A girl standing on road holds her umbrella at \(45^{\circ}\) with the vertical to keep the rain away. If she starts running without umbrella with a speed of \(15 \sqrt{2} \; kmh ^{-1}\), the rain drops hit her head vertically. The speed of rain drops with respect to the moving girl is ...........  \(kmh ^{-1}\)

In a plane \(EM\) wave, the electric field oscillates sinusoidally at a frequency of \(5 \times 10^{10} \mathrm{~Hz}\) and an amplitude of \(50 \mathrm{Vm}^{-1}\). The total average energy density of the electromagnetic field of the wave is _______. [Use \(\varepsilon_0=8.85 \times 10^{-12} \mathrm{C}^2 / \mathrm{Nm}^2\) ]

The mid points of two small magnetic dipoles of length \(d\) in end-on positions, are separated by a distance \(x, (x > > d)\). The force between them is proportional to \(x^{-n}\) where \(n\) is

Two coherent point sources \(S_1\) and \(S_2\) are separated by a small distance '\(d\)' as shown. The fringes obtained on the screen will be

Consider an electron in a hydrogen atom, revolving in its second excited state (having radius \(4.65\, \mathop A\limits^o \)). The de-Broglie wavelength of this electron is....\(\mathop A\limits^o \)

A force on an object of mass \(100\, g\) is \((10 \hat{i}+5 \hat{j}) N\). The position of that object at \(t=\) \(2 s\) is \((a \hat{i}+b \hat{j}) m\) after starting from rest. The value of \(\frac{a}{b}\) will be..........

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

List\(-I\)	List\(-II\)
\((A)\) Angular momentum	\((I)\) \(\left[ ML ^2 T ^{-2}\right]\)
\((B)\) Torque	\((II)\) \(\left[ ML ^{-2} T ^{-2}\right]\)
\((C)\) Stress	\((III)\) \(\left[ ML ^2 T ^{-1}\right]\)
\((D)\) Pressure gradient	\((IV)\) \(\left[ ML ^{-1} T ^{-2}\right]\)

Choose the correct answer from the options given below:

The cut-off voltage of the diodes (shown in figure) in forward bias is \(0.6 \,V\). The current through the resister of \(40 \,\Omega\) is ........... \(mA\).

In the given figure the magnetic flux through the loop increases according to the relation \(\phi_{B}(t)=10 t^{2}+20 t\), where \(\phi_{B}\) is in milliwebers and \(t\) is in seconds. The magnitude of current through \({R}=2 \,\Omega\) resistor at \({t}=5\, {s}\) is \(....\,{mA}\).

Electric field of plane electromagnetic wave propagating through a non-magnetic medium is given by \({E}=20 \cos \left(2 \times 10^{10} {t}-200 {x}\right) \,{V} / {m} .\) The dielectric constant of the medium is equal to : (Take \(\mu_{{r}}=1\) )

The longest wavelength associated with Paschen series is _______. (Given \(R_H=1.097 \times 10^7 \mathrm{SI}\) unit)

An air bubble of volume \(1\,cm ^3\) rises from the bottom of a lake \(40\,m\) deep to the surface at a temperature of \(12^{\circ}\,C\). The atmospheric pressure is \(1 \times 10^5 Pa\), the density of water is \(1000\,kg / m ^3\) and \(g =10\,m / s ^2\). There is no difference of the temperature of water at the depth of \(40\,m\) and on the surface. The volume of air bubble when it reaches the surface will be \(..........\,cm^{3}\)

Three concentric spherical metallic shells \(X , Y\) and \(Z\) of radius \(a , b\) and c respectively \([ a < b < c ]\) have surface charge densities \(\sigma,-\sigma\) and \(\sigma\), respectively. The shells \(X\) and \(Z\) are at same potential. If the radii of \(X\) and \(Y\) are \(2\,cm\) and \(3\,cm\), respectively.The radius of shell \(Z\) is \(......cm\).