Three capacitors are connected in the arms of a triangle ABC as shown in figure. 5 V is applied between A and B. The voltage between B and C is

• 2 V

• 1 V

• 3 V

• 1.5 V

Two point charges + 5 µC and − 2 µC are kept at a distance of 1 m in free space. The distance between the two zero potential points on the line joining the charges is

• $\frac{2}{7} \mathrm{m}$

• $\frac{2}{3} \mathrm{m}$

• $\frac{22}{21} \mathrm{m}$

• $\frac{20}{21} \mathrm{m}$

A negatively charged oil drop is prevented from falling under gravity by applying a vertical electric field 100 Vm^-1. If the mass of the drop is 1.6 x 10^-3  g, the number of electrons carried by the drop is (g = 10 ms^-2)

• 10¹⁸

• 10¹⁵

• 10¹²

• 10⁹

In the circuit shown, the current through 8 Ω is same before and after connecting E. The value of E is

• 12 V

• 6 V

• 4 V

• 2 V

An electric bulb rated 500 W at 100 V is used in a circuit having a 200 V supply. The resistance R that must be put in series with the bulb, so that the bulb draws 500 W is

• 10 Ω

• 15 Ω

• 20 Ω

• 25 Ω

The focal lengths of the objective and of the eye-piece of a compound microscope are f₀ and f_e respectively. If L is the tube length and D, the least distance of distinct vision, then its angular magnification, when the image is formed at infinity is

• $\left(1 - \frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}}\right) \left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

• $\left(1 + \frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}}\right) \left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

• $\frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}} \left(\frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

• $\frac{\mathrm{L}}{{\mathrm{f}}_{\mathrm{o}}} \left(1 + \frac{\mathrm{D}}{{\mathrm{f}}_{\mathrm{e}}}\right)$

57.

The velocity of a moving galaxy is 300 kms^-1 and the apparent change in wavelength of a spectral line emitted from the galaxy is observed as 0.5 nm. Then, the actual wavelength of the spectral line is

• 3000 $\stackrel{\circ }{\mathrm{A}}$

• 5000 $\stackrel{\circ }{\mathrm{A}}$

• 6000 $\stackrel{\circ }{\mathrm{A}}$

• 4500 $\stackrel{\circ }{\mathrm{A}}$

An astronomical telescope has an angular magnification of magnitude 5 for distant objects. The separation between the objective and the eye-piece is 36 cm and the final image is formed at infinity. The focal length f_o of the objective and f_e of the eye-piece are respectively

• 45 cm and 9 cm

• 50 cm and 10 cm

• 7.2 cm and 5 cm

• 30 cm and 6 cm

If the reflected image formed is magnified and virtual, then the mirror system is

• concave only

• convex only

• plane

• concave or convex

A vessel of depth x is half filled with oil of refractive index µ₁ and the other half is filled with water of refractive index µ₂. The apparent depth of the vessel when viewed from above is

• $\frac{\mathrm{x} \left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}{2 {\mathrm{\mu }}_1{\mathrm{\mu }}_2}$

• $\frac{\mathrm{x} {\mathrm{\mu }}_1{\mathrm{\mu }}_2}{2 \left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}$

• $\frac{\mathrm{x} {\mathrm{\mu }}_1{\mathrm{\mu }}_2}{\left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}$

• $\frac{2\mathrm{x} \left({\mathrm{\mu }}_1 + {\mathrm{\mu }}_2\right)}{{\mathrm{\mu }}_1{\mathrm{\mu }}_2}$