A \(2\, \mu F\) capacitor \(C _{1}\) is first charged to a potential difference of \(10\, V\) using a battery.Then the battery is removed and the capacitor is connected to an uncharged capacitor \(C _{2}\) of \(8\, \mu F\). The charge in \(C _{2}\) on equilibrium condition is \(\ldots\,\mu C\). (Round off to the Nearest Integer)

In a ferromagnetic material, below the curie temperature, a domain is defined as:

A wire of length \(L\) is hanging from a fixed support. The length changes to \(L _{1}\) and \(L _{2}\) when masses \(1 \,kg\) and \(2 \,kg\) are suspended respectively from its free end. Then the value of \(L\) is equal to ..................

Given below are two statements. One is labelled as Assertion A and the other is labelled as Reason \(R\). Assertion \(A\) : If \(dQ\) and \(dW\) represent the heat supplied to the system and the work done on the system respectively. Then according to the first law of thermodynamics \(d Q=d U-d W\). Reason \(R :\) First law of thermodynamics is based on law of conservation of energy. In the light of the above statements, choose the correct answer from the option given below :

In Young's double slit experiment, the fringe width of the interference pattern produced on the screen is \(2.4\) \(\mu\)m. If the experiment is carried out in another medium having refractive index \(1.2\), the fringe width will be _____ \(\mu\)m.

What happens to the inductive reactance and the current in a purely inductive circuit if the frequency is halved ?

Activities of three radioactive substances \(A , B\) and \(C\) are represented by the curves \(A, B\) and \(C,\) in the figure. Then their half-lives \(T _{\frac{1}{2}}( A ): T _{\frac{1}{2}}( B ): T _{\frac{1}{2}}( C )\) are in the ratio

A solid sphere and solid cylinder of identical radii approach an incline with the same linear velocity (see figure). Both roll without slipping all throughout. The two climb maximum heights \(h_{sph}\) and \(h_{cyl}\) on the incline. The radio \(\frac{{{h_{sph}}}}{{{h_{cyl}}}}\) is given by

A moving coil galvanometer has resistance \(50\,\Omega \) and it indicates full deflection at \(4\,mA\) current. A voltmeter is made using this galvanometer and a \(5\,k\Omega \) resistance. The maximum voltage, that can be measured using this voltamenter, will be close to ......\(V\)

Two insulated circular loop \(A\) and \(B\) radius ' \(a\) ' carrying a current of ' \(\mathrm{I}\) ' in the anti clockwise direction as shown in figure. The magnitude of the magnetic induction at the centre will be _______.

The centre of a wheel rolling on a plane surface moves with a speed \(v_{0} .\) A particle on the rim of the wheel at the same level as the centre will be moving at a speed \(\sqrt{x}\, v_{0}\). Then the value of \(x\) is ...... .

The reverse breakdown voltage of a Zener diode is \(5.6\, V\) in the given circuit. The current \(I_z\) through the Zener is......\(mA\)