A particle of mass m having negative charge −q is projected at an angle θ with x-axis. There exists a uniform electric field E and a uniform magnetic field B along x-axis. The particle will return to its initial point after n complete  revolutions in time t. What is n here?

Let particle completes n revolutions in time t, then t = nT⇒   t=n2πmqBIf particle has to return to its initial point, then displacement along x-axis during this time should be zero.Sx = uxt +12  axt2⇒   0=v cos θt −12  qEm t2⇒  v cos θ=  qE2m t⇒  v cos θ=  qE2m  ×  n 2πmqB ⇒  n  =  BvcosθπE