For the reaction sequence given below, the correct statement(s) is(are)

The correct statements for the given reaction sequence are:
Q gives effervescence with aq. NaHCO3.
S gives Bayer’s test.

Let us analyze the reaction sequence step-by-step:

1. Structure of the Starting Material:
The starting material shown in the image is a 6-membered lactone (cyclic ester) with a benzyl group (${\text{-CH}}_2\text{Ph}$) at the 4-position: 4-benzyltetrahydro-2H-pyran-2-one.

2. Conversion of the Lactone to P:
Treating the lactone with a strong reducing agent like lithium aluminium hydride (${\text{LiAlH}}_4$) reduces the cyclic ester group, opening the ring to yield a 1,5-diol:
$\text{Lactone}\stackrel{{\text{LiAlH}}_4}{\to }\text{P}$
The structure of P is:
${\text{HO-CH}}_2{\text{-CH}}_2{\text{-CH(CH}}_2{\text{Ph)-CH}}_2{\text{-CH}}_2\text{-OH}$
This is 3-benzylpentane-1,5-diol. Because the central carbon atom is bonded to two identical 2-hydroxyethyl groups (${\text{-CH}}_2{\text{CH}}_2\text{OH}$), it is symmetric and lacks chiral centers. Thus, P is optically inactive.

3. Conversion of P to Q:
Jones reagent (${\text{CrO}}_3-{\text{H}}_2{\text{SO}}_4$) oxidizes both primary alcohol groups of P to carboxylic acids:
$\text{P}\stackrel{{\text{CrO}}_3-{\text{H}}_2{\text{SO}}_4}{\to }\text{Q}$
The structure of Q is a dicarboxylic acid:
${\text{HOOC-CH}}_2{\text{-CH(CH}}_2{\text{Ph)-CH}}_2\text{-COOH}$
Since Q is a carboxylic acid, it reacts with aqueous sodium bicarbonate (${\text{NaHCO}}_3$) to liberate carbon dioxide gas, producing effervescence:
$\text{R-COOH}+{\text{NaHCO}}_3\to \text{R-COONa}+{\text{H}}_2\text{O}+{\text{CO}}_2\uparrow$
Hence, the statement "Q gives effervescence with aq. NaHCO3" is correct.

4. Conversion of Q to R:
Heating Q with soda-lime ($\text{NaOH and CaO,}\Delta$) results in decarboxylation (removal of both carboxyl groups as carbon dioxide):
$\text{Q}\stackrel{\text{NaOH, CaO,}\Delta }{\to }\text{R}$
The structure of R is:
${\text{CH}}_3{\text{-CH(CH}}_2{\text{Ph)-CH}}_3$
which is isopropylbenzene (cumene). Since cumene is an alkylbenzene (aromatic hydrocarbon) and not an alkyne, the statement "R is an alkyne" is incorrect.

5. Conversion of P to S:
Heating the diol P with concentrated sulfuric acid (${\text{H}}_2{\text{SO}}_4$) at 443 K causes acid-catalyzed dehydration. The two primary alcohol groups undergo elimination to form carbon-carbon double bonds:
$\text{P}\stackrel{{\text{H}}_2{\text{SO}}_4\text{, 443 K}}{\to }\text{S}$
The structure of S is:
${\text{CH}}_2{\text{=CH-CH(CH}}_2{\text{Ph)-CH=CH}}_2$
Because S is an alkene (diene), it contains carbon-carbon double bonds and therefore reacts positively to Bayer’s test (decolorization of cold, dilute, alkaline potassium permanganate solution). Hence, the statement "S gives Bayer’s test" is correct.