Let f(x) be a quadratic polynomial such that
f(–1) + f(2) = 0. If one of the roots of f(x) = 0
is 3, then its other root lies in :

If momentum (P), area (A) and time (T) are taken to be the fundamental quantities then the dimensional formula for energy is

A particle is moving 5 times as fast as an electron. The ratio of the de-Broglie wavelength of the particle to that of the electron is 1.878 $$ \times $$ 10^–4. The mass of the particle is close to

An inductance coil has a reactance of 100 $$\Omega $$. When an AC signal of frequency 1000 Hz is applied to the coil, the applied voltage leads the current by 45^o. The self-inductance of the coil is