If $\cos (\alpha+\beta)=\frac{4}{5}$,$\sin (\alpha-\beta)=\frac{5}{13}$ and $\alpha, \beta$ are between $0$ and $\frac{\pi}{4}$,then $\tan 2\alpha$ is equal to

In which of the following is the $P - O - P$ bond present?

$A$ river of salty water is flowing with a velocity $2 ~m/s$. If the density of the water is $1.2 ~g/cc$,then the kinetic energy of each cubic metre of water is

$A$ closed hollow insulated cylinder is filled with gas at $0^{\circ} C$ and also contains an insulated piston of negligible weight and negligible thickness at the middle point. The gas in one side of the piston is heated to $100^{\circ} C$. If the piston moves $5 ~cm$, the total length of the hollow cylinder is: (in $~cm$)

$\int e^x \left( \frac{2+\sin 2x}{1+\cos 2x} \right) dx$ is equal to

Identify the product $(A)$ of the following reaction: $C_2H_5-O-C_2H_5 + CO \xrightarrow[500 \ atm]{BF_3 / 150^{\circ}C} A$