Concept:
Mughal painting developed strongly under imperial patronage.
Akbar played a major role in organizing painters, establishing royal workshops, and encouraging illustrated manuscripts.
Step 1: Check Assertion (A).
Akbar is considered the real founder of the Mughal School of Painting.
He invited many artists to his court and gave strong patronage to painting.
So, Assertion (A) is correct.
Step 2: Check Reason (R).
Reason says that Akbar did not take great care to furnish the imperial atelier.
This is incorrect.
Akbar actually took great interest in the imperial painting workshop.
He organized artists and encouraged illustrated works such as the Hamzanama.
Step 3: Final conclusion.
Assertion is correct, but Reason is incorrect.
Hence:
\[
\boxed{\text{(C)}}
\]