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I don't have idea about PSIT, If you are looking for best university for B.Tech CSE course, I would say Lovely professional University is best University to pursue this course. CSE is one of the branches in LPU having wonderful placements. Most of students get placed in reputed companies with few opting for higher studies. Special inputs in the form of placement classes are given to students to hone their skills and prepare them for placements. Students also go for on-job training (OJT) where they are paid stipend too. The course provides instil knowledge in the major areas of Computer Science and Engineering such as Artificial Intelligence, Networking, Databases, Data Analytics, Web Development and Cloud Computing. Student will be given an option to go for 4 weeks study tour to USA/ European countries or any other country
Professional Enhancement- In addition to core curricula, course offers subjects like communication, analytical and soft skills to enhance personality and employability. University has tie -ups with Upgrade for few B.Tech specializations. It is one of its kind, undergraduate programme to impart expertise of Machine Learning and Artificial Intelligence having the right mix of industry and academic experts. Artificial Intelligence and Machine Learning are increasingly augmenting and extending to practically every technology enabled service, gadget or application. From Google to Microsoft to Apple, Computer Science students of LPU are working with hundreds of leading IT giants of the world. CSE/IT students secured salary package of up to Rs 42 LPA and placement opportunities from companies like Amazon, Adobe, Bosch Engineering, VMware, Cognizant Technology Solutions, Kony India, SAP Labs, Schneider Electric India, HP India, LG Soft India, ITC Infotech, Capgemini, Tech Mahindra, KPIT, Morgan Stanley, Drishti Soft Solutions, etc. Last year Tanya Arora from B.Tech CSE got 42 LPA from Microsoft. The package really depends on what he can show to the recruiters that, how much he is worth or deserved. There were some students who cracked the placement and got offered 42 LPA, while many failed to do so. On an average the CSE students of LPU is offered and placed in the starting package of 4.5 TO 6 LPA (Fixed salary) while there may be cases of students getting less than that or more than that.

Yes, you are eligible to pursue M.Sc. Chemistry, as you have completed B.Sc. Chemistry. The basic pre-requisite to pursue a part time course in M.Sc. Is that you should have completed your Bachelors either in Science or in engineering. Few colleges/institutes may require you to appear for a qualifying examination to gain admission.
Here is a list of Universities offering M.Sc. Chemistry through distance learning:
Annamalai University
Alagappa University
Andhra University
Berhampur University
Bharathiar University
Dr BR Ambedkar Open University
Kakatiya University
Madurai Kamaraj University
Maharishi Markandeshwar University
Manonmaniam Sundaranar University of Madras
Madhya Pradesh Bhoj Open University
Nalanda Open University
Nagarjuna University
Periyar University
Sri Venkateswara University
Regards.

As you have asked to tell about how to do MBA without any entrance exam. Yes, you can do an MBA through distance learning or a correspondence from any of these colleges distance learning programme. Sikkim Manipal University, XLRI Management Institute-Jamshedpur, FMS (Faculty of Management Studies), ISB (Indian School of Business-Hyderabad), SPJIMR, SP Jain Institute of Management and Research, IMT (Institute of Management Technology-Ghaziabad), Nirma Institute of Management-Ahmedabad, IRMA (Institute of Rural Management), Anand, XIMB (Xavier Institute of Management Bhubaneshwar), Amity Business School-Noida, LIBA (Loyola Institute of Business Administration), JRE Group of Institutions, Maharishi Dayanand University and Kurukshetra University.
Best of luck.

In order to pursue a science course at any of these colleges, they will have to appear for an entrance. Some popular B.Sc and M.Sc entrance exams that science aspirants should consider giving in order to secure admission in a good college. Are mentioned at the link provided below:
https://www.shiksha.com/science/articles/top-bsc-msc-entrance-exams-in-india-blogId-13484
Which course is better? The career opportunities for both these graduates are many. But most MNCs prefer MCA graduates to M.Sc graduates. This is because the MCA graduates are well aware of the software applications. But for developing new software, M.Sc graduates are preferred. MCAs are most suitable for the working purposes in various companies. While considering a bright career, MCA course will be better than M.Sc in computer science.
Regards.