Yes you have to fill only one common application form to apply for Xaviers Admission Test for admission in various colleges through XAT score .

Important Dates (2014)
Form Notification Aug 12, 2013
Last Date for XAT Registration Dec 2, 2013
Download of Admit Cards Dec 18 - Dec 31, 2013
Last Date for XLRI Registration Dec 21, 2013
Receipt of XLRI forms Dec 29, 2013
Exam Date Jan 5, 2014
Results Jan 31, 2014

Now dates for XAT examination is over , next time exam notification will publish in December month of 2014 year .

XAT exam syllabus :
Analytical Reasoning and Decision Making:-

Conditions and Grouping Test
Data Arrangement Test:- Complex Arrangement
Logical Ability(Caselets)
Decision Making

Verbal Ability :-
English Grammar based questions
English Proficiency :- Analogy, Fill in the Blanks, Parajumble, Cloze Test
English Comprehension
Logical Reasoning:- Fact Inference Judgement, Passage Conclusion, Statement Argument

Data Interpretation and Quantitative Ability:-
Data Interpretation:- Caselets, Table Chart
Data Sufficency

Quantitative Ability :-
Elementary Mathematics
Arithmetic:- Number System, Ratio and Proportion
Additional Topic in Arithmetic:- Problems on Trains, Clock and Calendar, Mixtures and Alligation
Unitary Method:- Time and Distance
Commercial Maths:- Profit and Loss, Interest
Geometry:- Triangles, Circles
Mensuration
Algebra:- Permutation and Combinations, Sequence And Series
Trigonometry:- Heights and Distance
Linear Programming
Coordinate Geometry:- Cartesian Plane and lines
Probability


Some list of colleges under XAT:
Acharya School of Management,Bangalore
Affinity Business School,Bhubaneshwar
Algol School of Management & Technology,Gurgaon
Bengal Institute of Business Studies, Kolkata
Dept of Management Studies, Goa University,GOA
HDF School of Management, GOA
Indian Business Academy,Bangalore
Indus World School of Business, Greater Noida
Institute for Technology and Management, Navi mumbai
International School of Business and Media, Pune
KIIT School of Management, Bhubaneshwar
Loyola Institute of Business Administration, Chennai
MITCON Institute of Management (MIMA),Pune