A bomb is dropped by an aeroplane flying horizontally with a velocity $$200 \mathrm{~km} / \mathrm{hr}$$ and at a height of $$980 \mathrm{~m}$$. At the time of dropping a bomb, the distance of the aeroplane from the target on the ground to hit directly is $$\left(g=9.8 \mathrm{~m} / \mathrm{s}^2\right)$$

A series combination of resistor 'R' and capacitor 'C' is connected to an a.c. source of angular frequency '$$\omega$$'. Keeping the voltage same, if the frequency is changed to $$\frac{\omega}{3}$$ the current becomes half of the original current. Then the ratio of capacitive reactance and resistance at the former frequency is

A double slit experiment is immersed in water of refractive index 1.33. The slit separationis 1 $$\mathrm{mm}$$ and the distance between slit and screen is $$1.33 \mathrm{~m}$$. The slits are illuminated by a light of wavelength $$6300\,\mathop A\limits^o $$. The fringewidth is

Two small drops of mercury each of radius '$$R$$' coalesce to form a large single drop. The ratio of the total surface energies before and after the change is