The charge accumulated on the capacitor connected in the following circuit is________ \(\mu \mathrm{C}\) (Given \(\mathrm{C}=150\  \mu \mathrm{F}\))

The linear mass density of a thin rod \(A B\) of length \(L\) varies from \(A\) to \(B\) as \(\lambda( x )=\lambda_{0}\left(1+\frac{ x }{ L }\right),\) where \(x\) is the distance from A. If \(M\) is the mass of the rod then its moment of inertia about an axis passing through \(A\) and perpendicular to the rod is\(......ML^{2}\)

The energy released per fission of nucleus of \({ }^{240} X\) is \(200 MeV\). The energy released if all the atoms in \(120 g\) of pure \({ }^{240} X\) undergo fission is \(........\times 10^{25}\,MeV\).\(\left(\right.\) Given \(\left.N_A=6 \times 10^{23}\right)\)

A capacitor P with capacitance \( 10\times10^{-6} F \) is fully charged with a potential difference of 6.0 V and disconnected from the battery. The charged capacitor P is connected across another capacitor Q with capacitance \( 20\times10^{-6} F \). The charge on capacitor Q when equilibrium is established will be \( \alpha\times10^{-5} C \).(assume capacitor \(Q\) does not have any charge initially),The value of \( \alpha \) is __________ .

When a particle executes \(SHM\) the nature of graphical representation of velocity as a function of displacement is :

An expression for a dimensionless quantity \(P\) is given by \(P=\frac{\alpha}{\beta} \log _{e}\left(\frac{ kt }{\beta x }\right)\); where \(\alpha\) and \(\beta\) are constants, \(x\) is distance ; \(k\) is Boltzmann constant and \(t\) is the temperature. Then the dimensions of \(\alpha\) will be

Given are statements for certain thermodynamic variables,
(A) Internal energy, volume (V) and mass (M) are extensive variables.
(B) Pressure (P), temperature (T) and density ( \(\rho\) ) are intensive variables.
(C) Volume (V), temperature (T) and density ( \(\rho\) ) are intensive variables.
(D) Mass (M), temperature (T) and internal energy are extensive variables.

Choose the correct answer from the options given below :

A light ray is incident on a glass slab of thickness \(4 \sqrt{3} \mathrm{~cm}\) and refractive index \(\sqrt{2}\). The angle of incidence is equal to the critical angle for the glass slab with air. The lateral displacement of ray after passing through glass slab is _______ \(\mathrm{cm}\). \(\left(\right.\) Given \(\left.\sin 15^{\circ}=0.25\right)\)

A solid sphere and a solid cylinder of same mass and radius are rolling on a horizontal surface without slipping. The ratio of their radius of gyrations respectively \(\left( k _{\text {sph }}: k _{ cyl }\right)\) is \(2: \sqrt{ x }\), then value of \(x\) is .............

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 ........... \(mA\).

The height of any point \(P\) above the surface of earth is equal to diameter of earth. The value of acceleration due to gravity at point \(P\) will be : (Given \(g=\) acceleration due to gravity at the surface of earth)

Match List-I with List-II.

LIST - I	LIST - II
(A) Isobaric	(I) ΔQ = ΔW
(B) Isochoric	(II) ΔQ = ΔU
(C) Adiabatic	(III) ΔQ = zero
(D) Isothermal	(IV) ΔQ = ΔU + PΔV

\(\Delta \mathrm{Q}=\) Heat supplied
\(\Delta \mathrm{W}=\) Work done by the system
\(\Delta \mathrm{U}=\) Change in internal energy
\(\mathrm{P}=\) Pressure of the system
\(\Delta \mathrm{V}=\) Change in volume of the system
Choose the correct answer from the options given below: