A particle executes SHM with a time period of 10 secs. At what times will the velocity of the particle be maximum, if at t = 0, the particle starts from x = -A

The particle will have its maximum speed at the mean position. 
The time taken to reach other extreme from its starting point (first extreme x = -A) will be T/2 = 5 secs. 

Thus, the particle will be at the mean position at 2.5 s on its onwards journey and again at 7.5 s in its return journey. At these positions, the speed is maximum

The option (d) is the correct option