I'm assuming these are three separate questions?
1) Seems incomplete.
2) As the particle is in equilibrium, the resultant of all the forces acting on it will be zero. We can see that the forces acting on the body are its weight, the tension in the string and the force P.
So, resolve the forces in the horizontal and vertical directions.
In the horizontal direction,
Now in the vertical direction, The resultant of , and must be zero.
Now [tex]W=mg[tex] by definition where m is the body's mass (=5kg) and
but P=T from the first equation.
Hence (since sin30=cos60)
3)Use the same method. Components of forces in horizontal and vertical direction must add to give zero.