$\sec ^2(\tan ^{-1} 2) + \operatorname{cosec}^2(\cot ^{-1} 3)$ is equal to

At a certain place,a magnet makes $30$ oscillations per minute. At another place where the magnetic field is double,its time period will be:

$\int_0^\pi \frac{\theta \sin \theta}{1+\cos ^2 \theta} d \theta$ is equal to

$A$ parallel beam of light of wavelength $6000 \, \mathring{A}$ is diffracted by a single slit of width $0.3 \, \text{mm}$. The angular position of the first minima of the diffracted light is:

Chemiosmotic theory of $ATP$ synthesis in mitochondrion is based on

The reagent used in the preparation of aspirin from salicylic acid is