In how many ways can $3$ letters be posted in $4$ letter-boxes,if all the letters are not posted in the same letter-box?

If the sum of any two roots of the equation $x^3+p x^2+q x+r=0$ is zero,then

The ratio between kinetic and potential energies of a body executing simple harmonic motion,when it is at a distance of $\frac{1}{N}$ of its amplitude from the mean position is

If you are asked to classify the various algae into distinct groups,which of the following characters should you choose?

Blister copper is refined by stirring molten impure metal with green logs of wood because such a wood liberates hydrocarbon gases (like $CH_4$). This process $X$ is called . . . . . . and the metal contains impurities of $Y$ is . . . . . . .

The figure shows a system of logic gates. From the study of the truth table, it can be found that to produce a high output $(1)$ at $R$, we must have