}}$
d) μ_s = $\sqrt{1 - \frac{1}{n^{2}}}$

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2. A particle of mass 0.3 kg is subjected to a force F = -kx with k = 15 Nm^-1. What will be its initial acceleration, if it released from a point 20 cm away from the origin?
a) 3 ms^-2
b) 15 ms^-2
c) 5 ms^-2
d) 10 ms^-2

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1. A spring of spring constant 5 x 10³ N/m is stretched initially by 5 cm from the unstretched it position. Then the work required to stretch it further by another 5 cm is
a) 12.50 N-m
b) 18.75 N-m
c) 25.00 N-m
d) 6.25 N-m

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2. A bomb of mass 16 kg at rest explodes into two pieces of masses 4 kg and 12 kg. The velocity of the 12 kg mass is 4 ms^-1/ The kinetic energy of the other mass is
a) 144 J
b) 288 J
c) 192 J
d) 96 J

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1. A particle of mass m moves along line PC with velocity v as shown. What is the angular momentum of the particle about O?

a) mvL
b) mvl
c) mvr
d) zero

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2. Angular momentum of the particle rotating with a central force is constant due to
a) Constant force
b) Constant linear momentum
c) Zero torque
d) Constant torque

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1. Energy required to move a body of mass m from an orbit if radius 2R to 3R is
a) $\frac{GMm}{12R^{2}}$
b) $\frac{GMm}{3R^{2}}$
c) $\frac{GMm}{8R}$
d) $\frac{GMm}{6R}$

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2. The kinetic energy needed to project a body of mass m from the earth surface (radius R) to infinity is
a) $\frac{mgR}{2}$
b) 2mgR
c) mgR
d) $\frac{mgR}{4}$

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1. A wire elongates by l mm when a load w is hanged from it. If the wire goes over a pulley and two weights w each are hung at the two ends, the elongation of the wire will be (in mm)
a) l
b) 2l
c) Zero
d) $\frac{l}{2}$

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2. Two spheres of the same material have radii 1 m and 4 m and temperature 4000 K ad 2000 K respectively . The ration of the energy radiated per second by the first sphere to that by the second is
a) 1 : 1
b) 16 : 1
c) 4 : 1
d) 1 : 9

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1. Heat cannot be itself flow from a body at lower temperature to a body a higher temperature is a statement or consequence of
a) Second law of thermodynamics
b) Conservation of momentum
c) Conservation of mass
d) First law of thermodynamics

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2. During an adiabatic process, the pressure of a gas is found to be proportional to the cube of its absolute temperature. The ratio C_p/C_v for the gas is
a) 4/3
b) 2
c) 5/3
d) 3/2

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1. One mole of ideal monoatomic gas $\left ( \gamma = \frac{5}{3} \right )$ is mixed with one mole of diatomic gas $\left ( \gamma = \frac{7}{5} \right )$. What is γ for the mixture ? γ denotes the ratio of specific heat at constant pressure, to that at constant volume
a) $\frac{3}{2}$
b) $\frac{23}{15}$
c) $\frac{35}{23}$
d) $\frac{4}{3}$

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2. 1 mole of a gas with γ = $\frac{7}{5}$ is mixed with 1 mole of a gas with γ = $\frac{5}{3}$, then the value of γ for the resulting mixture is
a) $\frac{7}{5}$
b) $\frac{2}{5}$
c) $\frac{24}{16}$
d) $\frac{12}{7}$

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1. Two spring of force constants k₁ and k₂, are connected to a mass m as shown. The frequency of oscillation of the mass is f. If both k₁ and k₂ are made four times their original values, the frequency of oscillation becomes

a) $\frac{f}{2}$
b) $\frac{f}{4}$
c) 4f
d) 2f

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2. An observer moves towards a stationary source of sound, with a velocity one-fifth of the velocity of sound. What is the percentage increase in the apparent frequency?
a) Zero
b) 0.5%
c) 5%
d) 20%

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1. Capacitance (in F) of a spherical conductor having radius 1m, is
a) 1.1 x 10^-10
b) 10^-6
c) 9 x 10^-9
d) 10^-3

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2. Two positive charges of magnitude q are placed at the ends of a side 1 square of side 2a. Two negative charges of the same magnitude are kept at the other corners. Starting from rest, if a charge Q moves from the middle of side 1 to the centre of square, its kinetic energy at the centre of square is
a) $\frac{1}{4\pi \epsilon_{0}}\frac{2qQ}{a}\left (1 - \frac{1}{\sqrt{5}} \right )$
b) zero
c) $\frac{1}{4\pi \epsilon_{0}}\frac{2qQ}{a}\left (1 + \frac{1}{\sqrt{5}} \right )$
d) $\frac{1}{4\pi \epsilon_{0}}\frac{2qQ}{a}\left (1 - \frac{2}{\sqrt{5}} \right )$

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1. Two voltameters, one of copper and another of silver, are joined in parallel. When a total charge q flows through the voltameters, equal amount of metals are deposited. If the electrochemical equivalents of copper and silver are z₁ and z₂ respectively, the charge which flows through the silver voltameter is
a) $\frac{q}{1 + \frac{Z_{1}}{Z_{2}}}$
b) $\frac{q}{1 + \frac{Z_{2}}{Z_{1}}}$
c) $q\frac{z_{1}}{z{2}}$
d) $q\frac{z_{2}}{z{1}}$

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2. If in the circuit, power dissipation is 150W, then R is

a) 2Ω
b) 6Ω
c) 5Ω
d) 4Ω

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1. Needles N₁, N₂ and N₃ are made up of a ferromagnetic , a paramagnetic and a diamagnetic substance respectively. A magnet when brought close to them will
a) attract N₁ and N₂ strongly but repel N₃
b) attract N₁ strongly, N₂ weakly and repel N₃ weakly
c) attract N₁ strongly, but repel N₂ and N₃ weakly
d) attract all three of them

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2. If an ammeter is to be used in place of a voltmeter, then we must connect with the ammeter is
a) low resistance in parallel
b) high resistance in parallel
c) high resistance in series
d) low resistance in series

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1. An inductor (L = 100 mH), a resistor (R = 100Ω) and a battery (E = 100V) are initially connected in series as shown in the figure. After a long time the battery is disconnected after short circulating the points A and B. The current in the circuit 1 ms after the short circuit is

a) 1/eA
b) eA
c) 0.1A
d) NAB ω

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2. In an AC generator, a coil with N turns, all of all same area A and total total resistance R, rotates with frequency ω in a magnetic field B. The maximum value of emf generated in the coil is
a) N A B R ω
b) N A B
c) N A B R
d) N A B ω

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1. Which of the following radiations has the least wavelength?
a) γ-rays
b) β-rays
c) α-rays
d) X-rays

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2. An electromagnetic wave of frequency v = 3.0 MHz passes from vacuum into a dielectric medium and permittivity ε = 4.0. Then
a) wavelength is doubled and the frequency remains unchanged
b) wavelength is doubled and frequency becomes half
c) wavelength is halved and frequency remains unchanged
d) wavelength and frequency both remain unchanged

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1. Two lenses of power -15D and + 5D are in contact with each other. The focal length of the combination is
a) -20 cm
b) -10 cm
c) +20 cm
d) +10 cm

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2. To get three images of a single object, one should have two plane mirrors at an angle of
a) 60⁰
b) 90⁰
c) 120⁰
d) 30⁰

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1. A uniform electric field and a uniform magnetic field are acting along the same direction in a certain region. If an electron is projected along the direction of the fields with a certain velocity, then
a) its velocity will decrease will decrease
b) its velocity will increase
c) it will turn towards right of direction of motion
d) it will turn towards left of direction of motion

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2. If a source of power 4 kW produces 10²⁰ photons/secong , the radiation belong to a part of the sepctrum called
a) X-rays
b) ultraviolet rays
c) microwaves
d) γ-rays

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1. A nucleus distintegrates into two nuclear parts which have their velocities in the ratio 2 : 1. The ratio of their nuclear sizes will be
a) 2^1/3 : 1
b) 1 : 3^1/2
c) 3^1/2 : 1
d) 1 : 2^1/2

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2. Suppose an electron is attracted towards the origin by a force , where k is a constant and r is the distance of the electron from the origin . By applying Bohr model to this sytem, the radius of the n^th orbital of the electron is found to be r_n and the kinetic energy of the electron to be T_n. Then which of the following is true?
a) T ∝ , r_n ∝ n²
b) T_n is independent of n, r_n ∝ n
c) T_n ∝ , r_n ∝ n
d) T_n ∝ , r_n ∝ n²

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1. In a common base amplifier, the phase difference between the input signal voltage and output voltage is
a) $\frac{\pi}{4}$
b) π
c) zero
d) $\frac{\pi}{2}$

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2. By increasing the temperature, the specific resistance of a conductor and a semiconductor
a) increases for both
b) decreases for both
c) increases, decreases respectively
d) decreases, increaes respectively

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1. This question has statement 1 and statement 2. Of the four choices given after the statements, choose the one that best describes the two statements.
Statement 1. Sky wave signals are used for long distance radio communication. These signals are in general, less stable than ground wave signals.
Statement 2 The state of ionosphere varies from hour to hour, day to day and season to season.
a) Statement 1 is true, Statement 2 is true, Statement 2 is the correct explanation of Statement 1
b) Statement 1 is true , Statement 2 is true, Statement 2 is not the correct explanations of Statement 1
c) Statement 1 is false, Statement 2 is true
d) Statement 1 is true, Statement 2 is false

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2. The logic circuit shown below has the input waveforms A and B as shown. Pick out the correct output wavefrom.


a)
b)
c)
d)

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