Let's analyze each reaction:
n-Hexane with Mo2O3 at 773K and 10-20 atm: This is catalytic reforming or aromatization. n-Hexane can be converted to benzene under these conditions.
Acetylene (Ethyne) with Red Hot Iron Tube at 873 K: This is a classic method for synthesizing benzene. Three molecules of acetylene undergo cyclic polymerization to form benzene.
Benzenediazonium Ion with Warm Water: Benzenediazonium ion (C6H5N2+) reacts with warm water to form phenol (C6H5OH), not benzene. The diazonium group is replaced by a hydroxyl group.
Benzoate with Sodalime and Heat: This is decarboxylation. The benzoate loses CO2 to form benzene.
Therefore, the reaction that does not produce benzene as a major product is the reaction of benzenediazonium ion with warm water.
For the thermal decomposition of \( N_2O_5(g) \) at constant volume, the following table can be formed, for the reaction mentioned below: \[ 2 N_2O_5(g) \rightarrow 2 N_2O_4(g) + O_2(g) \] Given: Rate constant for the reaction is \( 4.606 \times 10^{-2} \text{ s}^{-1} \).


Consider a water tank shown in the figure. It has one wall at \(x = L\) and can be taken to be very wide in the z direction. When filled with a liquid of surface tension \(S\) and density \( \rho \), the liquid surface makes angle \( \theta_0 \) (\( \theta_0 < < 1 \)) with the x-axis at \(x = L\). If \(y(x)\) is the height of the surface then the equation for \(y(x)\) is: (take \(g\) as the acceleration due to gravity) 
A sphere of radius R is cut from a larger solid sphere of radius 2R as shown in the figure. The ratio of the moment of inertia of the smaller sphere to that of the rest part of the sphere about the Y-axis is : 