$(a)\;11\qquad(b)\;10\qquad(c)\;9\qquad(d)\;4$

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Volume of one balloon which is to be filled

$= \large\frac{4}{3}\pi (\large\frac{21}{2})^3$

= 4851 mL

= 4.851 litre

Let n balloon are filled , then volume of $H_2$ occupied by balloons = $4851\times n $

Also cylinder will not be empty and it will occupy volume of

$H_2 $= 2.82 litre

$\therefore$ Total volume occupied by $H_2$ at NTP = $4.851\times n + 2.82 litre$

$\therefore$ at STP

$P_1 = 1 atm$

$V_1 = 4.851\times n + 2.82$

$T_1 = 273 K$

Available $H_2$

$P_2 = 200\;atm$

$T_2 = 300K$

$V_2 = 2.82\;litre$

$\therefore \large\frac{P_1V_1}{T_1} = \large\frac{P_2V_2}{T_2}$

$\large\frac{1\times(4.851n + 2.82)}{273} = \large\frac{20\times2.82}{300}$

$\Rightarrow n = 10$

Hence answer is (B)

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