You may not get into one of the desired colleges as the cut-offs are much higher even in the consecutive lists. Sometimes it decreases only by 0.1% and getting to 89.5% from 98% at that rate is not easy. Also, you don't belong to any quota and the percentage will

Hi, Anurag.

Aside of the Allahabad university, you can try for these four of the colleges in Allahabad. 

These are the top engineering colleges in Allahabad 

• Motilal Nehru National Institute of Technology Allahabad Prayagraj
• Institute of Engineering and Rural Technology, Allahabad
• Sam Higginbottom Institute of Agriculture Technology and Science, Allahabad

There are many colleges for Architecture. The choice of the college would be based on your rank and in which state you can go for studies. As you have a very good score in NATA, I am suggesting you some of the good colleges where you can have the admission;

Hi Anurag,

There are many colleges in Delhi which are providing integrated BA.B.ed courses. Some of the colleges you need to check out for these integrated courses are,

Lady Irwin College.

Maharshi Valmiki College of Education.

Jesus Mary college.

Gargi college.

Aditi Mahavidyalaya.

Mata Sundari College.

Shyama Prasad Mukherji college.

Yes you have a chance to get admission in Don Bosco , Goa. But you have to wait for second list atleast. 

You can visit this link to know all necessary details on Don Bosco college, Goa -

https://www.careers360.com/colleges/don-bosco-college-panjim

All the best hope this helps!

As you mentioned you completed your intermediate with mathematics so, there is no way to left in between of path. You have work harder to improve your math instead of running away from it. 

In my opinion you should have to join BTech and work on your mathematics. 

Good  Luck

Yes , you can take hotel management course as per your wish .It doesn't Have any connection between them.

I hope this information will help you. 

Good  Luck  !!