(A) is true. A randomised block design requires every block to hold all $s$ treatments. When the natural block size is smaller than $s$ — limited plot space, litter size, a day's testing capacity — an RBD can only be run by inflating blocks until they are internally heterogeneous, which inflates the error mean square. A BIBD keeps blocks small and homogeneous, and can therefore give a smaller error variance and higher efficiency.

(C) is false because of the word always. A BIBD recovers only part of the treatment information within blocks; its efficiency factor

$E=\frac{\lambda s}{rk} < 1$

is strictly less than one. If blocks can be made homogeneous at full size $k=s$ , the RBD is the better design.

(D) is false. The parameters are heavily constrained. They must satisfy

$sr=bk, \qquad \lambda(s-1)=r(k-1), \qquad b \ge s \quad(\text{Fisher's inequality}),$

and even parameter sets meeting all of these need not correspond to an existing design.

(B) is false. A BIBD is symmetric precisely when $b=s$ (equivalently $r=k$ ), the boundary case of Fisher's inequality — not under the stated inequality $b>r+s-k$ . Indeed, putting $b=s$ and $r=k$ into that expression gives $r+s-k=s=b$ , so the strict inequality $b>r+s-k$ actually fails for a symmetric design.