Option 1: an extremely angry and irritated look -> Uma is not angry; she is desperate and frightened, trying to protect her exercise-book from being taken.
Option 2: a look of total excitement -> The context shows Uma is in distress, pleading with others not to expose her secret, not excited.
Option 3: a look showing celebration -> Uma is clearly in trouble and distressed, not celebrating anything.
Option 4: a look of request and prayer -> "Supplication" literally means a humble request or prayer; Uma is desperately begging her husband with her eyes not to take the book.
Hence, Option 4 -> The word "supplication" means a humble, earnest request or prayer. In this context, Uma is silently pleading with her husband through her eyes, begging him not to take away her exercise-book, which represents her only way of experiencing songs since she cannot sing -> correct