A mass with M = 122kg is attached to the bottom of a block-and-tackle pulley system.How much tension force is needed to keep the mass at its current position?

The answer depends upon the amount of friction and the number of ropes and blocks in the block and tackle system.

See
http://science.howstuffworks.com/transport/engines-equipment/pulley.htm

In an ideal systen with one block, the answer would be half the weight of the mass.