Abar magnet is tied to a string and suspended freely. if the magnet is given a small swing, then what will be the direction in which the suspended magnet will come to rest? select one: a. east-south b. east –west c. north –east d. north –south

That depends on HOW you suspended it.

-- If you suspended the 'bar' so that it's hanging up and down, with its poles on the top and bottom, then it won't come to rest in any particular position.

-- If you tie the string in the middle of the 'bar', then balance it so that it's suspended horizontally, with its poles at the same height, and then you give it a small spin, it'll spin back and forth several times, and eventually come to rest with its North pole pointing North, and its South pole pointing South.

The whole question is written poorly.  The least bad answer is choice-d .

one person pulls 90n one way and the other has 100n pulling the other way.

so the net force = 90 - 100 = -10n,

or the ans can be 10n if the picture shows -90n and 100n instead.