Consider a compound slab consisting of two, different materials having equal lengths, thicknesses and thermal conductivities K and  2 K respectively. The equivalent thermal conductivity of the slab is

• $\sqrt{2} \mathrm{K}$

• 3 K

• $\frac{4}{3} \mathrm{K}$

• $\frac{2}{3} \mathrm{K}$

An ideal black body at room temperature is thrown into a furnance. It is observed that

• it is the darkest body at all times

• it cannot be distinguished at all times

• initially it is the darkest body and later it becomes brightest

• initially it is the darkest body and later it cannot be distinguished

If temperature of the sun were to increase from T to 2 T and its radius from R to 2R, then how many times the radiant energy will be received on the earth ?

• 4

• 16

• 32

• 64

44.

A black body has a wavelength of λ at temperature 2000 K. Its corresponding wavelength at temperature 3000 K will be

• $\frac{2\mathrm{\lambda }}{3}$

• $\frac{3\mathrm{\lambda }}{2}$

• $\frac{4\mathrm{\lambda }}{9}$

• $\frac{9\mathrm{\lambda }}{4}$

According to first law of thermodynamics

• energy is conserved

• mass is conserved

• heat is constant in isothermal process

• heat neither enters nor leaves system

Ten moles of an ideal gas at constant temperature 500 K is compressed from 50 L to 5 L. Work done in the process is (Given, R = 8.31 J-mol^-1 - K^-1 )

• - 1.2 x 10⁴ J

• - 2.4 x 10⁴ J

• - 4.8 x 10⁴ J
  
  

• - 9.6 x 10⁴ J

Two charged spheres separated by a distance d exert some force (F) on each other. If they are immersed in a liquid of dielectric constant 4, then what is the force exerted, if all other conditions are same ?

• 2F

• 4F

• $\frac{\mathrm{F}}{2}$

• $\frac{\mathrm{F}}{4}$

An uncharged sphere of metal is placed inside a charged parallel plate capacitor. The electric lines of force will look like

The electric potential at a point on the axis of an electric dipole depends upon the distance r(>> a) of the point from centre of the dipole as

• ∝ r

• ∝ $\frac{1}{\mathrm{r}}$

• ∝ $\frac{1}{{\mathrm{r}}^2}$

• ∝ $\frac{1}{{\mathrm{r}}^3}$

A charge q is located at the centre of a cube. The electric flux through any face is

• $\frac{4\mathrm{\pi q}}{6 \left(4{\mathrm{\pi \epsilon }}_0\right)}$

• $\frac{\mathrm{\pi q}}{6\left(4{\mathrm{\pi \epsilon }}_0\right)}$

• $\frac{\mathrm{q}}{6\left(4{\mathrm{\pi \epsilon }}_0\right)}$

• $\frac{2\mathrm{\pi q}}{6\left(4{\mathrm{\pi \epsilon }}_0\right)}$