Correct answer is - a) They need not do anything.

• Infinitive
Verb এর present form এর আগে to বসিয়ে Infinitive গঠন করা হয়।
- অর্থাৎ, Infinitive = to + verb.
Infintive দুই রকম হতে পারে-
1. To-যুক্ত infinitive এবং
2. To-বিহীন infinitive বা Bare Infinitive.
Infinitive form বিভিন্ন ভাবে ব্যবহৃত হতে পারে।
যেমন: Subject of verb, Object of verb, Complement of verb, object of preposition, etc.

• Bare Infinitive
নিম্নলিখিত verb-এর পরে infinitive (to) বসে না।
(a) can, do, may, must, shall, will এর পরেঃ
- I may help you.
- He must do it.

(b) need এবং dare - auxiliary verb হিসেবে ব্যবহৃত হলেঃ
- I dared not wake him.
- They need not do anything.
কিন্তু ordinary verb হিসেবে ব্যবহৃত হলে তাদের পরে infinitive বসে।
- I did not/didn't dare to wake him.
- They do not/don't need to do anything.

(c) feel, hear, let, see, make, watch-এর পরেঃ
- I saw him go.
- The old man watched his companions fall down dead.

কিন্তু Passive Voice-এ see, hear, এবং make এর পরে full infinitive ব্যবহৃত হয়।
Active: I saw him go.
Passive:He was seen to go.

(d) Had better, had rather, had sooner, would rather/would sooner, rather than/sooner t
as soon ইত্যাদির পরেঃ
- You had better start at once (to start নয়)

(e) "Than" Conjunction-এর পরে to উহ্য থাকে।
- I would rather die than beg.

Source: Advance Learner’s English Grammar & Composition by Chowdhury & Hossain.