The relative error in the determination of the surface area of sphere is $$\alpha $$. Then the relative error in the determination of its volume is :

In the given circuit all resistances are of value $$R$$ $$ohm$$ each. The equivalent resistance between $$A$$ and $$B$$ is :

Two electrons are moving with non-relativistic speed perpendicular to each other. If corresponding de Broglie wavelength are $${\lambda _1}$$ and $${\lambda _2},$$ their de Broglie wavelength in the frame of reference attached to their center of masses :

A tuning fork vibrates with frequency $$256$$ $$Hz$$ and gives one beat per second with the third normal mode of vibration of an open pipe. What is the length of the pipe ? (Speed of sound in air is $$340\,m{s^{ - 1}}$$)