Hello,

Based on your JEE Main score of 52 and category rank of 58,842 (in Tamil Nadu), it might be difficult for you to secure admission in NIT Trichy, IIIT, or IIITDM Kancheepuram, based on previous year cut-off trends.

1. NIT Trichy (National Institute of Technology Trichy) : The cut-off for general category students is usually very high, and even for reserved categories, it remains competitive. Your rank is likely to be far from the required cut-off in most branches.

2. IIITDM Kancheepuram : Similar to NITs, IIITDM also has a high cut-off, but it may vary slightly. Your rank may be challenging for some of the top branches, though you might have a slim chance in some lower-demand branches.

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3. IIITs : The cut-offs in IIITs also tend to be quite high. With your current rank, securing admission into the top branches might be tough, but again, there could be a chance for some lesser-demand branches.

In short, based on the previous year's trends, getting admission into these institutes with the given rank might be challenging, but you could explore other options or consider waiting for spot rounds or other counselling options.

Hope it helps !