The indicated air speed which produces the maximum rate of climb in a piston engine air craft changes as height increases. This is neccessary to
a) maitain the maximum surplus power
b) maintain the maximum surplus thrust
c) maintain the minimum total drag
d) maintain the maximum possible engine power

Rate of climb for a piston prop combination relates to how much spare power you have up your sleeve. This relates, in turn to the shape of the power available and power required curves (these curves change with altitude and we are just looking to find the speed where these curves are furthest apart at any condition) ... so, let's look at the question alternatives

The indicated air speed which produces the maximum rate of climb in a piston engine air craft changes as height increases. This is necessary to

a) maintain the maximum surplus power This sounds good, could be OK

b) maintain the maximum surplus thrust Close, but we are talking power, not thrust. Probably not an option

c) maintain the minimum total drag Minimum drag has naught to do with max climb rate. Not an option

d) maintain the maximum possible engine power Not at all, we are after the power which gives us the biggest gap between power required and power available. That won't be maximum power. Not an option.

I'd run with (a)

thanks alot