# Two resistors of resistance, $$100$$ $$\Omega$$ and $$200$$ $$\Omega$$ are connected in parallel in an electrical circuit. The ratio of the thermal energy developed in $$100$$ $$\Omega$$ resistor to that in $$200$$ $$\Omega$$ resistor in a given time is: 1. $$4:1$$ 2. $$1:2$$ 3. $$2:1$$ 4. $$1:4$$

Subtopic:  Heating Effects of Current |
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Two hollow conducting spheres of radii $$R_1$$ and $$R_2$$ $$\left ( R_1\gg R_2 \right )$$ have equal charges. The potential would be:

 1 dependent on the material property of the sphere 2 more on bigger sphere 3 more on smaller sphere 4 equal on both the spheres
Subtopic:  Electric Potential |
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The angular speed of a flywheel moving with uniform angular acceleration changes from $$1200$$ rpm to $$3120$$ rpm in $$16$$ s. The angular acceleration in rad/s² is:
1. $$104 \pi$$
2. $$2\pi$$
3. $$4\pi$$
4. $$12\pi$$
Subtopic:  Rotational Motion: Kinematics |
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When light propagates through a material medium of relative permittivity, $$\varepsilon_{r}$$ and relative permeability, $$\mu_{r}$$ the velocity of light, $$v$$ is given by:
($$c$$ = velocity of light in vacuum)
1. $$v=\dfrac{{c}}{\sqrt{\varepsilon_{r} \mu_{{r}}}}$$
2. $$v={c}$$
3. $$v=\sqrt{\dfrac{\mu_{{r}}}{\varepsilon_{{r}}}}$$
4. $$v=\sqrt{\dfrac{\varepsilon_{{r}}}{\mu_{{r}}}}$$
Subtopic:  Properties of EM Waves |
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A long solenoid of radius $$1~\text{mm}$$ has $$100$$ turns per mm. If $$1~\text{A}$$ current flows in the solenoid, the magnetic field strength at the centre of the solenoid is:
 1 $$6.28 \times 10^{-4} ~\text{T}$$ 2 $$6.28 \times 10^{-2}~\text{T}$$ 3 $$12.56 \times 10^{-2}~\text{T}$$ 4 $$12.56 \times 10^{-4} ~\text{T}$$
Subtopic:  Magnetic Field due to various cases |
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A shell of mass m is at rest initially. It explodes into three fragments having masses in the ratio $$2:2:1$$. If the fragments having equal masses fly off along mutually perpendicular directions with speed $$v,$$ the speed of the third (lighter) fragment is:
 1 $$3 \sqrt{2} v$$ 2 $$v$$ 3 $$\sqrt{2} v$$ 4 $$2 \sqrt{2} v$$
Subtopic:  Linear Momentum |
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As the temperature increases, the electrical resistance:

 1 decreases for conductors but increases for semiconductors. 2 increases for both conductors and semiconductors. 3 decreases for both conductors and semiconductors. 4 increases for conductors but decreases for semiconductors.
Subtopic:  Energy Band theory |
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A biconvex lens has radii of curvature, $$20$$ cm each. If the refractive index of the material of the lens is $$1.5,$$ the power of the lens is:
 1 infinity 2 $$+2$$ D 3 $$+20$$ D 4 $$+5$$ D
Subtopic:  Lenses |
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Given below are two statements:
 Statement I: Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element $$I(dl)$$ of a current-carrying conductor only. Statement II: Biot-Savart's law is analogous to Coulomb's inverse square law of charge $$q,$$ with the former being related to the field produced by a scalar source, $$Idl$$ while the latter being produced by a vector source, $$q.$$

 1 Statement I is incorrect but Statement II is correct. 2 Both Statement I and Statement II are correct. 3 Both Statement I and Statement II are incorrect. 4 Statement I is correct but Statement II is incorrect.
Subtopic:  Biot-Savart Law |
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A square loop of side $$1$$ m and resistance $$1$$ $$\Omega$$ is placed in a magnetic field of $$0.5$$ T. If the plane of the loop is perpendicular to the direction of the magnetic field, the magnetic flux through the loop is:
 1 $$0$$ 2 $$2$$ weber 3 $$0.5$$ weber 4 $$1$$ weber
Subtopic:  Magnetic Flux |
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