CAT

Yes, you can apply for distance MBA/PGD programs without writing any entrance exam. The following are the few colleges offering the distance MBA programs as under.
1. NMIMS Global Access School for continuing education
Eligibility :- Bachelor's Degree in any discipline from any recognized University or an equivalent degree recognized by Association of Indian Universities (AIU) with minimum 50% marks at Graduation Level. Or less than 50% marks with two years of experience. Course Fee Rs. 76000/
2. Symbiosis center for distance learning (SCDL)
Eligibility: - Bachelor's degree holder / Graduate in any discipline from a recognized University. Course Fee Rs 40000/
3. IGNOU
4. IMT-CDL Ghaziabad: Institute of Management Technology - Centre for Distance Learning
Eligibility: - Bachelor's Degree in any discipline from any recognized University or equivalent degree recognized by Association of Indian Universities (AIU). Course fee Rs 101000/.

CAT is much difficult over GMAT. CAT happens only once a year. While GMAT. You can take it over and over again within the same year. GMAT is much more organized in terms of syllabus, while CAT also has a syllabus outline, but it is quite broad. The IIMs do not release past question papers since the test has become computer based. GMAC releases the Official Guides that contain actual past GMAT questions. CAT has 3 sections as Quantitative aptitude, Verbal reasoning, Logical Reasoning and Data Interpretation, while GMAT has 4 sections: Quantitative Ability, Verbal Ability, Analytical Writing Assessment, and Integrated Reasoning. Further, CAT will have 100 questions divided into the 3 sections (34, 32 LR&DI, 34), GMAT has 1 essay, 12 IR questions, 37 quant, 41 verbal.