The modern Assamese script has its roots in:

Siddham script
Devanagari script
Brahmi script
Kharosthi script

The correct answer is: c) Brahmi script.

The Brahmi script is an ancient writing system that originated in India. It is the ancestor of many modern scripts, including Devanagari, Bengali, and Assamese. The Brahmi script was first used to write Sanskrit, but it was later adapted to write other languages, such as Pali, Prakrit, and Assamese.

The Siddham script is a writing system that was used to write Sanskrit and other Indian languages. It is derived from the Brahmi script, but it has its own unique features. The Siddham script is no longer in common use, but it is still used by some Buddhist monks.

The Devanagari script is a writing system that is used to write Hindi, Marathi, Nepali, and other Indian languages. It is derived from the Brahmi script, and it is one of the most widely used writing systems in the world.

The Kharosthi script is an ancient writing system that was used to write Sanskrit, Prakrit, and other Indian languages. It originated in the northwestern part of India, and it was used from the 3rd century BCE to the 7th century CE. The Kharosthi script is no longer in common use, but it is still used by some scholars.

In conclusion, the modern Assamese script has its roots in the Brahmi script. The Brahmi script is an ancient writing system that originated in India. It is the ancestor of many modern scripts, including Devanagari, Bengali, and Assamese. The Brahmi script was first used to write Sanskrit, but it was later adapted to write other languages, such as Pali, Prakrit, and Assamese.