Two radioactive materials A and B have decay constants 10$$\lambda $$ and $$\lambda $$, respectively. It initially they have the same number of nuclei, then the ratio of the number of nuclei of A to that of B will be 1/e after a time :

A 25 × 10^–3 m³ volume cylinder is filled with 1 mol of O₂ gas at room temperature (300K). The molecular diameter of O₂, and its root mean square speed, are found to be 0.3 nm, and 200 m/s, respectively. What is the average collision rate (per second) for an O₂ molecule ?

A stationary source emits sound waves of frequency 500 Hz. Two observers moving along a line passing through the source detect sound to be of frequencies 480 Hz and 530 Hz. Their respective speeds are, in ms–1, (Given speed of sound = 300 m/s)

Given below in the the left column are different modes of communication using the kinds of waves given the right column.

A	Optical Fibre communication	P	Ultrasound
B	Radar	Q	Infrared Light
C	Sonar	R	Microwaves
D	Mobile Phones	S	Radio Waves