Step 1: Spot the odd role.
Three names in the list are famous for grammar and word study: Yaska, Panini and Patanjali. Such scholars study meaning, so they would defend the idea that words have meaning. The odd one who attacks it is likely Kautsa.
Step 2: Use the Nirukta.
Yaska's Nirukta is a text on the origin and meaning of Vedic words. In it Yaska takes up an objection from Kautsa, who said mantras are meaningless because their order is fixed and many words seem unclear.
Step 3: Read Yaska's response.
Yaska rejects the objection and says a lack of understanding lies in the reader, not in the hymn. By replying, Yaska shows that he is the opponent of Kautsa's view.
Step 4: Rule out the grammarians.
Panini fixed the rules of Sanskrit grammar and Patanjali explained those rules. Neither of them is known for calling the hymns meaningless.
Step 5: Conclude.
Only Kautsa fits the claim in the question, so the answer is option 4.
Step 6: Note the common mix-up.
Students often pick Yaska because his name is tied to the debate. But Yaska is the person who answers the charge, not the one who makes it. Keeping the roles of attacker and defender apart avoids this mistake.
Final Answer:
Kautsa is the scholar who called Vedic hymns meaningless.
\[ \boxed{\text{Option 4: Kautsa}} \]