In Van der Waals equation of state for a non-ideal gas,the term that accounts for intermolecular forces is

The solution of $\tan y \frac{dy}{dx} = \sin(x+y) + \sin(x-y)$ is

Select the incorrect statement.

The Cartesian form of the polar equation $\theta = \tan^{-1} 2$ is

$A$ radioactive material decays by simultaneous emission of two particles with respective half-lives $1620 \, years$ and $810 \, years$. The time (in years) after which one-fourth of the material remains is

An azeotropic solution of two liquids has a boiling point lower than either of them when it: