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The electrostatic potential in a charged spherical region of radius r varies as $$V=ar^{3}+b$$, where a and b are constants. The total charge in the sphere of unit radius is $$\alpha \times \pi a\in_{\circ}$$. the value of $$\alpha$$ is_____. (permittivity of vacuum is $$\in_{\circ}$$)
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Three masses 200 kg, 300 kg and 400 kg are placed at the vertices of an equilateral triangle with sides 20 m. They are rearranged on the vertices of a bigger triangle of side 25 m and with the same centre. The work done in this process ____ J. (Gravitational constant $$G=6.7 \times 10^{-11} Nm^{2}/kg^{2}$$)
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A boy throws a ball into air at 45° from the horizontal to land it on a roof of a building of height H . If the ball attains maximum height in 2 s and lands on the building in 3 s after launch, then value of H is ___ m. $$(g=10m/s^{2})$$
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Three charges+ 2q, +3q and -4q are situated at (0, -3a), (2a, 0) and (-2a, 0) respectively in the x y plane. The resultant dipole moment about origin is ___ .
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A cylindrical block of mass M and area of cross section A is floating in a liquid of density $$\rho$$ and with its axis vertical. When depressed a little and released the block starts oscillating. The period of oscillation is ___
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Au unpolarised light is incident at an inteiface of two dielectric media having refractive indices of 2 (incident medium) and $$2\sqrt{3}$$ (medium) respectively. To satisfy the condition that reflected and refracted rays are perpendicular to each other, the angle of incidence is ___.
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Density of water at 4 °C and 20 °C are $$1000 kg/m^{3}\text{ and }998kg/m^{3}$$ respectively. The increase in internal energy of 4 kg of water when it is heated from 4 °C to 20 °C is_____ J.
(specific heat capacity of water = $$4.2\times\ 10^3$$J / kg K. and 1 atmospheric pressure $$=10^{5}Pa$$)
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Match the LIST-I with LIST-II
Choose the correct answer from the options given below:
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There are three co-centric conducting spherical shells A, B and C of radii a, b and c respectively (c > b > a) and they are charged with charge $$q_{1},q_{2}\text{ and }q_{3}$$ respectively. The potentials of the spheres A, Band C respectively, are :
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A spring of force constant 15 N/m is cut into two pieces. If the ratio of their length is 1:3, then the force constant of smaller piece is __ /m.
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A brass wire of length 2 m and radius 1 mm at 27 °C is held taut between two rigid supports. Initially, it was cooled to a temperature of -43 °C, creating a tension T in the wire. The temperature to which the wire has to be cooled in order to increase the tension in it to 1.4T, is ____ °C.
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For the series LCR circuit connected with 220 V, 50 Hz a.c source as shown in the figure, the power factor is $$\frac{\alpha}{10}$$. The value of $$\alpha$$ is______.
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Two resistors 2Ω and 3Ω are connected in the gaps of bridge as shown in figure. The null point is obtained with the contact of jockey at some point on wire XY. When an unknown resistor is connected in parallel with 3Ω resistor, the null point is shifted by 22.5 cm toward Y. The resistance of unknown resistor is ____ Ω .
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Two electrons are moving in orbits of two hydrogen like atoms with speeds $$3\times 10^{5} m/s \text{ and } 2.5\times 10^{5} m/s$$ respectively. If the radii of these orbits are nearly same then the possible order of energy states are ____ respectively.
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Match the LIST-I with LIST-II
Choose the correct answer from the options given below:
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The exit surface of a prism with refractive index n is coated with a material having refractive index $$\frac{n}{2}$$. When this prism is set for minimum angle of deviation, it exactly meets the condition of critical angle. The prism angle is ___ .
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Two resistors of 100Ω each are connected in series with a 9 V batte1y. A voltmeter of 400Ω resistance is connected to measure the voltage drop across one of the resistors. The voltmeter reading is ____ V.
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Given below are two statements:
Statement I: For all elements, greater the mass of the nucleus, greater is the binding energy per nucleon.
Statement II: For all elements, nuclei with less binding energy per nucleon transforms to nuclei with greater binding energy per nucleon.
In the light of the above statements, choose the correct answer from the options given below
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Two masses 400 g and 350 g are suspended from the ends of a light string passing over a heavy pulley of radius 2 cm. When released from rest the heavier mass is observed to fall 81 cm in 9 s. The rotational inertia of the pulley is ___ $$kg.m^{2}$$.$$(g=9.8 m/s^{2})$$
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In a microscope of tube length 1O cm two convex lenses are arranged with focal length of 2 cm and 5 cm. Total magnification obtained with this system for normal adjustment is $$(5)^{k}$$ The value of k is ___.
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In the given figure, the blocks A, B and C weigh 4 kg, 6 kg and 8 kg, respectively. The coefficient of sliding friction between any two surfaces is 0.5. The force F required to slide the block C with constant speed is __ N. (Use $$g=10m/s^{2}$$)
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A gas of certain mass filled in a closed cylinder at a pressure of 3.23 kPa has temperature 50 °C. The gas is now heated to double its temperature. The modified pressure is __ Pa.
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A short bar magnet placed with its axis at 30° with an external field of 800 Gauss, experiences a torque of 0.016 N.m. The work done in moving it from most stable to most unstable position is $$\alpha \times 10^{-3}J$$. The value of $$\alpha$$ is ___.
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Sixty four rain drops of radius 1 mm each falling down w-ith a terminal velocity of 10 cm/s coalesce to fonn a bigger drop. The terminal velocity of bigger drop is_____cm/s
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A voltage regulating circuit consisting of Zener diode, having break-down voltage of 10 V and maximum power dissipation of 0.4 W, is operated at 15 V. The approximate value of protective resistance in this circuit is ___ Ω.
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