The diagram below shows a hydraulic lift. $A$ force is applied at side $1$ and an output force is generated at side $2$. Which of the following is true?

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

An aluminium ring $B$ faces an electromagnet $A$. The current $I$ through $A$ can be altered. Which of the following statements is correct?

$A$ rod of glass $(\mu = 1.5)$ with a square cross-section is bent into the shape shown in the figure. $A$ parallel beam of light falls on the plane flat surface $A$ as shown. If $d$ is the width of a side and $R$ is the radius of the inner circular arc, then for what maximum value of $\frac{d}{R}$ will light entering the glass slab through surface $A$ emerge from the glass through surface $B$?

The disease known as fluorosis is caused by the reaction of fluorine with which of the following?

$A$ cricketer can throw a ball to a maximum horizontal distance of $100 \, m$. The speed with which he throws the ball is (to the nearest integer) (in $m/s$).