The rearrangement of phenyl esters to $o-$ and $p-$ hydroxy ketones in the presence of $AlCl_3$ is known as:

If the angle $2 \theta$ is acute,then the acute angle between the pair of straight lines $x^2(\cos \theta - \sin \theta) + 2xy \cos \theta + y^2(\cos \theta + \sin \theta) = 0$ is:

Which of the following reagents reacts with benzaldehyde to produce $1$-phenylethanol?

If $x^y=y^x$, then $x(x-y \log x) \frac{d y}{d x}$ is equal to :

Let $a \neq 0$ and $p(x)$ be a polynomial of degree greater than $2$. If $p(x)$ leaves remainders $a$ and $-a$ when divided respectively by $x+a$ and $x-a$,then the remainder when $p(x)$ is divided by $x^2-a^2$ is:

Water is flowing with a velocity of $2\,m/s$ in a horizontal pipe where the cross-sectional area is $2 \times 10^{-2}\, m^2$ at a pressure of $4 \times 10^4\, Pa$. The pressure at a cross-section of area $0.01\, m^2$ in $Pa$ will be: