two particles,each having a mass m are placed at a separation d in a uniform magnetic field

both of  opposite charges q with same magnitude (with magnetic field into the plane of ur screen)

at time t=0 both the particles are projected towards each other,each with a speed of v.Than at what instant will a colllision occur between the particles if v = v_m

 You have not mentioned what is vm. I am assuming that vm is the minimum velocity required for collision which will happen if cyclotron radius is d/2. 

If v = 2vm , the radius of circular path will be 2*(d/2) = d.

Vertical displacement of particles = d/2. If @ is the angle subtended by their path on the center of circle then 

sin(@) = (d/2)/d = 1/2 Sp @ = pi/6

So time taken = (pi/6)/(2pi)*Time of one revolution = (1/12)*(2*pi*m/(qB)) =pi*m/(6qB)