Which of the following sentences uses a modal wrongly?

The correct answer is Option (3) → Mr Bose needs not come to the office on Saturdays.

Need not takes no -s:

• The given sentence says “needs not come”.
• With not and a base verb (the simple form of the verb, like go, eat), need works as a modal.
• A modal never takes -s, even after he, she or a name. So “needs not” is wrong.
• Corrected: Mr Bose need not come to the office on Saturdays.

Why the Other Options are Incorrect?

Option 1: Ought we to wait for Kiran before we cut the cake? This sentence is correct. “Ought” keeps its to even in a question.

Option 2: You should have told me about the leaking pipe yesterday. This sentence is correct. Should have + past participle (V3) shows that the right thing was not done in the past.

Option 4: The fire exits of the hall must be kept clear during the function. This sentence is correct. Must be + V3 is the passive form of “must”, as the exits receive the action.