The electrostatic potential due to an electric dipole at a distance '\(r\)' varies as _______.

An electric power line having total resistance of 2 Ω, delivers 1 kW of power of 250 V. The percentage efficiency of transmission line is: __________ .

What is the current through the battery in the circuit shown below?

The current in an inductor is given by \(\mathrm{I}=(3 \mathrm{t}+8)\) where \(t\) is in second. The magnitude of induced emf produced in the inductor is \(12 \mathrm{mV}\). The selfinductance of the inductor _______ \(\mathrm{mH}\).

Two point charges \(q_1\,(\sqrt {10}\,\,\mu C)\) and \(q_2\,(-25\,\,\mu C)\) are placed on the \(x-\) axis at \(x = 1\,m\) and \(x = 4\,m\) respectively. The electric field (in \(V/m\) ) at a point \(y = 3\,m\) on \(y-\) axis is, [ take \({\mkern 1mu} {\mkern 1mu} \frac{1}{{4\pi {\varepsilon _0}}} = 9 \times {10^9}{\mkern 1mu} {\mkern 1mu} N{m^2}{C^{ - 2}}{\rm{ }}\) ]

A circular coil of \(1000 \,\,turns\) each with area \(1\, m ^{2}\) is rotated about its vertical diameter at the rate of one revolution per second in a uniform horizontal magnetic field of \(0.07 \,T\). The maximum voltage generation will be......... \(V\).

A loop ABCDA , carrying current \(\mathrm{I}=12 \mathrm{~A}\), is placed in a plane, consists of two semi-circular segments of radius \(R_1=6 \pi \mathrm{~m}\) and \(\mathrm{R}_2=4 \pi \mathrm{~m}\). The magnitude of the resultant magnetic field at center O is \(\mathrm{k} \times 10^{-7} \mathrm{~T}\). The value of k is ______ (Given \(\mu_0=4 \pi \times 10^{-7} \mathrm{Tm} \mathrm{A}^{-1}\))

In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).

Consider two uniform discs of the same thickness and different radii \(R _{1}= R\) and \(R _{2}=\alpha R\) made of the same material. If the ratio of their moments of inertia \(I_{1}\) and \(I_{2}\), respectively, about their axes is \(I _{1}: I _{2}=1: 16\) then the value of \(\alpha\) is

Match List-I with List-II.

	List-I		List-II
A.	Coefficient of viscosity	I.	\(\left[ ML ^{-1} T^{-2}\right]\)
B.	Surface tension	II.	\(\left[ ML ^2 T^{-2}\right]\)
C.	Pressure	III.	\(\left[ ML ^0 T^{-2}\right]\)
D.	Surface energy	IV.	\(\left[ ML ^{-1} T^{-1}\right]\)

Choose the correct answer from the options given below :

Match List\(-I\) with List\(-II.\)

List\(-I\)	List\(-II\)
\((a)\) \(10\, km\) height over earth's surface	\((i)\) Thermosphere
\((b)\) \(70\, km\) height over earth's surface	\((ii)\) Mesosphere
\((c)\) \(180\, km\) height over earth's surface	\((iii)\) Stratosphere
\((d)\) \(270\, km\) height over earth's surface	\((iv)\) Troposphere

If two metallic plates of equal thicknesses and thermal conductivities \({K_1}\) and \({K_2}\) are put together face to face and a common plate is constructed, then the equivalent thermal conductivity of this plate will be

The electric potential at the surface of an atomic nucleus \((Z=50)\) of radius \(9 \times 10^{-13} cm\) is \(\alpha \times 10^6 V\). What is the value of \(\alpha\)?
(Charge of proton \(1.6 \times 10^{-19} C\) )