Select the most appropriate idiom for the underlined part in the given sentence:
Sohan was very much perplexed to find that his younger brother Mohan had taken poison.

The correct option is At his wit’s end.

Explanation:
The idiom "at one's wit's end" means to be completely perplexed, bewildered, or at a total loss as to what to do next. In the given sentence, Sohan was extremely confused and distressed upon finding that his brother had taken poison, which precisely matches the meaning of being very much perplexed or at his wit's end.

Meanings of the other options:
• At any rate: Whatever the case may be; in any event.
• At logger heads: In strong disagreement or conflict with someone.
• At his disposal: Available for someone to use as they wish.