The \(rms\) speeds of the molecules of Hydrogen, Oxygen and Carbondioxide at the same temperature are \({V}_{{H}}, {V}_{0}\) and \({V}_{{C}}\) respectively then

Two ideal electric dipoles \(A\) and \(B\) having their dipole moment \(p_{1}\) and \(p_{2}\) respectively are placed on a plane with their centres at \(O\) as shown in the figure. At point \(C\) on the axis of dipole \(A\), the resultant electric field is making an angle of \(37^{\circ}\) with the axis. The ratio of the dipole moment of \(A\) and \(B, \frac{P_{1}}{P_{2}}\) is \(....\) (take \(\left.\sin 37^{\circ}=\frac{3}{5}\right)\)

A longitudinal wave is represented by \(x =10 \sin 2 \pi\left( nt -\frac{ x }{\lambda}\right) \,cm\). The maximum particle velocity will be four times the wave velocity if the determined value of wavelength is equal to .....................

The electric field in a plane electromagnetic wave is given by \(\overrightarrow{{E}}=200 \cos \left[\left(\frac{0.5 \times 10^{3}}{{m}}\right) {x}-\left(1.5 \times 10^{11} \frac{{rad}}{{s}} \times {t}\right)\right] \frac{{V}}{{m}} \hat{{j}}\) If this wave falls normally on a perfectly reflecting surface having an area of \(100 \;{cm}^{2}\). If the radiation pressure exerted by the \(E.M.\) wave on the surface during a \(10\, minute\) exposure is \(\frac{{x}}{10^{9}} \frac{{N}}{{m}^{2}}\). Find the value of \({x}\).

The stored charge in the capacitor in steady state of the following circuit is ________ \(\mu\)C.

List\(-I\)	List\(-II\)
\(UV\) rays	\((i)\) Diagnostic tool in medicine
\(X-\) rays	\((ii)\) Water purification
Microwave	\((iii)\) Communication, Radar
Infrared wave	\((iv)\) Improving visibility in foggy days

Choose the correct answer from the options given below.

The ratio of de-Broglie wavelength of an \(\alpha\)-particle and a proton accelerated from rest by the same potential is \(\frac{1}{\sqrt{ m }}\), the value of \(m\) is \(........\)

Two capacitors of capacitances \(C\) and \(2\, C\) are charged to potential differences \(V\) and \(2\, V\), respectively. These are then connected in parallel in such a manner that the positive terminal of one is connected to the negative terminal of the other. The final energy of this configuration is\(.....CV^2\)

A radioactive substance decays to \(\left(\frac{1}{16}\right)^{t h}\) of its initial activity in \(80\, days.\) The half life of the radioactive substance expressed in days is ... .

A small block slides down from the top of hemisphere of radius \(R=3\, {m}\) as shown in the figure. The height \('h'\) at which the block will lose contact with the surface of the sphere is \(.............  \;\;m\). (Assume there is no friction between the block and the hemisphere)

The dimension of stopping potential \(\mathrm{V}_{0}\) in photoelectric effect in units of Planck's constant \(h\), speed of light \(c\) and Gravitational constant \(G\) and ampere \(A\) is