This question requires evaluating the accuracy of three statements concerning the geography of major rivers in India.

Indian Rivers Statement Analysis

Statement 1: Barak River Origin

The first statement claims that the Barak River, the headstream of the Meghna, originates in the hills of Meghalaya. Let's analyze this:

• The Barak River is a significant trans-boundary river in Northeast India and Bangladesh.
• It originates in the **Manipur hills** in Northeast India.
• From Manipur, it flows through the state of Assam and then enters Bangladesh, where it merges with the Gumti River and eventually forms the Meghna River.
• Therefore, the claim that the Barak River rises in the hills of Meghalaya is incorrect.

Statement 2: Ghaggar River Course

The second statement asserts that the Ghaggar River does not drain into the sea and gets lost in the Rajasthan desert. Let's examine this:

• The Ghaggar River is an intermittent river, meaning it flows primarily during the monsoon season.
• It originates in the Shivalik Hills of Himachal Pradesh and flows through Haryana and Rajasthan.
• Crucially, the Ghaggar River typically **does not reach the sea** (like the Arabian Sea or the Bay of Bengal).
• Its waters often dissipate into the arid sands of the Thar Desert in Rajasthan, near the Pakistan border, or terminate in the Sarsuti, Ghaggar, and Hakra river beds.
• Thus, this statement accurately describes the Ghaggar River's fate.

Statement 3: Brahmaputra Tributaries

The third statement identifies Puthimari and Manas as important tributaries of the Brahmaputra River. Let's verify:

• The Brahmaputra River is a major river flowing through Tibet (as Yarlung Tsangpo), Northeast India, and Bangladesh.
• Several rivers join the Brahmaputra as tributaries.
• The **Manas River** is a major trans-boundary river in the Himalayan foothills, flowing through Tibet, Bhutan, and India, and it is a significant northern tributary of the Brahmaputra.
• The **Puthimari River** is another important river in Assam that flows into the Brahmaputra.
• Therefore, this statement correctly identifies Puthimari and Manas as key tributaries of the Brahmaputra.

Conclusion on River Statements

Based on the analysis:

• Statement 1 is incorrect because the Barak River originates in Manipur, not Meghalaya.
• Statement 2 is correct as the Ghaggar River disappears in the Rajasthan desert and does not reach the sea.
• Statement 3 is correct as Puthimari and Manas are indeed tributaries of the Brahmaputra River.

Therefore, the correct statements are 2 and 3.