The ratio of the coefficient of volume expansion of a glass container to that of a viscous liquid kept inside the container is \(1 : 4\). What fraction of the inner volume of the container should the liquid occupy so that the volume of the remaining vacant space will be same at all temperatures ?

Consider a situation in which reverse biased current of a particular \(P-N\) junction increases when it is exposed to a light of wavelength \(\le 621\, {nm}\). During this process, enhancement in carrier concentration takes place due to generation of hole-electron pairs. The value of band gap is nearly. (In \({eV}\))

Acceleration due to gravity on the surface of earth is ' \(g\) '. If the diameter of earth is reduced to one third of its original value and mass remains unchanged, then the acceleration due to gravity on the surface of the earth is \(\ldots\ldots\) g.

Every planet revolves around the sun in an elliptical orbit : \(A.\) The force acting on a planet is inversely proportional to square of distance from sun. \(B.\) Force acting on planet is inversely proportional to product of the masses of the planet and the sun \(C.\) The centripetal force acting on the planet is directed away from the sun. \(D.\) The square of time period of revolution of planet around sun is directly proportional to cube of semi-major axis of elliptical orbit. Choose the correct answer from the options given below :

When a light of a given wavelength falls on a metallic surface the stopping potential for photoelectrons is 3.2 V . If a second light having wavelength twice of first light is used, the stopping potential drops to 0.7 V . The wavelength of first light is _________ m .
\(\left( h =6.63 \times 10^{-34} J . s , e =1.6 \times 10^{-19} C , c =3 \times 10^8 m / s \right)\)

An atom absorbs a photon of wavelength \(500\,nm\) and emits another photon of wavelength \(600\,nm\). The net energy absorbed by the atom in this process is \(n \times 10^{-4}\,eV\). The value of \(n\) is ............ [Assume the atom to be stationary during the absorption and emission process] \(\left(\right.\)Take \(h =6.6 \times 10^{-34}\,Js\) and \(\left.c =3 \times 10^8\,m / s \right)\)

Spherical insulating ball and a spherical metallic ball of same size and mass are dropped from the same height. Choose the correct statement out of the following (Assume negligible air friction)

First, a set of \({n}\) equal resistors of \(10\; \Omega\) each are connected in series to a battery of emf \(20\; {V}\) and internal resistance \(10\; \Omega .\) A current \(I\) is observed to flow. Then, the \(n\) resistors are connected in parallel to the same battery. It is observed that the current is increased \(20\) times, then the value of \(n\) is .... .

A certain gas is isothermally compressed to \(\left(\dfrac{1}{3}\right)^{rd}\) of its initial volume (\(V_o = 3\) litre) by applying required pressure. If the bulk modulus of the gas is \(3 \times 10^5\) N/m\(^2\), the magnitude of work done on the gas is _______ J.

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

List\(-I\)	List\(-II\)
\((a)\) Phase difference between current and voltage in a purely resistive \(AC\) circuit	\((i)\) \(\frac{\pi}{2} ;\) current leads voltage
\((b)\) Phase difference between current and voltage in a pure inductive \(AC\) circuit	\((ii)\) zero
\((c)\) Phase difference between current and voltage in a pure capacitive \(AC\) circuit	\((iii)\) \(\frac{\pi}{2} ;\) current lags voltage
\((d)\) Phase difference between current and voltage in an \(LCR\) series circuit	\((iv)\) \(\tan ^{-1}\left(\frac{X_{C}-X_{L}}{R}\right)\)

Choose the most appropriate answer from the options given below:

Particle \(A\) of mass \(m_{A}=\frac{m}{2}\) moving along the \(x-\)axis with velocity \(v_{0}\) collides elastically with another particle \(B\) at rest having mass \(m _{ B }=\frac{ m }{3}\) If both particles move along the \(x-\)axis after the collision, the change \(\Delta \lambda\) in \(de-\)Broglie wavelength of particle \(A,\) in terms of its \(de-\)Broglie wavelength \(\left(\lambda_{0}\right)\) before collision is

Given below are two statements:
Statement I: The hot water flows faster than cold water.
Statement II: Soap water has higher surface tension as compared to fresh water.
In the light above statements, choose the correct answer from the options given below.