Formation of the nodule is induced by

The correct option is IAA.

Nodule formation in leguminous plants is a complex symbiotic process initiated by the interaction between the host plant roots and soil bacteria, typically of the genus Rhizobium.
During this process, plant hormones (phytohormones) play a crucial role in regulating cell division and differentiation to form the functional nodule structure.

Among the various phytohormones, auxins are essential for initiating cell divisions in the root cortex. IAA (Indole-3-acetic acid) is the naturally occurring primary auxin in plants.
It is synthesized by both the plant host and the symbiotic bacteria. The localized accumulation of IAA in the root cortex stimulates the mitotic divisions necessary for the initiation and development of the root nodule. While synthetic auxins like IBA (Indole-3-butyric acid) and NAA (Naphthalene acetic acid) can influence root growth in general, the natural induction of nodule formation during symbiosis is specifically driven by endogenous IAA.