A spring of force constant \( k \) is cut into lengths of ratio \( ...

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A spring of force constant \( k \) is cut into lengths of ratio \( 1: 2 \) \( : 3 \). They are connected in series and the new force constant is \( k \). Then they are connected in parallel and force constant is \( k^{\prime \prime} \). Then \( k^{\prime}: k^{\prime \prime} \) is
[NEET 2017]
\( \mathrm{P} \)
(a) \( 1: 6 \)
(b) \( 1: 9 \)
(c) \( 1: 11 \)
(d) \( 1: 14 \)
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