

Phthalimide undergoes the following transformations:
In the presence of KOH, the acidic hydrogen of phthalimide is removed, forming the phthalimide anion.
The phthalimide anion then reacts with benzyl chloride via an S\(_N2\) reaction, leading to the formation of product 'P'.
In product 'P':
The benzene ring contributes \(3 \, \pi\)-bonds.
Each carbonyl group (C=O) provides \(2 \, \pi\)-bonds, giving a total of \(4 \, \pi\)-bonds for both groups.
The benzyl group attached to nitrogen contributes \(1\) additional \(\pi\)-bond.
Thus, the total number of \(\pi\)-bonds in product 'P' is:
\[3 + 2 + 2 + 1 = 8\]
In the given figure, the blocks $A$, $B$ and $C$ weigh $4\,\text{kg}$, $6\,\text{kg}$ and $8\,\text{kg}$ respectively. The coefficient of sliding friction between any two surfaces is $0.5$. The force $\vec{F}$ required to slide the block $C$ with constant speed is ___ N.
(Given: $g = 10\,\text{m s}^{-2}$) 
Two circular discs of radius \(10\) cm each are joined at their centres by a rod, as shown in the figure. The length of the rod is \(30\) cm and its mass is \(600\) g. The mass of each disc is also \(600\) g. If the applied torque between the two discs is \(43\times10^{-7}\) dyne·cm, then the angular acceleration of the system about the given axis \(AB\) is ________ rad s\(^{-2}\).

Match the LIST-I with LIST-II for an isothermal process of an ideal gas system. 
Choose the correct answer from the options given below: