Two vectors $$\overrightarrow X $$ and $$\overrightarrow Y $$ have equal magnitude. The magnitude of ($$\overrightarrow X $$ $$-$$ $$\overrightarrow Y $$) is n times the magnitude of ($$\overrightarrow X $$ + $$\overrightarrow Y $$). The angle between $$\overrightarrow X $$ and $$\overrightarrow Y $$ is :

A system consists of two types of gas molecules A and B having same number density 2 $$\times$$ 10²⁵/m³. The diameter of A and B are 10 $$\mathop A\limits^o $$ and 5 $$\mathop A\limits^o $$ respectively. They suffer collision at room temperature. The ratio of average distance covered by the molecule A to that of B between two successive collision is ____________ $$\times$$ 10^$$-$$2

A light beam of wavelength 500 nm is incident on a metal having work function of 1.25 eV, placed in a magnetic field of intensity B. The electrons emitted perpendicular to the magnetic field B, with maximum kinetic energy are bent into circular are of radius 30 cm. The value of B is ___________ $$\times$$ 10^$$-$$7 T.

Given hc = 20 $$\times$$ 10^$$-$$26 J-m, mass of electron = 9 $$\times$$ 10^$$-$$31 kg

A 16 $$\Omega$$ wire is bend to form a square loop. A 9V supply having internal resistance of 1$$\Omega$$ is connected across one of its sides. The potential drop across the diagonals of the square loop is _______________ $$\times$$ 10^$$-$$1 V