1. Out of the following pairs, which one does not have identical dimensions?
a) Angular momentum and Planck constant
b) Impulse and momentum
c) Moment of inertia and moment of a force
d) Work and torque

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2. 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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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 ball whose kinetic energy is E, is projected at an angle of 45⁰ to the horizontal . The kinetic energy of the ball at the highest point of its flight will be
a) E
b) $\frac{E}{\sqrt{2}}$
c) $\frac{E}{2}$
d) Zero

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1. The minimum velocity ( in ms^-1) with which a car driver must traverse a flat curve of radius 150 m and coefficient of friction 0.6 to avoid skidding is
a) 60
b) 30
c) 15
d) 25

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2. A spring balance is attached to the ceiling of a lift. A man hangs his bag on the spring and the spring reads 49 N, when the lift is stationary. If the lift moves downward with an acceleration of 5 ms^-2, the reading of the spring balance will be
a) 24 N
b) 74 N
c) 15 N
d) 49 N

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1. A bullet fired into a fixed target loses half of its velocity after penetrating 3 cm. How much further it will penetrate before coming to rest, assuming that it faces constant resistance to motion?
a) 3.0 cm
b) 2.0 cm
c) 1.5 cm
d) 1.0 cm

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2. An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range
a) 200 J - 500 J
b) 2 x 10⁵ J - 3 x 10⁵ J
c) 20000 J - 50000 J
d) 2000 J - 5000 J

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1. Let $\vec{F}$ be the force acting on a particle having position vector $\vec{r} \ and \ \vec{\tau}$ be the torque of this force about the origin. Then
a) $\vec{r} . \tau = 0 \ and \ \vec{F}. \tau \neq 0$
b) $\vec{r}.\vec{\tau} \neq \ and \ \vec{F} . \vec{\tau} = 0$
c) $\vec{r}.\vec{\tau} \neq \ and \ \vec{F} . \vec{\tau} \neq 0$
d) $\vec{r} . \tau = 0 \ and \ \vec{F}. \vec{\tau} = 0$

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2. Two identical particles move towards each other with velocity 2v and v respectively. The velocity of centre of mass is
a) v
b) $\frac{v}{3}$
c) $\frac{v}{2}$
d) zero

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1. If g is the acceleration due to gravity on the earth surface, the gain in the potential energy of an object of mass m raised from the surface of the earth to a height equal to the radius R of the earth, is
a) 2 mgR
b) $\frac{1}{2}mgR$
c) $\frac{1}{4}mgR$
d) mgR

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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. According to Newton law of cooling, the rate of cooling of a body is proportional to (Δ θ)ⁿ, where Δ θ is the difference of the temperature of the body and the surroundings, and n is equal to
a) 2
b) 3
c) 4
d) 1

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2. If a ball of steel (density ρ = 7.8 g cm^-3) attains a terminal velocity of 10 cm^-1 when falling in a tank of water (coefficient of viscosity η_water = 8.5 x 10^-4 Pa -s) then its terminal velocity in glycerine (ρ = 12 g cm^-3 , η = 13.2 Pa -s) would be nearly
a) 1.6 x 10^-5 cms^-1
b) 6.25 x 10^-4 cms^-1
c) 6.45 x 10^-4 cms^-1
d) 1.5 x 10^-5 cms^-1

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1. A container with insulating walls is divided into two equal parts by a partition fitted with a valve. One part is filled with an ideal gas at a pressure p and temperature T, whereas the other part is completely evacuated. If the valve is suddenly opened, the pressure and temperature of the gas will be
a) $\frac{p}{2}$, T
b) $\frac{p}{2}$, $\frac{T}{2}$
c) p, T
d) p , $\frac{T}{2}$

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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. Three perfect gases at absolute temperatures T₁, T₂ and T₃ are mixed. The masses of molecules are m₁, m₂ and m₃ and the number of molecules are n₁, n₂ and n₃ respectively . Assuming no loss of energy, the final temperature of the mixture is
a) $\frac{n_{1}T_{1} + n_{2}T_{2} + n_{3}T_{3}}{n_{1}+ n_{2} + n_{3}}$
b) $\frac{n_{1}T_{1}^{2} + n_{2}T_{2}^{2} + n_{3}T_{3}^{2}}{n_{1}T_{1}+ n_{2}T_{2} + n_{3}T_{3}}$
c) $\frac{n_{1}^{2}T_{1}^{2} + n_{2}^{2}T_{2}^{2} + n_{3}^{2}T_{3}^{2}}{n_{1}T_{1}+ n_{2}T_{2} + n_{3}T_{3}}$
d) $\frac{\left ( T_{1} + T_{2} + T_{3} \right )}{3}$

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2. At what temperature is the rms velocity of a hydrogen molecule equal to that of an oxygen molecule at 47⁰C?
a) 80K
b) -73K
c) 3K
d) 20K

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1. Statement I Two longitudinal waves given by equations -y₁ (x,t) = 2a sin(ω - kx) and y₂(x,t) = asin(2ωt - 2kx) will have equal intensity.
Statement II Intensity of waves of given frequency in same medium is proportional to square of amplitude only.
a) Statement I is false, Statement II is true
b) Statement I is true, Statement II is false
c) Statement I is true, Statement II true; Statement II is the correct explanation of Statement I
d) Statement I is true, Statement II is true; Statement II is not correct explanation of Statement I

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2. A mass M is suspended from a spting of negligible mass. The spring is pulled a little and then released so that the mass executes SHM of time period T. If the mass is increased by m, the time period becomes 5T/3, then the ratio of $\frac{m}{M}$ is
a) $\frac{3}{5}$
b) $\frac{25}{9}$
c) $\frac{16}{9}$
d) $\frac{5}{3}$

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1. A thin emi-circular ring of radius r has a positive charge q distributed uniformly over it. The net $\vec{E}$ at the centre O is

a) $\frac{q}{4\pi^{2}\epsilon_{0}r^{2}}\hat{j}$
b) $-\frac{q}{4\pi^{2}\epsilon_{0}r^{2}}\hat{j}$
c) $-\frac{q}{4\pi^{2}\epsilon_{0}r^{2}}\hat{j}$
d) $\frac{q}{2\pi^{2}\epsilon_{0}r^{2}}\hat{j}$

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2. The work done in placing a charge of 8 x 10^-18C on a condenser of capacity 100μF is
a) 16 x 10^-32J
b) 3.1 x 10^-26J
c) 4 x 10^-32J
d) 32 x 10^-32 J

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1. If 400Ω of resistance is made by adding four Ω resistance of tolerance 5% , then the tolerance of the combination is
a) 20%
b) 5%
c) 10%
d) 15%

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2. 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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1. Relative permittivity and permeability of a material are ε_r and μ_r respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
a) ε_r = 0.5, μ_r = 1.5
b) ε_R = 1.5, μ_r = 0.5
c) ε_r = 0.5, μ_r = 0.5
d) ε_r = 1.5μ_r = 1.5

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2. A horizontal straight wire 20m long extending from east to west is fallling with a speed of 5.0 m/s, at right angles to the horizontal component of the earths magnetic field 0.30 x 10 Wb/m². The instantaneous value of the emf induced in the wire will be
a) 6.0 mV
b) 3 mV
c) 4.5 mV
d) 1.5 mV

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1. Alternating current cannot be measured by DC ammter because
a) AC cannot pass through DC ammeter
b) AC changes direction
c) average value of current for complete cycle is zero
d) DC ammeter will get damaged

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2. 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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1. The rms value of the electric field of the light coming from the sum is 720 NC^-1. The average total energy density of the electromagnetic wave is
a) 4.58 x 10^-6 Jm-3
b) 6.37 x 10^-19 Jm^-3
c) 81.35 x 10^-12 Jm^-3
d) 3.3 x 10^-3 Jm^-3

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2. 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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1. The refractive index of glass is 1.520 for red light and 1.525 for blue light. Let D₁ and D₂ be angles of minimum deviation for red and blue light respectively in a prism of this glass. Then
a) D₁ < D₂
b) D₁ = D₂
c) D₁ can be less than or greater than D₂ depending upon the angle of prism
d) D₁ > D

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2. Which of the folowing is used in optical fibres?
a) Total internal reflection
b) Scattering
c) Diffraction
d) Refraction

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1. The surface a metal is islluminated with the light of 400 nm. The kinetic energy of the ejected photoelectrons was found to be 1.68 eV. The work function of the metal is (hc = 1240 eV-nm)
a) 3.09 eV
b) 1.42 eV
c) 151 eV
d) 1.68 eV

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2. Photon of frequency v has a momentum associated with it. If c is the velocity of light , the momentum is
a) $\frac{v}{c}$
b) hvc
c) $\frac{hv}{c^{2}}$
d) $\frac{hv}{c}$

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1. An alpha nucleus of energy $\frac{1}{2}mv^{2}$ bombards a heavy nuclear target of charge Ze. Then the distance of closest approach for the alpha nucleus will be proportional to
a) v²
b) $\frac{1}{m}$
c) $\frac{1}{v^{4}}$
d) $\frac{1}{Ze}$

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2. If 13.6 eV energy is required to ionize the hydrogen atom, then the energy required to remove an electron from n = 2 is
a) 10.2 eV
b) zero
c) 3.4 eV
d) 6.8 eV

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1. The electrical conductivity of a semiconductor increases when electromagnetic radiation of wavelength shorter than 2480 nm, is incident on it. The band in (eV) for the semiconductor is
a) 1.1 eV
b) 2.5 eV
c) 0.5 eV
d) 0.7 eV

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2. 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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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. 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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