Concept:
Monazite sands contain rare earth elements along with thorium. During the extraction of rare earths, thorium is obtained as a by-product. However, Kakrapar-1 is a Pressurized Heavy Water Reactor (PHWR) using uranium fuel, not the world's first thorium reactor.
Step 1: Evaluate Assertion (A).
\[
\boxed{\text{Assertion (A) is True}}
\]
Step 2: Evaluate Reason (R).
Kakrapar-1 does not use thorium as its primary fuel.
\[
\boxed{\text{Reason (R) is False}}
\]
Hence,
\[
\boxed{\text{(C)}}
\]