Step 1: Identification of Compound P

1. Molecular Formula and Functional Group: The compound P has the molecular formula ${C_{11}}{H_{12}}{O_2}$ and is an organic acid, which implies the presence of a carboxylic acid group ($-COOH$).

2. Oxidation Product: P can be easily oxidized to a dibasic acid which reacts with ethylene glycol to produce the polymer dacron. Dacron is a polyester formed from the condensation of terephthalic acid (benzene-1,4-dicarboxylic acid) and ethylene glycol. This strongly indicates that the dibasic acid is terephthalic acid.

3. Structure of P: Since P oxidizes to terephthalic acid, P must be a para-substituted benzoic acid. The structure can be represented as $p-R-C_6H_4-COOH$, where R is a side chain that can be oxidized to a $-COOH$ group.

4. Side Chain Formula: Let's determine the formula of the side chain R.

   • The formula of the $p-C_6H_4-COOH$ part is $C_7H_5O_2$.
   • Subtracting this from the molecular formula of P (${C_{11}}{H_{12}}{O_2}$): ${C_{11}}{H_{12}}{O_2} - {C_7}{H_5}{O_2} = {C_4}{H_7}$
   • So, the side chain R has the formula $-C_4H_7$.

5. Degree of Unsaturation (DoU): For ${C_{11}}{H_{12}}{O_2}$, the DoU is $11 + 1 - \frac{12}{2} = 6$. A benzene ring accounts for 4 DoU and the carbonyl group ($C=O$) in the carboxylic acid accounts for 1 DoU. This leaves $6 - 4 - 1 = 1$ DoU for the side chain $-C_4H_7$, which means it must contain a double bond or a ring.

6. Ozonolysis: The problem states that ozonolysis of P gives an aliphatic ketone as one of the products. Ozonolysis cleaves C=C double bonds. For an aliphatic ketone to be formed as a separate molecule, the structure of the side chain attached to the ring must be of the form $-CH=C(R_1)(R_2)$. Ozonolysis ($O_3$, then reductive workup with $Zn/H_2O$) would yield $p-(OHC)-C_6H_4-COOH$ and $R_1-CO-R_2$ (a ketone).

7. Structure of the Side Chain: The side chain is $-C_4H_7$. We need to find $R_1$ and $R_2$ such that the total structure $-CH=C(R_1)(R_2)$ has 4 carbons and 7 hydrogens. The ketone formed is $R_1-CO-R_2$. The simplest aliphatic ketone is acetone, $(CH_3)_2CO$. If the ketone is acetone, then $R_1 = CH_3$ and $R_2 = CH_3$.

   • Let's check the formula for the side chain $-CH=C(CH_3)_2$: It has $1+1+2 = 4$ carbon atoms and $1+3+3 = 7$ hydrogen atoms. The formula is $-C_4H_7$. This matches our requirement.
   • Thus, the side chain is the 2-methylprop-1-enyl group.

8. Final Structure of P: Combining all the information, the structure of P is 4-(2-methylprop-1-enyl)benzoic acid.

$P = HOOC - \langle \bigcirc \rangle - CH=C(CH_3)_2$

Step 2: Reaction Sequence to form R

1. P to intermediate: P reacts with thionyl chloride ($SOCl_2$). This reagent converts a carboxylic acid into an acid chloride.

$HOOC - \langle \bigcirc \rangle - CH=C(CH_3)_2 \xrightarrow{SOCl_2} Cl-CO - \langle \bigcirc \rangle - CH=C(CH_3)_2$

2. Intermediate to Q: The resulting acid chloride undergoes Friedel-Crafts acylation with benzene in the presence of anhydrous $AlCl_3$. The acyl group attaches to the benzene ring to form a ketone, Q.

$Cl-CO - \langle \bigcirc \rangle - CH=C(CH_3)_2 + C_6H_6 \xrightarrow{Anhyd. AlCl_3} C_6H_5-CO - \langle \bigcirc \rangle - CH=C(CH_3)_2$ Structure of Q is (4-(2-methylprop-1-enyl)phenyl)(phenyl)methanone.

3. Q to R: Compound Q is treated with $H_2$ over a Palladium-Carbon catalyst ($Pd-C$). Catalytic hydrogenation reduces both the carbon-carbon double bond and the ketone group. The reduction of a diaryl ketone like this one under these conditions typically leads to the corresponding methylene group ($CH_2$), a reaction known as hydrogenolysis.

   • Reduction of the C=C bond: $-CH=C(CH_3)_2 \rightarrow -CH_2-CH(CH_3)_2$ (isobutyl group)
   • Reduction of the C=O group: $-CO- \rightarrow -CH_2-$ (methylene bridge)

   So, the final product R is:

$C_6H_5-CH_2 - \langle \bigcirc \rangle - CH_2-CH(CH_3)_2$

The name of this compound is 1-benzyl-4-isobutylbenzene.

Step 3: Comparison with Options

Let's examine the given options:

• Option A: This structure matches our derived structure for R, which is 1-benzyl-4-isobutylbenzene.
• Option B: The bridge between the two rings is $CH(CH_3)$, which is incorrect.
• Option C: The isobutyl group is attached to the wrong benzene ring. The side chain was originally on the ring derived from benzoic acid.
• Option D: The substituents are incorrect.

Therefore, the correct structure for compound R is given in option A.