which type of transmission allows an infinite adjustment of tractor speed within a range without any gear…

Brief Explanations:

Hydrostatic drive uses hydraulic fluid to transmit power and can provide a continuous range of speeds without gear - shifting. Mechanical shift involves changing gears, synchromesh is a feature related to smooth gear - shifting in mechanical transmissions, and hydraulic assist is mainly for providing force assistance rather than speed adjustment without gear - shifting.

Answer:

A. Hydrostatic drive