Complete the sentence with the suitable Modal from the options given…

The correct answer is Option (2) → need not go

"Need" as a modal verb:

• As a modal, need not means it is not necessary.
• Like other modals, it is followed by the base form of the verb without "to": need not go, need not worry.
• For an unnecessary action that was already done, the form is need not have + past participle: you need not have gone.
• This sentence: the speaker already has a pen drive, so going to the market now is unnecessary: "you need not go to the market".
  Example: You need not go to the bank; I can pay the bill online.

Complete sentence: I have a pen drive so you need not go to the market for purchasing one.

Why the Other Options are Incorrect?

Option 1: need not to have gone — Incorrect.

• Modal "need not" takes no "to"; the past form is "need not have gone".
• Even that form refers to an action already done, which does not suit the present situation of the sentence.

Option 3: need not going — Incorrect. A modal is never followed by an -ing form.

Option 4: need not to go — Incorrect. The modal "need not" does not take "to"; with "to", the ordinary verb form is "do not need to go".

Contrast: need not go = the action is not necessary now; need not have gone = the action was done, but it was not necessary.