Introduction:
Jaychandra, also known as Jaichand, was the ruler of Kannauj and one of the most powerful kings in Northern India during the 12th century. He is famously remembered for not assisting Prithviraja Chauhan, the king of Delhi, in his war against Muhammad Ghori. The correct answer is option 'B,' which states that Jaychandra thought if the power of the Chauhans were destroyed, it would clear the way for his own supremacy in the North.

Reasoning:
There are several reasons why Jaychandra did not help Prithviraja Chauhan in his war against Muhammad Ghori. These reasons are based on historical accounts and the political situation prevailing during that time.

1. Rivalry:
Jaychandra and Prithviraja Chauhan were not on good terms due to a long-standing rivalry between their kingdoms. Jaychandra saw Prithviraja as a rival for power and influence in Northern India. Helping Prithviraja in his war against Ghori would have meant strengthening his rival's position, which went against Jaychandra's own aspirations for supremacy.

2. Ambitions for Supremacy:
Jaychandra had ambitions of establishing himself as the paramount ruler of Northern India. He saw Prithviraja Chauhan as an obstacle to his aspirations and believed that if the power of the Chauhans was destroyed, it would clear the way for his own supremacy. By not helping Prithviraja, Jaychandra hoped to weaken his rival and enhance his own position.

3. Strategic Considerations:
Jaychandra may have also considered the strategic implications of assisting Prithviraja in his war against Ghori. Ghori was a formidable invader who had already defeated Prithviraja in the First Battle of Tarain. Jaychandra may have assessed that joining forces with Prithviraja would not guarantee victory and could potentially expose his own kingdom to Ghori's aggression. Therefore, he chose to prioritize his own kingdom's security over assisting Prithviraja.

4. Political Calculations:
Jaychandra may have calculated that by not helping Prithviraja, he could maintain a neutral stance and potentially negotiate with Ghori later. He may have believed that aligning with Ghori could offer him benefits such as protection, trade opportunities, or even a chance to expand his own kingdom at the expense of Prithviraja's weakened state.

Conclusion:
In conclusion, Jaychandra's decision not to help Prithviraja Chauhan in his war against Muhammad Ghori was primarily driven by his own ambitions for supremacy in Northern India. He viewed Prithviraja as a rival and believed that weakening the Chauhans would pave the way for his own rise to power. This decision was influenced by the historical rivalry between their kingdoms, Jaychandra's strategic considerations, and his political calculations.