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]

A cell, shunted by a 8 $$\Omega$$ resistance, is balanced across a potentiometer wire of length 3 m. The balancing length is 2 m when the cell is shunted by 4 $$\Omega$$ resistance. The value of internal resistance of the cell will be ____________ $$\Omega$$.