Given the analogy: Taj Mahal : Agra :: India Gate : New Delhi :: Gateway of India : ?, choose the correct option.

The problem asks us to find the relationship between the given pairs of words and then apply the same relationship to the third pair to find the missing word.

The given analogy is:
তাজমহল : আগ্রা :: ইন্ডিয়া গেট : নয়াদিল্লি :: গেটওয়ে অফ ইন্ডিয়া : ?

Let's analyze the first two pairs:

1. তাজমহল : আগ্রা (Taj Mahal : Agra) The Taj Mahal is a famous monument located in the city of Agra.

2. ইন্ডিয়া গেট : নয়াদিল্লি (India Gate : New Delhi) The India Gate is a famous monument located in the city of New Delhi.

The relationship established is: Monument : City where the monument is located.

Now, we apply this relationship to the third pair:
গেটওয়ে অফ ইন্ডিয়া : ? (Gateway of India : ?)

The Gateway of India is a famous monument. We need to identify the city where it is located.
The Gateway of India is located in Mumbai.

Let's check the given options:

1. চেন্নাই (Chennai)
2. অমৃতসর (Amritsar)
3. ব্যাঙ্গালোর (Bengaluru)
4. মুম্বাই (Mumbai)

Based on our analysis, the correct city is Mumbai.

The final answer is $\text{মুম্বাই}$.