Reaction of glucose acetal with acetic anhydride The following problem was asked in JEE Mains 2020 (Sept 2, Shift 1),

Consider the following reactions:
$\ce{ (i) Glucose + ROH -&gt;[dry HCl] Acetal -&gt;[$x$ eq. of (CH3CO)2O] acetyl derivative }$
$\ce{ (ii) Glucose -&gt;[Ni/H2] A -&gt;[$y$ eq. of (CH3CO)2O] acetyl derivative }$
$\ce{ (iii) Glucose -&gt;[$z$ eq. of (CH3CO)2O] acetyl derivative }$
What are $x, y,$ and $z$ in these reactions, respectively?

I know that the reaction in (i) is acetal formation (used to protect aldehyde), and that alcohol reacts with anhydrides to form acids. As, there are only 5 hydroxyl group in acetyl deriv. of (i), so $x=5$.
In (ii), carbonyl part of glucose reduces to hydroxyl group, so $y=6$. And, in (iii), glucose directly reacts with anhydride, so $z=5$.
But, my answer was wrong (x only), as per the key. What am I doing wrong?

The answer given is,

 x = 4, y = 6, z = 5
I think there's nothing to discussed about this further as all comments directing to the correct answer: $x = 4, \ y = 6,$ and $ z = 5.$ I think it's better show in the structures:

Glucose is naturally occurring in pyranose hemiacetal form. When subjected to react with $\ce{H+/R-OH}$, the remaining acetal hydroxy group (anomeric hydroxyl group) will undergoes alkylation. Thus, the first scheme is showing alkylation of this anomeric hydroxyl group by methanol (Ref.1). The resultant methylglucose has four free hydroxy group, hence, $x = 4$.
When subjected to reduction with suitable conditions (e.g., $\ce{Ni/H2}$, $\ce{Ru/C/H2}$, etc.), the hemiacetal group would be reduced to a $\ce{-CH2OH}$ group (second scheme in the image). The resultant product is sorbitol (Ref.2), which has six free hydroxy groups, hence, $y = 6$.
Finally, pyranose glucose structure has five free hydroxy groups, hence, $z = 5$.

References:

B. Helferich, W. Schäfer (Checked by H. T. Clarke and M. R. Brethen), &quot;$\alpha$-methyl d-Glucoside,&quot; Org. Synth. 1926, 6, 64 (DOI: 10.15227/orgsyn.006.0064).
J. Wildschut, J. Arentz, C.B. Rasrendra, R.H. Venderbosch, H.J. Heeres, &quot;Catalytic Hydrotreatment of Fast Pyrolysis Oil: Model Studies on Reaction Pathways for the Carbohydrate Fraction,&quot; Environmental Progress &amp; Sustainable Energy 2009, 28(3), 450-460 (https://doi.org/10.1002/ep.10390).