If you're looking for a top engineering college in India, the National Institute of Technology (NIT) Trichy is a great option to consider, better than IIT Dhanbad. Here are some reasons why:

• CS and other branches: NIT Trichy is known for its strong programs in computer science (CS) and other engineering branches. This means you can expect a high quality of education in these fields.
• Excellent placements: NIT Trichy has a great track record when it comes to placements. This means that many students who graduate from NIT Trichy can secure well-paying jobs in top companies.
• World-class infrastructure: NIT Trichy has invested in top-notch infrastructure to support student learning. This includes modern classrooms, well-equipped labs, and other facilities.
• Experienced teachers: The faculty at NIT Trichy are highly experienced and knowledgeable. They are committed to providing students with a high-quality education and helping them succeed.
• The best environment for teaching and learning: NIT Trichy offers a supportive and collaborative learning environment, which can be beneficial for student success. Additionally, the college offers a range of extracurricular activities and student clubs to help students develop new skills and interests.

It's worth noting that while a college's reputation can be important, it's not the only factor to consider when choosing a college. It's important to also consider your own needs and preferences, such as location, campus culture, and program offerings. However, if you're looking for a strong engineering program with a good track record of placements and top-notch facilities, NIT Trichy is a college to consider.

Without any second thoughts, IITKGP is a far better option than IIT Dhanbad in terms of both worth and recognition. The primary reason is its legacy and early establishment. To give you a better picture I am going to entail the pros and causes of IIT KGP bringing to light both sides of the coin.

Pros

• You will get the chance to pursue the subject that interests you and fuel your passion. 
• Mechanical branch is much more preferred than metallurgy.
• IIT ISM is developing at a fast pace and will soon overtake other institutes after its inauguration of the biggest library in India.

Cons:

• Petroleum engineering does not guarantee good placements. Around 50% of the batch remains and placed and the situation is a result of a steady decline in petroleum industries in India.
• Dhanbad is not a very promising city in terms of exposure and opportunities.
• Electrical engineering failed to offer decent placement in the past, and the IIT tag does not seem to improve the situation.

The final decision is for you to make.

Both IIT Roorkee and ISM Dhanbad are reputed Engineering institutions offering excellent education as well as opportunities. Being an IIT, Roorkee does have a slight advantage over ISM, though ISM too is going to be an IIT one day.

The infrastructure of both institutes is equally good with IIT Roorkee having a slight advantage over ISM because of its early establishment. However, ISM is fast developing and has a beautiful campus. It’s going to house Asia's largest library soon.

Branch-wise, both Applied Mathematics and MNC comprise Mathematical concepts but with a different perspectives. Applied Mathematics has pure math and only those who want to pursue research in the same should go for it. MNC on the other hand is a blend of Maths as well as Computing (coding) and is more in demand than Applied Mathematics. Its scope is also wider than APM and has better placement opportunities.

Eventually, it’s a matter of preferences and not the credibility and worth of the branch that you should focus on.

All three colleges, IIT Dhanbad, IIT BHU, and MNNIT Allahabad, are well-reputed and offer quality education in their respective fields. However, the choice between the three ultimately depends on your personal preferences and career goals. Here are some points to consider:

IIT Dhanbad (CS):

Pros:

• One of the top-ranked engineering colleges in India.
• Strong faculty with research expertise in various fields of Computer Science.
• Good industry collaborations and placement opportunities.

Cons: Relatively new compared to some of the other IITs, so may not have as established an alumni network.

IIT BHU (Electrical):

Pros:

• One of the oldest and most prestigious engineering colleges in India.
• Strong faculty with research expertise in various fields of Electrical Engineering.
• Good industry collaborations and placement opportunities.

Cons: As an Electrical Engineering program, it may not have as many opportunities to specialize in Computer Science.

MNNIT Allahabad (CS):

Pros:

• One of the top-ranked NITs in India.
• Strong faculty with research expertise in various fields of Computer Science.
• Good industry collaborations and placement opportunities.

Cons: May not have as established an alumni network compared to the older IITs.

Based on the above factors, it would be recommended to consider IIT Dhanbad (CS) as the best option among the aforementioned colleges.

The choice of the Institute depends on where your interest lies. If you want to study core Geology, then 3-year MSc(tech) course is an excellent option. Both the institutes have below-average core placements with ISM fairing a tad bit better. Irrespective of the Institute and branch, to secure placements you need to be among the top rankers.

My cousin had to choose between IIT Kharagpur‘s MSc in Geophysics and ISM’s MSc(tech) in Geology. She went for Geophysics eventually as he did not consider it wise to waste 3-years in a post-graduate program. In Fact, many of her batchmates dropped IIT Roorkee’s geology and went for Geophysics at IIT KGP. They did not find the teaching and quality of education at IIT Roorkee’s Geology branch as per IIT standards.

I would suggest you go for ISM. But if you too share the same opinion as mine and don’t want to waste 3 years, go for Roorkee and prepare for GATE from the start.

Both Jadavpur University and ISM Dhanbad are reputed institutes. ISM was already quite reputed across India and after getting the IIT tag, the institute has improved quite significantly. 

• If you are getting branches like CSE/ECE at JU and offbeat branches at IIT ISM, then you should definitely choose JU. 
• Another advantage of choosing JU is the negligible fee. For a 4 year long B.Tech you will need to pay only around 10,000. 

So, take these factors into consideration, and choose according to your convenience.