The value of $$\int\limits_{{{ - \pi } \over 2}}^{{\pi \over 2}} {{1 \over {1 + {e^{\sin x}}}}dx} $$ is:

Number of molecules in a volume of 4 cm³ of a perfect monoatomic gas at some temperature T and at a pressure of 2 cm of mercury is close to?
(Given, mean kinetic energy of a molecule
(at T) is 4 $$ \times $$ 10^–14 erg, g = 980 cm/s², density of
mercury = 13.6 g/cm³)

An electron is constrained to move along the y-axis with a speed of 0.1 c (c is the speed of light) in the presence of electromagnetic wave, whose electric field is
$$\overrightarrow E = 30\widehat j\sin \left( {1.5 \times {{10}^7}t - 5 \times {{10}^{ - 2}}x} \right)$$ V/m.
The maximum magnetic force experienced by the electron will be :
(given c = 3 $$ \times $$ 10⁸ ms^–1 and electron charge = 1.6 $$ \times $$ 10^–19 C)

Three different processes that can occur in an ideal monoatomic gas are shown in the P vs V diagram. The paths are labelled as A $$ \to $$ B, A $$ \to $$ C and A $$ \to $$ D. The change in internal energies during these process are taken as E_AB, E_AC and E_AD and the work done as W_AB, W_AC and W_AD.
The correct relation between these parameters are :