Step-by-step Derivations:

1. Analyze the Question's Core Requirement: The question asks to identify the starting compound(s) Q which, upon reaction with sodium thiophenoxide (PhSNa), yield a major organic product containing sulfur. A compound containing sulfur will give a positive Carius test. The Carius test involves oxidizing the organic compound with $Na_2O_2$ (or fuming nitric acid), which converts sulfur into sulfuric acid/sulfate. Subsequent addition of $BaCl_2$ precipitates the sulfate as white $BaSO_4$.

   The central task is to predict the major product of the reaction between each option Q and PhSNa and check if it contains sulfur.

2. Analyze the Reagent: PhSNa is sodium thiophenoxide. It is a source of the strong, soft nucleophile, thiophenoxide ion ($PhS^-$). It will participate in nucleophilic substitution reactions.

3. Evaluate Each Option:

   • Option A: Q is benzhydryl chloride ($Ph_2CHCl$). This is a secondary benzylic halide. The reaction is a nucleophilic substitution where the $PhS^-$ nucleophile replaces the chloride ($Cl^-$) leaving group. $Ph_2CHCl + PhSNa \rightarrow Ph_2CH-SPh + NaCl$ The carbocation intermediate ($Ph_2CH^+$) is highly stabilized by two phenyl rings, favoring an $S_N1$ mechanism, while the strong nucleophile $PhS^-$ also allows for an $S_N2$ pathway. Regardless of the mechanism, the substitution product, diphenylmethyl phenyl sulfide ($Ph_2CH-SPh$), is the major product. This product contains sulfur. Therefore, it will give a positive Carius test. Option A is correct.

   • Option B: Q is benzoyl chloride (PhCOCl). This is an acyl chloride. The reaction is a nucleophilic acyl substitution. The $PhS^-$ attacks the electrophilic carbonyl carbon, and $Cl^-$ is eliminated. $PhCOCl + PhSNa \rightarrow PhCO-SPh + NaCl$ The product is S-phenyl thiobenzoate, which contains sulfur. However, acyl chlorides are extremely reactive and readily hydrolyze, even with trace amounts of moisture that might be present in the solvent or if the PhSNa was prepared in a protic solvent. $PhCOCl + H_2O \rightarrow PhCOOH + HCl$ The hydrolysis of benzoyl chloride is a very fast reaction. It's plausible that under typical (non-anhydrous) laboratory conditions, the competing hydrolysis reaction could lead to benzoic acid (PhCOOH) as the major product. Since benzoic acid does not contain sulfur, it would not give a positive Carius test. Given the high reactivity of PhCOCl towards water compared to other substrates, it is reasonable to assume hydrolysis could be the dominant pathway, making the desired sulfur-containing compound a minor product. Therefore, Option B is likely incorrect as per the 'major product' condition.

   • Option C: Q is N,N-dimethylformamide ($HCONMe_2$). This is an amide. Amides are significantly less reactive towards nucleophilic substitution than acyl chlorides or alkyl halides. The leaving group would be the dimethylamide anion ($(CH_3)_2N^-$), which is a very strong base and thus a very poor leaving group. No significant reaction is expected to occur between DMF and PhSNa under normal conditions. $HCONMe_2 + PhSNa \rightarrow No \, Reaction$ Thus, no sulfur-containing product is formed. Option C is incorrect.

   • Option D: Q is benzenesulfonyl chloride ($PhSO_2Cl$). This is a sulfonyl chloride. The reaction is a nucleophilic substitution at the electrophilic sulfur atom. The $PhS^-$ nucleophile attacks the sulfur, and $Cl^-$ is eliminated. $PhSO_2Cl + PhSNa \rightarrow PhSO_2-SPh + NaCl$ The product is S-phenyl benzenethiosulfonate. While sulfonyl chlorides can also undergo hydrolysis, they are generally less reactive towards water than acyl chlorides. The reaction with a strong nucleophile like $PhS^-$ is efficient and expected to yield the sulfur-containing compound as the major product. This product contains sulfur and will give a positive Carius test. Option D is correct.

4. Conclusion: Based on the analysis, the substrates in options A and D will react with PhSNa to form major products containing sulfur. The substrate in option B is highly susceptible to hydrolysis, which may result in a non-sulfur-containing major product. The substrate in option C is unreactive. Therefore, the correct options are A and D.