You can choose any of the below
How convincing is Nyāya-Vaiśeṣika’s analysis of reality as an ontology of seven ‘categories of things that exist’ (padārthas)? [Feel free to address what you wish of this theory, e.g. their theory of substances and qualities/actions, their theory of universals and particularities, their theory of the relation of inherence (samavāya), viz. identity-in-difference, (and whether inherence is both coherent and sufficient to integrate their pluralistic ontology into a unified whole).]
• Examine and assess Nyāya-Vaiśeṣika’s theory of the self (ātman) and of what constitutes liberation (mokṣa).
• Examine and assess Nyāya-Vaiśeṣika’s doctrine that the effect does not exist in its cause (asatkāryavāda). You may wish to consider here their mereological arguments claiming that wholes are ontologically distinct from their parts.
• Examine and assess Nyāya-Vaiśeṣika’s theory of the realism of universals (sāmānya) and/or their theory of the realism of nonexistences (abhāva).
• Assess Nyāya’s theory of valid inference (anumāna), including whether their doctrine of the invariable concomitance/pervasion of properties solves the problem of induction.
• Assess the debate between Nyāya’s doctrine of four valid means of knowledge (pramāṇa) and the Materialist (Carvāka) School’s doctrine that perception is the only valid means of knowledge (pramāṇa).
• Does Nyāya theory of the valid means of knowledge (pramāṇa) give a satisfactory account of what knowledge is, of what establishes what knowledge is, and of. how we know that we know?
Main sources:
Hiriyanna, M. (1932) Outlines of Indian Philosophy, Delhi, Motilal Banarsidass.
Radhakrishnan, S. & Moore, C. A. (eds.) (1957) A Source Book in Indian Philosophy, Princeton, Princeton University Press, referred to below as SB
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