All resistances in figure are \(1\,\Omega\) each. The value of current ' \(I\) ' is \(\frac{a}{5}\,A\). The value of \(a\) is

A certain charge \(Q\) is divided into two parts \(q\) and \((Q-q) .\) How should the charges \(Q\) and \(q\) be divided so that \(q\) and \((Q-q)\) placed at a certain distance apart experience maximum electrostatic repulsion?

A rod of length \(10\) cm lies along the principle axis of a concave mirror of focal length \(10\) cm as shown in figure. The length of the image is _____ cm.

A electron of hydrogen atom on an excited state is having energy \(E_n=-0.85 \mathrm{eV}\). The maximum number of allowed transitions to lower energy level is _______.

A motor operating on 100 V draws a current of 1 A. If the efficiency of the motor is \(91.6 \%\), then the loss of power in units of \(\mathrm{cal} / \mathrm{s}\) is

Uniform magnetic fields of different strengths \(\left(B_1\right.\) and \(B_2\)), both normal to the plane of the paper exist as shown in the figure. A charged particle of mass m and charge q , at the interface at an instant, moves into the region 2 with velocity \(v\) and returns to the interface. It continues to move into region 1 and finally reaches the interface. What is the displacement of the particle during this movement along the interface?

(Consider the velocity of the particle to be normal to the magnetic field and \(B_2 \gt B_1\))

Same gas is filled in two vessels of the same volume at the same temperature. If the ratio of the number of molecules is \(1: 4\), then \(A.\) The \(r.m.s\). velocity of gas molecules in two vessels will be the same. \(B.\) The ratio of pressure in these vessels will be \(1: 4\) \(C.\) The ratio of pressure will be \(1: 1\) \(D.\) The \(r.m.s.\) velocity of gas molecules in two vessels will be in the ratio of \(1: 4\)

Two identical conducting spheres with negligible volume have \(2.1\, nC\) and \(-0.1\, nC\) charges, respectively. They are brought into contact and then separated by a distance of \(0.5 \,m\). The electrostatic force acting between the spheres is \(.......... \, \times 10^{-9} \,N\) [Given : \(4 \pi \varepsilon_{0}=\frac{1}{9 \times 10^{9}} SI\) unit]

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

List - \(I\)	List - \(II\)
\((a)\) Source of microwave frequency	\((i)\) Radioactive decay on nucleus
\((b)\) Source of infrared frequency	\((ii)\) Magnetron
\((c)\) Source of Gamma Rays	\((iii)\) Inner shell electrons
\((d)\) Source of \(X-\)rays	\((iv)\) Vibration of atoms and molecules
	\((v)\) \(LASER\)
	\((vi)\) \(RC\) circuit

Choose the correct answer from the options given below :

A thin circular disc is in the \(xy\) plane as shown in the figure. The ratio of its moment of inertia about \(z\)  and \(z'\)  axes will be

Particle \(A\) of mass \(m _{1}\) moving with velocity \((\sqrt{3} \hat{i}+\hat{j})\, ms ^{-1}\) collides with another particle \(B\) of mass \(m _{2}\) which is at rest initially. Let \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) be the velocities of particles \(A\) and \(B\) after collision respectively. If \(m _{1}=2\, m _{2}\) and after collision \(\overrightarrow{ V }_{1}=(\hat{ i }+\sqrt{3} \hat{ j })\, ms ^{-1},\) the angle between \(\overrightarrow{ V }_{1}\) and \(\overrightarrow{ V }_{2}\) is\(......^o\)

A capacitor of capacitance \(900\,\mu F\) is charged by a \(100\,V\) battery. The capacitor is disconnected from the battery and connected to another uncharged identical capacitor such that one plate of uncharged capacitor connected to positive plate and another plate of uncharged capacitor connected to negative plate of the charged capacitor. The loss of energy in this process is measured as \(x \times 10^{-2}\,J\). The value of \(x\) is \(..............\)