The function of management which establishes relation between authority and responsibility is:

Organising

The correct answer is option 2- organising.

Organizing involves assigning duties, setting up authorities and allocating resources to execute a plan. It groups the tasks into manageable work units. Organising essentially implies a process which coordinates human efforts, assembles resources and integrates both into a unified whole to be utilised for achieving specified objectives. Organising can be defined as a process that initiates implementation of plans by clarifying jobs and working relationships and effectively deploying resources for attainment of identified and desired results (goals). Thus, it establishes the authority/responsibility relationship.