Quiescent centre occurs in  

Quiescent centre occurs in root apex.

Plants have a particular form of tissue called a meristem. It is made up of meristematic cells that are still developing and can divide. Three different forms of meristematic tissues can be found in plants: apical, intercalary, and lateral.
The tips of roots and shoots are where the apical meristem is located. The intercalary meristem is found near the base of stem nodding and on leaf blades. The woody section of the plants is where the lateral meristem is located.

All cells can divide numerous times in the root apex, which is a small region near the tip of the root from which all principal root tissues are produced. Cell division happens very slowly in the quiescent centre, which is a region of the apical meristem of a root. If the tissue around them is harmed, the cells can still continue meristematic activity.

Hence the correct answer is option B.