A beam of electromagnetic radiation of intensity 6.4 × 10^–5 W/cm² is comprised of wavelength, $$\lambda $$ = 310 nm. It falls normally on a metal (work function $$\phi $$ = 2eV) of surface area of 1 cm². If one in 10³ photons ejects an elctron, total number of electrons ejected in 1 s is 10^x. (hc = 1240 eVnm, 1eV = 1.6 × 10^–19 J), then x is _____.

A litre of dry air at STP expands adiabatically to a volume of 3 litres. If $$\gamma $$ = 1.40, the work done by air is : (3^1.4 = 4.6555) [Take air to be an ideal gas]

A particle (m = 1 kg) slides down a frictionless track (AOC) starting from rest at a point A (height 2 m). After reaching C, the particle continues to move freely in air as a projectile. When it reaching its highest point P (height 1 m), the kinetic energy of the particle (in )) is :
(Figure drawn is schematic and not to scale; take g = 10 ms^-2)

A parallel plate capacitor has plates of area A separated by distance 'd' between them. It is filled with a dielectric which has a dielectric constant that varies as k(x) = K(1 + $$\alpha $$x) where 'x' is the distance measured from one of the plates. If (ad) << 1, the total capacitance of the system is best given by the expression :