21.

Two temperature scales A and B are related by $\frac{\mathrm{A} - 42}{110} = \frac{\mathrm{B} - 72}{220}$. At which temperature two scales have the same reading ?

• − 42°

• − 72°

• + 12°

• − 40°

An ideal gas is compressed isothermally until its pressure is doubled and then allowed to expand adiabatically to regain its original volume (γ = 1.4 and 2^-1.4 = 0.38). The ratio of the final to initial pressure is

• 0.76 : 1

• 1 : 1

• 0.66 : 1

• 0.86 : 1

Air inside a closed container is saturated with water vapour. The air pressure is p and the saturated vapour pressure of water is $\overline{\mathrm{p}}$. If the mixture is compressed to one-half of its volume by maintammg temperature constant, the pressure becomes

• $\mathrm{2}\left(\mathrm{p} + \overline{\mathrm{p}}\right)$

• $2\mathrm{p} + \overline{\mathrm{p}}$

• $\left(\mathrm{p} + \overline{\mathrm{p}}\right)/2$

• $\mathrm{p} + 2\overline{\mathrm{p}}$

1.56 x 10⁵ J of heat is conducted through a 2 m² wall of 12 cm thick in 1 h. Temperature difference between the two sides of the wall is 20° C. The thermal conductivity of the material of the wall is (in W m^-1 K^-1)

• 0.11

• 0.13

• 0.15

• 1.2

A diver at a depth of 12 m in water $\left(\mathrm{\mu } = \frac{4}{3}\right)$ sees the sky in a cone-of semivertical angle

• ${\sin }^{-1}\left(\frac{4}{3}\right)$

• ${\tan }^{-1}\left(\frac{4}{3}\right)$

• ${\sin }^{-1}\left(\frac{3}{4}\right)$

• 90°

The charge on the capacitor of capacitance C shown in the figure below will be

• C E

• $\frac{\mathrm{C} \mathrm{E} {\mathrm{R}}_1}{{\mathrm{R}}_1 + \mathrm{r}}$

• $\frac{\mathrm{C}\hspace{0.17em}\mathrm{E}\hspace{0.17em}{\mathrm{R}}_2}{{\mathrm{R}}_2 + \mathrm{r}}$

• $\frac{\mathrm{C}\hspace{0.17em}\mathrm{E}\hspace{0.17em}{\mathrm{R}}_1}{{\mathrm{R}}_2 + \mathrm{r}}$

The resistance across A and B in the figure below will be 

• 3R

• R

• $\frac{\mathrm{R}}{3}$

• None of the above

Five equal resistance, each of resistance R are connected as shown in figure below. A battery of V volt is connected between A and B. The current flowing in FC will be

• $\frac{3\mathrm{V}}{\mathrm{R}}$

• $\frac{\mathrm{V}}{\mathrm{R}}$

• $\frac{\mathrm{V}}{2\mathrm{R}}$

• $\frac{2\mathrm{V}}{\mathrm{R}}$

Two cells with the same emf E and different internal resistances r₁ and r₂ are connected in series to an  external resistance R. The value of R so that the potential difference across the first cell be zero, is

• $\sqrt{{\mathrm{r}}_1{\mathrm{r}}_2}$

• r₁ + r₂

• r₁ − r₂

• $\frac{{\mathrm{r}}_1 + {\mathrm{r}}_2}{2}$

Current through ABC and A' B'C' is I. What is the magnetic field at P ? BP = PB' = r (Here C' B' PBC are collinear)

• $\mathrm{B} = \frac{1}{4\mathrm{\pi }} \frac{2\mathrm{I}}{\mathrm{r}}$

• $\mathrm{B} = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \left(\frac{2\mathrm{I}}{\mathrm{r}}\right)$

• $\mathrm{B} = \frac{{\mathrm{\mu }}_0}{4\mathrm{\pi }} \left(\frac{\mathrm{I}}{\mathrm{r}}\right)$

• Zero