Step 1: Lamotrigine is a broad-spectrum antiepileptic that blocks voltage-gated sodium channels and reduces glutamate release. It has an elimination half-life of roughly 24 to 30 hours, allowing once or twice daily dosing. This makes option (c) correct.
Step 2: Lamotrigine is mood-stabilising and is actually effective in bipolar depression, so the statement that it has decreased efficacy in depression (a) is false.
Step 3: The first-line drug for absence seizures is ethosuximide (or valproate). Lamotrigine is an alternative, not the first choice, so option (b) is wrong.
Step 4: Lamotrigine IS metabolised in the liver, mainly by glucuronide conjugation, so option (d) is false. By elimination and by direct fact, the correct answer is its half-life of about 24 hours.