In a carnot engine, the temperature of reservoir is 527$$^\circ$$C and that of sink is 200 K. If the work done by the engine when it transfers heat from reservoir to sink is 12000 kJ, the quantity of heat absorbed by the engine from reservoir is ______________ $$\times$$ 10⁶ J.

A 220 V, 50 Hz AC source is connected to a 25 V, 5 W lamp and an additional resistance R in series (as shown in figure) to run the lamp at its peak brightness, then the value of R (in ohm) will be _____________.

In Young's double slit experiment the two slits are 0.6 mm distance apart. Interference pattern is observed on a screen at a distance 80 cm from the slits. The first dark fringe is observed on the screen directly opposite to one of the slits. The wavelength of light will be ____________ nm.

A beam of monochromatic light is used to excite the electron in Li^{+ +} from the first orbit to the third orbit. The wavelength of monochromatic light is found to be x $$\times$$ 10^$$-$$10 m. The value of x is ___________.

[Given hc = 1242 eV nm]