1. The dimensions of magnetic field in M, L, T and C (coulomb) is given as
a) [MLT^-1C^-1]
b) [MT²C^-2]
c) [MT^-1C^-1]
d) [MT²C^-1]

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2. 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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1. A mass m hangs with the help of a string wrapped around a pulley on a frictionless bearing. The pulley has mass m and radius R. Assuming pulley to be perfect uniform circular disc, the acceleration of the mass m, if the string does not slip on the pulley , is
a) g
b) $\frac{2}{3}g$
c) $\frac{g}{3}$
d) $\frac{3}{2}g$

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2. A particle of mass m is projected with a velocity v making an angle of 30⁰ with the horizontal. The magnitude of angular momentum of the projectile about the point of projection when the particle is at its maximum height h is
a) $\frac{\sqrt{3}}{2}\frac{mv^{2}}{g}$
b) Zero
c) $\frac{mv^{3}}{\sqrt{2}g}$
d) $\frac{\sqrt{3}}{16}\frac{mv^{3}}{g}$

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1. An annular ring with inner and outer radii R₁ and R₂ is rolling without slipping with a uniform angular speed. The ratio of the forces experienced by the two particles situated on the inner and outer parts of the ring, $\frac{F_{1}}{F_{2}}$ is
a) $\frac{R_{2}}{R_{1}}$
b) $\left (\frac{R_{1}}{R_{2}} \right )^{2}$
c) 1
d) $\frac{R_{1}}{R_{2}}$

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2. A block of mass m is connected to another block of mass M by a spring (massless ) of spring constant k. The blocks are kept on a smooth horizontal plane. Initially the blocks are at rest and the spring is unstretched. Then a constant force F starts acting on the block of mass M to pull it. Find the force on the block of mass m.
a) $\frac{mF}{M}$
b) $\frac{\left ( M+m \right )F}{m}$
c) $\frac{mF}{\left ( m+M \right )}$
d) $\frac{Mf}{\left ( m+M \right )}$

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1. A body is moved along a straight line by a machine delivering a constant power. The distance moved by the body in time t is proportional to
a) t^3/4
b) t^3/2
c) t^1/4
d) t^1/2

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2. The potential energy of a 1 kg particle free to move along the x-axis is given by
v (x) = $\left ( \frac{x^{4}}{4}-\frac{x^{2}}{2} \right )$ The total mechanical energy of the particle is 2 J. Then, the maximum speed ( in ms^-1) is
a) $\frac{3}{\sqrt{2}}$
b) √2
c) $\frac{1}{\sqrt{2}}$
d) 2

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1. For the given uniform square lamina ABCD, whose centre is O

a) $\sqrt{2}I_{AC}$ = I_EF
b) I_AD = 3 I_EF
c) I_AC = I_EF
d) I_AC = $\sqrt{2}I_{EF}$

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2. A thin circular ring of mass m and radius R is rotating about its axis with a constant angular velocity ω. Two objects each of mass M are attached gently to the opposite ends of a diameter of the ring. The ring now rotates with an angular velocity ω =
a) $\frac{\omega\left (m + 2M \right )}{m}$
b) $\frac{\omega\left (m - 2M \right )}{\left (m + 2M \right )}$
c) $\frac{\omega m}{\left (m + M \right )}$
d) $\frac{\omega m}{\left (m + M \right )}$

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1. Two spherical bodies of mass M and 5M and radii R and 2R respectively are released in free space with initial separation between their centres equal to 12R. If they attract each other due to gravitational force only, then the distance covered by the smaller body just before collision is
a) 2.5 R
b) 4.5 R
c) 7.5 R
d) 1.5 R

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2. A particle of mass 10 g is kept on the surface of a uniform sphere of mass 100 kg and radius 10 cm.Find the work to be done against the gravitational force between them, to take the particle far away from the sphere, (you may take G = 6.67 x 10^-11 Nm²/kg^-2)
a) 13.34 x 10^-10 J
b) 3.33 x 10^-10 J
c) 6.67 x 10^-9 J
d) 6.67 x 10^-10 J

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1. Infrared radiations are detected by
a) Spectrometer
b) Pyrometer
c) Nanometer
d) Photometer

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2. A spherical solid ball of volume V is made of a material of density ρ₁. It is falling through a liquid of density ρ₂(ρ₂ < ρ₁). [Assume that the liquid applies a viscous force on ball that is proportional to the square of its speed v, ie, F_visvous = -kv²(K > 0)]. The terminal speed of the ball is
a) $\sqrt{\frac{Vg\left (\rho_{1} - \rho_{2} \right )}{k}}$
b) $\frac{Vg\rho_{1}}{k}$
c) $\sqrt{\frac{Vg\rho_{1}}{k}}$
d) $\frac{Vg\left (\rho_{1} - \rho_{2} \right )}{k}$

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1. A Carnot engine, having an efficiency of η = $\frac{1}{10}$ as heat engine , is used as a refrigerator. If the work done on the system is 10 J, the amount of energy absorbed from the reservoir at lower temperature is
a) 99 J
b) 90 J
c) 1 J
d) 100 J

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2. Which of the following statements is correct for any thermodynamics system?
a) The internal energy changes in all processes.
b) Internal energy and entropy are state functions.
c) The change in entropy can never be zero .
d) The work done in an adiabatic process is always zero.

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1. The potential energy function for the force between two atoms in a diatomic molecule is approximately given by U(x) = $\frac{a}{x^{12}} - \frac{b}{x^{6}}$ , where a and b are constant and x is the distance between the atoms. If the dissociation energy of the molecule is D = [U(x=∞) - U_{at equilibrium}], D is
a) $\frac{b^{2}}{2a}$
b) $\frac{b^{2}}{12a}$
c) $\frac{b^{2}}{4a}$
d) $\frac{b^{2}}{6a}$

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2. An insulated container of gas has two chambers seperated by an insulating partition. One of the chambers has volume V₁ and contains ideal gas at pressure p₁ and temperature T₂. If the partition is removed without doing any work on the gas, the final equilibrium temperature of the gas in the container will be
a) $\frac{T_{1}T_{2}\left ( p_{1}V_{1} + p_{2}V_{2} \right )}{p_{1}V_{1}T_{2} + p_{2}V_{2}T_{1}}$
b) $\frac{p_{1}V_{1}T_{1} + p_{2}V_{2}T_{2}}{p_{1}V_{1} + p_{2}V_{2}}$
c) $\frac{p_{1}V_{1}T_{2} + p_{2}V_{2}T_{1}}{p_{1}V_{1} + p_{2}V_{2}}$
d) $\frac{T_{1}T_{2}\left ( p_{1}V_{1} + p_{2}V_{2} \right )}{p_{1}V_{1}T_{1} + p_{2}V_{2}T_{2}}$

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1. The maximum velocity of a particle, executing simple harmonic motion with an amplitude 7mm, is 4.4 ms^-1. The period of oscillation is
a) 0.01s
b) 10s
c) 0.1 s
d) 100s

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2. A mass M, attached to a horizontal spring, executes SHM with amplitude A₁. When the mass M passes through its mean position then a smaller mass m is placed over it and both of them move together with amplitude A₂. The ratio of $\left (\frac{A_{1}}{A_{2}} \right )$
a) $\frac{M + m}{M}$
b) $\left (\frac{M}{M + m} \right )^{1/2}$
c) $\left (\frac{M + m}{m} \right )^{1/2}$
d) $\frac{M}{M + m}$

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1. A parallel plate capacitor is made by stacking n equally spaced plates connected alternatively . If the capacitance between any two plates is C, then the resultant xcapacitance is
a) (n-1)C
b) (n+1)C
c) C
d) nC

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2. A sheet of aluminium foil of negligible thickness is introduced between the plates of a capacitor. The capacitance of the capacitor
a) decreases
b) remains unchanged
c) becomes infinite
d) increases

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1. In the circuit, the galvanometer G shows zero deflection. If the batteries A and B have negligible internal resistance, the value of the resistor R will be

a) 200 Ω
b) 100 Ω
c) 500 Ω
d) 1000 Ω

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2. A 5V battery with internal resistance 2Ω and a 2V battery with internal resistance 1Ω are connected to a 10Ω resistor as shown in the figure.

The current in the 10Ω resistor is
a) 0.27 A, P₂ to P₁
b) 0.03 A, P₁ to P₂
c) 0.03A, P₂ to P₁
d) 0.27 A, P₁ to P₂

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1. A particle of charge -16 x 10^-18 C moving with velocity 10ms^-1 along the x-axis centres a region where a magnetic field of induction B is along the y-axis and an electric field of magnetic 10⁴Vm^-1 is along the negative z-axis . If the charged particle continues moving along the x-axis, the magnetic of B is
a) 10³ Wb/m²
b) 10⁵ Wb/m²
c) 10¹⁶ Wb/m²
d) 10^-3 Wb/m²

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2. A thin circular disk of radius R is uniformly charged with density σ > 0 per unit area. The disk rotates about its axis with a uniform anguilar speed ω. The magnetic moment of the disk is
a) 2πR⁴ω
b) πR⁴σω
c) $\frac{\pi R^{4}}{2}\sigma \omega$
d) $\frac{\pi R^{4}}{4}\sigma \omega$

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1. A metal consuctor of length 1m rotates vertically about one of its ends at anglular velocity 5 rad/s. If the horizontal component of earths magnetic field is 0.2 x 10^-4 T, then the emf developed between the two ends of the conductor is
a) 5μV
b) 50μV
c) 5mV
d) 50mV

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2. A coil having n turns and resistance RΩ is connected with a galvanometer of resistance 4R Ω. This combination is moved in time t seconds from a magnetic field W₁ weber to W₂ weber. The induced current in the circuit is
a) $\frac{W_{2} - W_{1}}{5Rnt}$
b) $-\frac{n\left (W_{2} - W_{1} \right )}{5RT}$
c) $-\frac{\left (W_{2} - W_{t} \right )}{Rnt}$
d) $-\frac{n\left (E_{2} - W_{2} \right )}{Rt}$

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1. Electromagnetic waves are transverse in nature is evident by
a) polarization
b) interference
c) reflection
d) diffraction

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2. A radiation of energy E falls normally on a perfectly reflecting surface. The momentum transferred to the surface is
a) $\frac{E}{c}$
b) $\frac{2E}{c}$
c) Ec
d) $\frac{E}{c^{2}}$

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1. In a Youngs double slit experiment the intension at a point where the path difference is $\frac{\lambda}{6}$ (λ being the wavelength of the light used) is I. If I₀ denotes the maximum intensity ,$\frac{I}{I_{0}}$ is equal to
a) $\frac{1}{\sqrt{2}}$
b) $\frac{\sqrt{3}}{2}$
c) $\frac{1}{2}$
d) $\frac{3}{4}$

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2. An astronomical telescope has a large aperture to
a) reduce spherical aberration
b) have high resolution
c) increase span of observation
d) have low dispersion

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1. Sodium and copper have work functions 2.3 eV and 4.5 eV respectively. Then the ratio of the wavelengths is nearest to
a) 1:2
b) 4:1
c) 2:1
d) 1:4

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2. 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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1. A solid which is not transparent to visible light and whose conductivity increases with temperature is formed by
a) ionic binding
b) covalent binding
c) van der Waals binding
d) metallic binding

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2. The part of a transistor which is most heavily doped to produce large number of majority carriers is
a) emitter
b) base
c) collector
d) can be any of the above three

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1. When npn transistor is used as an amplifier
a) electrons move from base to collector
b) holes move from either to base
c) electrons move from collector to base
d) holes move from base to emiiter

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2. For a transistor amplifier in common emitter configuration for load impedence of 1 kΩ
(h_fe = 50 and h_oe = 25μA/V, the current gain is
a) -5.2
b) -15.7
c) -24.8
d) -48.78

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1. Which of the following four alternatives is not correct?
a) to increase the sensitivity
b) to reduce the time lag between transmission and reception of the information signal
c) to reduce the size of antenna
d) to reduce the fractional band width, that is the ratio of the signal band width to the centre frequency

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2. Consider telecommunication through optical fibres. Which of the following statements is not true?
a) Optical fibres can be graded refractive index
b) Optical fibres are subjected to electromagnetic interference from outside
c) Optical fibres have extremely low transmission loss
d) Optical fibres may have homogeneous core with a suitable cladding

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