The correct answer is option 'A' - Sabarmati.

The Aravalli Range is one of the oldest mountain ranges in India, stretching across the states of Rajasthan, Gujarat, Haryana, and Delhi. It is a crucial watershed region and gives rise to several rivers. Among the given options, the Sabarmati River originates from the Aravalli Range.

Here is a detailed explanation of the rivers originating from the Aravalli Range:

1. Sabarmati:
The Sabarmati River originates from the Aravalli Range near the town of Udaipur in Rajasthan. It then flows through the states of Gujarat and finally meets the Arabian Sea near the city of Ahmedabad. The Sabarmati River basin is an important source of water for irrigation, domestic use, and industrial purposes.

2. Mahi:
The Mahi River is the second-largest river in Gujarat and also originates from the southern slopes of the Aravalli Range. It flows through the states of Rajasthan, Madhya Pradesh, and Gujarat before merging with the Arabian Sea near the town of Khambhat. The Mahi River basin is known for its rich biodiversity and supports various agricultural activities.

3. Ghaggar:
The Ghaggar River, also known as the Hakra River, is an intermittent river that flows through the states of Haryana, Punjab, and Rajasthan. It originates from the Shivalik Hills, which are an offshoot of the Aravalli Range. While the Ghaggar River does not flow continuously throughout the year and remains dry for most of the time, it carries water during the monsoon season.

4. Betwa:
The Betwa River is a tributary of the Yamuna River and flows through the states of Madhya Pradesh and Uttar Pradesh. It does not originate from the Aravalli Range but rather from the Vindhya Range. Therefore, it is not a river that originates from the Aravalli Range.

In summary, out of the given options, only the Sabarmati River originates from the Aravalli Range. The Mahi River originates from the southern slopes of the Aravalli Range, while the Ghaggar River originates from the Shivalik Hills, which are an offshoot of the Aravalli Range. The Betwa River, on the other hand, does not originate from the Aravalli Range.