Correct Answer: 10 cm

Solution : AB and CD are two chords of a circle intersecting externally at P
AB = 4 cm, CD = 11 cm and PD = 15 cm
If two chords AB and CD intersect at outer point P then,
PA × PB = PC × PD
Let the length of PA be $x$
PC = PD - CD
= 15 - 11
= PC = 4 cm
According to the question
PA × PB = PC × PD
⇒ $x$ × ($x$ + 4) = 15 × 4
⇒ $x$ = 6
PB = PA + AB
= 6 + 4
= 10
$\therefore$  The length of PB is 10 cm.
Hence, the correct answer is 10 cm.