An object may have
a) varying speed without having varying velocity
b) varying velocity without having varying speed
c) nonzero acceleration without having varying velocity
d) nonzero acceleration without having varying speed.

Speed is a scalar quantity while velocity is a vector quantity. 

An object can have constant speed but velocity will change since velocity is a vector quantity. 

Without having a varying speed non-zero acceleration is possible. Uniform circular motion is an example. 

Thus, B and D options are correct