An electric bulb is rated as \(200 \,W\). What will be the peak magnetic field (\(\times 10^{-8}\, T\)) at \(4\, m\) distance produced by the radiations coming from this bulb\(?\) Consider this bulb as a point source with \(3.5 \%\) efficiency.

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

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 \(1.6 \times 10^{-19} C\) )

A large drum having radius \(R\) is spinning around its axis with angular velocity \(\omega\), as shown in figure. The minimum value of \(\omega\) so that a body of mass M remains stuck to the inner wall of the drum, taking the coefficient of friction between the drum surface and mass M is \(\mu\), is :

A shunt of resistance \(1\,\Omega \) is connected across a galvanometer of \(120\,\Omega \) resistance. A current of \(5.5\, ampere\) gives full scale deflection in the galvanometer. The current that will give full scale deflection in the absence of the shunt is nearly ............... \(ampere\)

Given below are two statements:
Statement \(I\): Electromagnetic waves carry energy as they travel through space and this energy is equally shared by the electric and magnetic fields.
Statement \(II\): When electromagnetic waves strike a surface, a pressure is exerted on the surface.
In the light of the above statements, choose the most appropriate answer from the options given below:

Two radioactive materials \(A\) and \(B\) have decay constants \(10\,\lambda \) and \(\lambda \), respectively. If initially they have the same number of nuclei, then the ratio of the number of nuclei of a to that of \(B\) will be \(1/e\) after a time

A point particle of charge \(Q\) is located at \(P\) along the axis of an electric dipole 1 at a distance \(r\) as shown in the figure. The point P is also on the equatorial plane of a second electric dipole 2 at a distance r . The dipoles are made of opposite charge q separated by a distance \(2 a\). For the charge particle at P not to experience any net force, which of the following correctly describes the situation?

The one division of main scale of vernier callipers reads \(1\,mm\) and \(10\) divisions of Vernier scale is equal to the \(9\) divisions on main scale. When the two jaws of the instrument touch each other the \(zero\) of the Vernier lies to the right of \(zero\) of the main scale and its fourth division coincides with a main scale division. When a spherical bob is tightly placed between the two jaws, the \(zero\) of the Vernier scale lies in between \(4.1\,cm\) and \(4.2\,cm\) and \(6^{\text {th }}\) Vernier division coincides with a main scale division. The diameter of the bob will be \(.............10^{-2}\,cm\)

The de-Broglie wavelength associated with an electron and a proton were calculated by accelerating them through same potential of \(100\, V\). What should nearly be the ratio of their wavelengths ? \(\left( m _{ P }=1.00727\, u , m _{ e }=0.00055 \,u \right)\)

A coil of area A and N turns is rotating with angular velocity \(\omega\) in a uniform magnetic field \(\vec{B}\) about an axis perpendicular to \(\vec{B}\). Magnetic flux \(\varphi\) and induced \(\operatorname{emf} \varepsilon\) across it, at an instant when \(\vec{B}\) is parallel to the plane of coil, are :

A force \(\overrightarrow{ F }=(2+3 x) \hat{ i }\) acts on a particle in the \(x\) direction where \(F\) is in newton and \(x\) is in meter. The work done by this force during a displacement from \(x =0\) to \(x =4\,m\), is .......\(J\).

A convex lens of refractive index \(1.5\) and focal length \(18 cm\) in air is immersed in water. The change in focal length of the lens will be \(...........cm\).\(\left(\right.\) Given refractive index of water \(\left.=\frac{4}{3}\right)\)