In the following reactions, P, Q, R, and S are the major products. The correct statement(s) about P, Q, R, and S is(are):

Correct Statements:
1. Compounds Q and R are the same.
2. R does not undergo aldol condensation and S does not undergo Cannizzaro reaction.

Step-by-step Identification of Products P, Q, R, and S:

1. Formation of P:
The starting material is 1-tert-butyl-4-ethylbenzene.
Reaction with alkaline $KMn{O}_4$ followed by acidic hydrolysis oxidizes the ethyl group containing benzylic hydrogens into a carboxylic acid substituent ($-COOH$). The tert-butyl group lacks benzylic hydrogens and remains resistant to oxidation.
Thus, product P is 4-tert-butylbenzoic acid (a monocarboxylic acid).

2. Formation of Q:
The starting material is methyl 3-(chlorocarbonyl)benzoate.
Treatment with aqueous $NaOH$ hydrolyzes the reactive acyl chloride group ($-COCl$) as well as the ester group ($-COOMe$) to carboxylate salts, which upon acidification ($H_3{O}^{+}$) yield benzene-1,3-dicarboxylic acid (isophthalic acid).
Thus, product Q is isophthalic acid.

3. Formation of R:
The starting material is methyl 3-(3-cyanophenyl)-3-oxopropanoate.
(i) Hydrolysis with $H_3{O}^{+},\Delta$ hydrolyzes the nitrile group ($-CN$) into a carboxylic acid ($-COOH$) and the ester into a β-keto acid, which readily undergoes thermal decarboxylation to give 3-acetylbenzoic acid.
(ii) Subsequent reaction with chromic acid ($H_{2}Cr{O}_4$, haloform-like or oxidative cleavage of acetyl group) oxidizes the acetyl group ($-COC{H}_3$) into a carboxylic acid group.
Thus, product R is also benzene-1,3-dicarboxylic acid (isophthalic acid).

4. Formation of S:
The starting material is 2-(4-bromophenyl)-1,3-dioxolane.
(i) Reaction with $Mg$ in dry ether forms a Grignard reagent at the aromatic bromide position.
(ii) Reaction with $C{O}_2$ followed by $H_3{O}^{+}$ introduces a carboxylic acid group ($-COOH$) and hydrolyzes the cyclic acetal protection back into a formyl group ($-CHO$), yielding 4-formylbenzoic acid.
(iii) Treatment with ammoniacal $AgN{O}_3$ (Tollens' reagent) selectively oxidizes the aldehyde group ($-CHO$) to a carboxylic acid group.
Thus, product S is benzene-1,4-dicarboxylic acid (terephthalic acid).

Evaluation of Statements:

• P and Q are monomers of polymers dacron and glyptal, respectively: Incorrect. Terephthalic acid (S) and ethylene glycol form Dacron, while phthalic acid (or isophthalic acid Q) and glycerol form Glyptal. P is 4-tert-butylbenzoic acid, which is not a monomer for Dacron.

• P, Q, and R are dicarboxylic acids: Incorrect. Q and R are dicarboxylic acids, but P is a monocarboxylic acid.

• Compounds Q and R are the same: Correct. Both Q and R are benzene-1,3-dicarboxylic acid (isophthalic acid).

• R does not undergo aldol condensation and S does not undergo Cannizzaro reaction: Correct.
- Product R (isophthalic acid) has no α-hydrogens next to a carbonyl group of an aldehyde/ketone to form an enolate, so it does not undergo aldol condensation.
- Product S (terephthalic acid) contains only carboxylic acid groups (no aldehyde functionality), so it cannot undergo the Cannizzaro reaction.