My preference would be
XL
Tiss
Ranchi

There are many people who excel at two sections in CAT and score less in one (mostly unintentionally and/or because of time management issues) and nonetheless such aspirants end up in top colleges since there overall CAT percentile is decent. So I would suggest you not to give up hope and prepare well and give CAT a shot.
Now coming back to your background, since your qualification add to the diversity factor you will have those points which will compensate the lack of maths skills. Now about the colleges, you can refer to the Career360 ranking and choose among them but I would you to make a list of around 10 colleges which are categorized as your best-case scenario colleges, realistic scenario college and backup colleges. I hope this answer helps you.

IIFT is a 53 year old college which has a specialized MBA- IB (International Business) and has two branches, one in New Delhi and another one in Kolkata. Kolkata campus is relatively younger one. The total number of seats are 210 in IIFT. The entrance and selection process is tough so you can expect a great peer group, which should be a important criteria for any b-school aspirant since if your group is good you/they will push yourself/you to be better at things and come out of your comfort zone. Next is the quality of faculty which is great and you can find more about the same on their website. Another important criteria is the location, in New Delhi it is location at a very good location and is in the heart of the city so you won't have any problems and can enjoy a city life. Next about the placements, the average package for 2017 is 18.4 lpa and there are ample amount of foreign placements that happen in IIFT (although the final placement average is calculated by taking the foreign placement package into consideration, it still makes for a decent figure).The batch size is also decent and you won't feel like being lost in the crowd.IIFT has also been consistantly ranked among one of the top colleges in India as per Career360 (Ranked 14)

If XAT is held in Kathmandu, you can appear for the exam from that centre. In that case you will be exempted from taking the test. Otherwise you  can take GMAT and apply through that score.