What is obtained when an aqueous solution of aluminum chloride is heated to dryness?

$A$ parallel plate capacitor with oil (dielectric constant $K = 2$) between the plates has capacitance $C$. If the oil is removed,the capacitance of the capacitor becomes:

$\frac{d}{{dy}}\left( {{{\sin }^{ - 1}}\left( {\frac{{3y}}{2} - \frac{{{y^3}}}{2}} \right)} \right) =$

$A$ simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed at a distance $2L/3$ directly below the fixed pivot point. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?

Which of the following is the correct electronic configuration of $Cr$ $(Z=24)$?

An object takes $n$ times as much time to slide down a $45^{\circ}$ rough inclined plane as it takes to slide down a perfectly smooth inclined plane of the same inclination. The coefficient of kinetic friction between the object and the rough incline is given by: