The magnitude of magnetic induction at mid-point \(O\) due to current arrangement as shown in Fig will be

For which of the following particles will it be most difficult to experimentally verify the deBroglie relationship?

The electric field of a plane electromagnetic wave is given by \(\overrightarrow{\mathrm{E}}=\mathrm{E}_{0} \frac{\hat{\mathrm{i}}+\hat{\mathrm{j}}}{\sqrt{2}} \cos (\mathrm{kz}+\omega \mathrm{t})\) At \(\mathrm{t}=0,\) a positively charged particle is at the point \((\mathrm{x}, \mathrm{y}, \mathrm{z})=\left(0,0, \frac{\pi}{\mathrm{k}}\right) .\) If its instantaneous velocity at \((t=0)\) is \(v_{0} \hat{\mathrm{k}},\) the force acting on it due to the wave is

The circuit shown in the figure consists of a charged capacitor of capacity \(3\, \mu F\) and a charge of \(30\, \mu C\). At time \(t =0,\) when the key is closed, the value of current flowing through the \(5\, M \Omega\) resistor is \('x'\) \(\mu-A\). The value of \('x'\) to the nearest integer is .........

If the distance between object and its two times magnified virtual image produced by a curved mirror is \(15 \mathrm{~cm}\), the focal length of the mirror must be _______.

Six equal resistances are connected between points \(P, Q\) and \(R\) as shown in figure. Then net resistance will be maximum between

Given below are two statements: Statement \(I\) : In hydrogen atom, the frequency of radiation emitted when an electron jumps from lower energy orbit \(\left( E _{1}\right)\) to higher energy orbit \(\left( E _{2}\right)\), is given as \(hf = E _{1}- E _{2}\). Statement \(II\) : The jumping of electron from higher energy orbit \(\left(E_{2}\right)\) to lower energy orbit \(\left(E_{1}\right)\) is associated with frequency of radiation given as \(f\) \(=\left( E _{2}- E _{1}\right) / h\) This condition is Bohr's frequency condition. In the light of the above statements, choose the correct answer from the options given below

The circuit contains two diodes each with a forward resistance of \(50\, \Omega\) and with infinite reverse resistance. If the battery voltage is \(6\, V\), the current through the \(120\, \Omega\) resistance is \(mA\)

Magnetic field in a plane electromagnetic wave is given by  \(\vec B = {B_0}\,\sin \,\left( {kx + \omega t} \right)\hat jT\)  Expression for corresponding electric field will be Where \(c\) is speed of light

The current flowing through the \(1 \Omega\) resistor is \(\frac{\mathrm{n}}{10} \ A.\) The value of \(n\) is _______.

A solid cylinder and a solid sphere, having same mass \(M\) and radius \(R\), roll down the same inclined plane from top without slipping. They start from rest. The ratio of velocity of the solid cylinder to that of the solid sphere, with which they reach the ground, will be.

Diameter of a steel ball is measured using a Vernier callipers which has divisions of \(0. 1\,cm\) on its main scale \((MS)\) and \(10\) divisions of its vernier scale \((VS)\) match \(9\) divisions on the main scale. Three such measurements for a ball are given as

S.No.	\(MS\;(cm)\)	\(VS\) divisions
\((1)\)	\(0.5\)	\(8\)
\((2)\)	\(0.5\)	\(4\)
\((3)\)	\(0.5\)	\(6\)

If the zero error is \(- 0.03\,cm,\) then mean corrected diameter is  ........... \(cm\)