For the given reaction:

'P' is

Correct Answer: The correct option is the second one, which represents cyclohexanecarboxylic acid (a cyclohexyl ring attached to a $-\mathrm{COOH}$ group).

Step-by-Step Explanation:

Step 1: Identify the reactant and its structure
The reactant shown in the question is 1,2-dicyclohexylethene:
$C_6{H}_{11}-\mathrm{CH}=\mathrm{CH}-C_6{H}_{11}$
It consists of a carbon-carbon double bond ($C=C$) where each alkene carbon is bonded to one hydrogen atom and one cyclohexyl ring.

Step 2: Understand the role of the reagent
The reagent specified is acidic potassium permanganate (${\mathrm{KMnO}}_4/H^{+}$). Under acidic conditions, potassium permanganate acts as a strong oxidizing agent that carries out the oxidative cleavage of alkenes.

Step 3: Determine the cleavage products
During oxidative cleavage with hot/acidic ${\mathrm{KMnO}}_4$:
1. The double bond ($C=C$) is completely broken.
2. The $-\mathrm{CH}=$ groups (monosubstituted alkene carbons) are oxidized past the aldehyde stage all the way to carboxylic acid groups ($-\mathrm{COOH}$).

Therefore, the reaction proceeds as follows:
$C_6{H}_{11}-\mathrm{CH}=\mathrm{CH}-C_6{H}_{11}+\left[O\right]\to 2C_6{H}_{11}-\mathrm{COOH}$
The major product 'P' obtained is cyclohexanecarboxylic acid.

Step 4: Match with the options
- The first option shows a cyclohexyl ring attached to a $-\mathrm{CHO}$ group (cyclohexanecarbaldehyde).
- The second option shows a cyclohexyl ring attached to a $-\mathrm{COOH}$ group (cyclohexanecarboxylic acid), which matches our derived product.
- The third option shows a vicinal diol (formed by cold, dilute, alkaline ${\mathrm{KMnO}}_4$).
- The fourth option shows a 1,2-diketone.

Thus, the correct product 'P' is represented by the structure in the second option.