A mixture of one mole of monoatomic gas and one mole of a diatomic gas (rigid) are kept at room temperature $$(27^{\circ }\mathrm{C})$$. The ratio of specific heat of gases at constant volume respectively is:

Two different adiabatic paths for the same gas intersect two isothermal curves as shown in P-V diagram. The relation between the ratio $$\frac{V_a}{V_d}$$ and the ratio $$\frac{V_b}{V_c}$$ is:

The heat absorbed by a system in going through the given cyclic process is :

If the collision frequency of hydrogen molecules in a closed chamber at $$27^{\circ }\mathrm{C}$$ is $$\mathrm{Z}$$, then the collision frequency of the same system at $$127^{\circ }\mathrm{C}$$ is :

During an adiabatic process, if the pressure of a gas is found to be proportional to the cube of its absolute temperature, then the ratio of $$\frac{{\mathrm{C}}_{\mathrm{P}}}{{\mathrm{C}}_{\mathrm{V}}}$$ for the gas is :

If $$\mathrm{n}$$ is the number density and $$\mathrm{d}$$ is the diameter of the molecule, then the average distance covered by a molecule between two successive collisions (i.e. mean free path) is represented by :

Given below are two statements: Statement (I) : Dimensions of specific heat is $$[{\mathrm{L}}^2{\mathrm{T}}^{-2}{\mathrm{K}}^{-1}]$$. Statement (II) : Dimensions of gas constant is $$[\mathrm{M}{\mathrm{L}}^2{\mathrm{T}}^{-1}{\mathrm{K}}^{-1}]$$. In the light of the above statements, choose the most appropriate answer from the options given below.

Energy of 10 non rigid diatomic molecules at temperature $$\mathrm{T}$$ is :

A total of $$48\mathrm{J}$$ heat is given to one mole of helium kept in a cylinder. The temperature of helium increases by $$2^{\circ }\mathrm{C}$$. The work done by the gas is: Given, $$\mathrm{R}=8.3\mathrm{J}{\mathrm{K}}^{-1}{\mathrm{mol}}^{-1}$$.

The specific heat at constant pressure of a real gas obeying $$P{V}^2=RT$$ equation is:

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the sample, is :

$C_1$ and $C_2$ are two hollow concentric cubes enclosing charges $2 Q$ and $3 Q$ respectively as shown in figure. The ratio of electric flux passing through $C_1$ and $C_2$ is :

An electric charge $$10^{-6}\mu \mathrm{C}$$ is placed at origin $$(0,0)$$ $$\mathrm{m}$$ of $$\mathrm{X}-\mathrm{Y}$$ co-ordinate system. Two points $$\mathrm{P}$$ and $$\mathrm{Q}$$ are situated at $$(\sqrt{3},\sqrt{3})\mathrm{m}$$ and $$(\sqrt{6},0)\mathrm{m}$$ respectively. The potential difference between the points $\mathrm{P}$ and $\mathrm{Q}$ will be :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : Work done by electric field on moving a positive charge on an equipotential surface is always zero. Reason (R) : Electric lines of forces are always perpendicular to equipotential surfaces. In the light of the above statements, choose the most appropriate answer from the options given below :

Force between two point charges $$q_1$$ and $$q_2$$ placed in vacuum at '$$r$$' cm apart is $$F$$. Force between them when placed in a medium having dielectric constant $$K=5$$ at '$$r/5$$' $$\mathrm{cm}$$ apart will be:

Two charges $$q$$ and $$3q$$ are separated by a distance '$$r$$' in air. At a distance $$x$$ from charge $$q$$, the resultant electric field is zero. The value of $$x$$ is :

Two charges of $$5Q$$ and $$-2Q$$ are situated at the points $$(3a,0)$$ and $$(-5a,0)$$ respectively. The electric flux through a sphere of radius '$$4a$$' having center at origin is :

An electric field is given by $$(6\hat{i}+5\hat{j}+3\hat{k})\mathrm{N}/\mathrm{C}$$. The electric flux through a surface area $$30\hat{i}{\mathrm{m}}^2$$ lying in YZ-plane (in SI unit) is :

A particle of charge '$$-q$$' and mass '$$m$$' moves in a circle of radius '$$r$$' around an infinitely long line charge of linear charge density '$$+\lambda$$'. Then time period will be given as : (Consider $$k$$ as Coulomb's constant)

The electrostatic potential due to an electric dipole at a distance '$$r$$' varies as :