The monument that has a dome which is said to be one of the largest in the world is Option 4: Gol Gumbaz in Bijapur, India.

Gol Gumbaz is a mausoleum located in the city of Bijapur, Karnataka, India. It was built by the Adil Shahi dynasty in the 17th century as the tomb of Sultan Muhammad Adil Shah. The main feature of Gol Gumbaz is its massive dome, which is one of the largest domes in the world. The dome has a diameter of 44 meters (144 feet) and is considered a remarkable architectural marvel.

The dome of Gol Gumbaz is a structural masterpiece. It is not supported by any pillars or columns, making it a prime example of engineering ingenuity. The weight of the dome is distributed evenly through its walls, which are 3 meters (10 feet) thick at the base. The inner surface of the dome is adorned with beautiful geometric patterns and intricate calligraphy.

Another remarkable aspect of Gol Gumbaz is its acoustic properties. The dome creates a unique echo effect, known as the "Whispering Gallery." Even the softest sound made at one end of the gallery can be heard clearly at the other end, nearly 38 meters (125 feet) away. This phenomenon has fascinated visitors for centuries and adds to the allure of Gol Gumbaz.

Gol Gumbaz has become an iconic landmark of Bijapur and attracts tourists from all over the world. Its grandeur and architectural brilliance make it a significant historical and cultural monument in India.

In contrast, let`s briefly discuss the other options:

- Option 1: Tomb of Sher Shah, Sasaram: Although the Tomb of Sher Shah in Sasaram, Bihar, India, is a notable monument, it does not have one of the largest domes in the world. Its architecture features a typical Mughal style, but its dome size is not comparable to Gol Gumbaz.

- Option 2: Jama Masjid, Delhi: The Jama Masjid in Delhi, India, is one of the largest mosques in India, but it does not have a dome that can be considered one of the largest in the world. It is known for its grandeur and architectural beauty, but its dome size is relatively smaller compared to Gol Gumbaz.

- Option 3: Tomb of Ghiyas-ud-din Tughlaq, Delhi: The Tomb of Ghiyas-ud-din Tughlaq, also known as Tughlaqabad Fort, is located in Delhi, India. It is an ancient fortress, but it does not have a dome as it was primarily built as a fortified structure and not a mausoleum.

To summarize, among the given options, Gol Gumbaz in Bijapur is the monument with a dome that is said to be one of the largest in the world. Its impressive size, architectural brilliance, and unique acoustic properties make it a standout attraction for visitors.