Infection of pneumonia occurs due to

$A$ solid cylinder of density $\rho_0$, cross-section area $A$ and length $l$ floats in a liquid of density $\rho$ $(> \rho_0)$ with its axis vertical, as shown. If it is slightly displaced downward and released, the time period of oscillation will be:

Which of the following reagents can form a hydrazone with alkanone?

If the line $ax + by + c = 0$ is a normal to the curve $xy = 1$,then

Which of the following relations is true?

If $y=\tan ^{-1}\left(\frac{\sqrt{1+a^2 x^2}-1}{a x}\right)$,then $\left(1+a^2 x^2\right) y^{\prime \prime}+2 a^2 x y^{\prime}$ is equal to