Step 1: Understand the platform in question.
SWAYAM is a Government of India MOOC platform, so we judge each statement by its three founding pillars: quality, access, and equity.
Step 2: Test statement K (quality content).
Courses are built by national coordinators like NPTEL, UGC, and IGNOU, so high-quality content is genuinely ensured. $K$ is correct.
Step 3: Test statement L (nominal cost).
The learning material is free; only the optional certification exam may carry a small fee. Saying content has a nominal cost is misleading, so $L$ is rejected.
Step 4: Test statements M and N.
$(M)$ SWAYAM does not directly grant degrees, it only supports certificates and credit transfer, so $M$ is wrong. $(N)$ The courses do span from Class IX up to postgraduate level, so $N$ is correct.
Step 5: Test statement O (open access).
SWAYAM is open to anyone, anywhere, at any time, making $O$ correct.
Step 6: Combine the surviving statements.
The correct objectives are $K$, $N$, and $O$, which is exactly option A.
\[ \boxed{\text{A. } K, N \text{ and } O} \]