Identify the correct statement. In the absence of external force.

a) The kinetic energy associated with the motion of centre of mass is conserved

b) Centre of mass is not accelerated

c) The centre of mass always move in curved line 

d) Centre of mass must be at rest

If $F_{ext}=M_{system}\times a_{cm}$.

If

 $$\begin{gathered} F_{ext}=0, \\ {a}_{cm}=0 \end{gathered}$$

Thus statement A is correct

Now kinetic energy of the system of particles = $\frac{1}{2}{M}_{system.}{v^2}_{cm}$

The total K.E. of the particles with respect to the system's centre of mass.
Since the centre of mass's $V_{cm}$velocity has remained constant since $F_{ext}=0$, (b) is true.

Hence the correct answer is a & b are correct.