$(a)\;11\qquad(b)\;12\qquad(c)\;9\qquad(d)\;10$

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Meq of HCl added to washing soda=$50\times 1=50$

Meq of HCl left,(i.e) used by $Ba(OH)_2$

$\Rightarrow $ Meq of $Ba(OH)_2$

$\Rightarrow 21.13\times 1.018\times 2$

$\Rightarrow 43.02$

Meq of HCl used for washing soda$=50-43.02$

$\Rightarrow 6.98$

Meq of HCl washing soda $(Na_2CO_3-xH_2O)$=6.98

$\large\frac{w}{\Large\frac{M}{2}}$$\times 1000=6.98$

$w=1g$

$\therefore M=286.5$

Mol wt of $Na_2CO_3xH_2O=46+60+18x=106+18x$

$106+18x=286.5$

$x=10$

$\therefore$ Degree of hydration=10

Hence (d) is the correct answer.

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