The President of the Students’ Union played into the hands of some political leaders and . . . . . . the students to go on a strike.

The correct answer is C. instigated.

To instigate means to encourage or stir up (something, especially trouble or an undesirable course of action). In this case, the President of the Students’ Union encouraged the students to go on strike by playing into the hands of some political leaders.

The other options are not as accurate. To invite means to ask someone to come to a place or event. To ignite means to set fire to something. To inspire means to fill someone with the urge or ability to do something.