Options B and D: 'In spite of' means 'without being affected by the particular factor mentioned'.
Here, it refers to the factor 'his illness'.
It completes the sentence in meaning: 'Without being affected by his illness, Mani will pass the exam'.
'Although' also means 'in spite of the fact that'. But, 'although' is a conjunction, whereas 'in spite of' is a preposition. The noun 'illness' is the object of the preposition 'in spite of'. 'Although would be followed by a clause 'although he is ill'.
Hence this word 'although' is not suitable in form and structure, and 'in spite of' is.
So, option B is correct and D is wrong.
Option A: 'On account of' means 'because of'. It refers to reason. But, the given sentence does not express the reason: Mani will not pass the exam because he is ill.
Option C: 'In event of' means 'if ____ happens'. It refers to a hypothetical condition, with its probable result. But the given sentence does not depend on condition.