A cube of ice floats partly in water and partly in kerosene oil. The ratio of volume of ice immersed in water to that in kerosene oil is _______.(specific gravity of Kerosene oil \(=0.8\), specific gravity of ice \(=0.9\) )

The magnetic field of an E.M. wave is given by \(\overrightarrow{\mathrm{B}}=\left(\frac{\sqrt{3}}{2} \hat{i}+\frac{1}{2} \hat{j}\right) 30 \sin \left[\omega\left(\mathrm{t}-\frac{z}{\mathrm{c}}\right)\right]\) (S.I. Units).
The corresponding electric field in S.I. units is :

The radiation corresponding to \(3 \rightarrow 2\) transition of a hydrogen atom falls on a gold surface to generate photoelectrons. These electrons are passed through a magnetic field of \(5 \times 10^{-4} \,{T}\). Assume that the radius of the largest circular path followed by these electrons is \(7\, {mm}\), the work function of the metal is \(.....\,{eV}\) (Mass of electron \(=9.1 \times 10^{-31} \,{kg}\) )

Asseretion \(A:\) If in five complete rotations of the circular scale, the distance travelled on main scale of the screw gauge is \(5\, {mm}\) and there are \(50\) total divisions on circular scale, then least count is \(0.001\, {cm}\). Reason \(R:\) Least Count \(=\frac{\text { Pitch }}{\text { Total divisions on circular scale }}\) In the light of the above statements, choose the most appropriate answer from the options given below:

A piece of wood of mass \(0.03\, kg\) is dropped from the top of a \(100\, m\) height building. At the same time, a bullet of mass \(0.02\, kg\) is fired vertically upward, with a velocity \(100\, ms^{- 1}\), from the ground. The bullet gets embedded in the wood. Then the maximum height to which the combined system reaches above the top of the building before falling below is ........ \(m\). \((g = 10\, ms^{-2})\)

A physical quantity C is related to four other quantities \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s as follows \(\mathrm{C}=\frac{\mathrm{pq}^2}{\mathrm{r}^3 \sqrt{\mathrm{~s}}}\)
The percentage errors in the measurement of \(\mathrm{p}, \mathrm{q}, \mathrm{r}\) and s are \(1 \%, 2 \% 3 \%\) and \(2 \%\) respectively. The percentage error in the measurement of C will be _____\(\%\).

In the given circuit, rms value of current \(\left( I _{ rms }\right)\) through the resistor \(R\) is :\(..........\,A\)

A signal of \(0.1\, kW\) is transmitted in a cable. The attenuation of cable is \(-5 \,dB\) per \(km\) and cable length is \(20\, km\). The power received at receiver is \(10^{-x} \, W\). The value of \(x\) is ....... . \(\left[\right.\) Gain in \(\left. dB =10 \log _{10}\left(\frac{ P _{0}}{ P _{i}}\right)\right]\)

A telegraph line of length \(100 \,km\) has a capacity of \(0.01\,\mu F / km\) and it carries an alternating current at \(0.5 \,kilo \,cycle \,per \,second\). If minimum impedance is required, then the value of the inductance that needs to be introduced in series is__________ \(m H\). \(\text { (if } \pi=\sqrt{10})\)

For designing a voltmeter of range \(50\,V\) and an ammeter of range \(10\,mA\) using a galvanometer which has a coil of resistance \(54\,\Omega\) showing a full scale deflection for \(1\,mA\) as in figure. \((A)\) for voltmeter \(R \approx 50\,k\Omega\) \((B)\) for ammeter \(r \approx 0.2\,\Omega\) \((C)\) for ammeter \(r \approx 6\,\Omega\) \((D)\) for voltmeter \(R \approx 5\,k \Omega\) \((E)\) for voltmeter \(R \approx 500 \Omega\) Choose the correct answer from the options given below

An inductor of \(10\, {mH}\) is connected to a \(20\, {V}\) battery through a resistor of \(10\, {k}\, \Omega\) and a switch. After a long time, when maximum current is set up in the circuit, the current is switched off. The current in the circuit after \(1\, \mu\, {s}\) is \(\frac{{x}}{100}\, {mA}\). Then \({x}\) is equal to ...... . (Take \(\left.{e}^{-1}=0.37\right)\)