took up/on

New2grammarLittle did I know what I was getting into when I took ([on/up]) the task.

1 Are there any mistakes?
2 Which of the three choiceS is correct?

Thanks.

on

Here's how I hear them.
took on the task -- assumed responsibility for the task
took up the task -- began to work on the task

took over the task (1)-- assumed the responsibility for the task after someone else had had it
took over the task (2) -- dominated or bullied everyone else in the performance of the task
took the task -- ??? -- consented or agreed to an order to