The rearrangement of phenyl esters to $o-$ and $p-$ hydroxy ketones in the presence of $AlCl_3$ is known as:

The inverse of the matrix $\left[\begin{array}{ccc}7 & -3 & -3 \\ -1 & 1 & 0 \\ -1 & 0 & 1\end{array}\right]$ is

Which organ in an adult human causes the least damage if removed?

Dividing the interval $[0,6]$ into $6$ equal parts and by using the trapezoidal rule,the value of $\int_0^6 x^3 dx$ is approximately:

An insulated cylindrical vessel is fitted with an insulated piston of negligible weight and negligible thickness at the midpoint of the vessel. The cylinder contains a gas at $0^{\circ} C$. When the gas is heated to $100^{\circ} C$,the piston moves through a length of $5 ~cm$. The total length of the cylindrical vessel in $cm$ is:

$A$ wire,which passes through the hole in a small bead,is bent in the form of a quarter of a circle. The wire is fixed vertically on the ground as shown in the figure. The bead is released from near the top of the wire and it slides along the wire without friction. As the bead moves from $A$ to $B$,the force it applies on the wire is