M.Sc

Yes, it is very much required.

You can apply for this course online/ offline with the required information. To be eligible to apply for this course, you need to have passed B.Sc. with Statistics and Mathematics as optional subjects and must have secured minimum 50% in Statistics at graduation level (for SC/ ST-45%).

Sorry, it does not offer M.Sc in analytical chemistry.

Yes, you can get private jobs after completing M.Sc in electronics and communication engineering. Some of the industries you can get employed in are mentioned below (Both private and public):
Research & development laboratories
Design & manufacture of Analog & Digital appliances
Industries related to VLSI, Embedded systems and DSP
Defense organizations like DRDO
Electrical products manufacturing sectors & companies, such as Intel, Philips, Mistral, Ample Communications, Ibex, Spa Computers, Cueflux Technologies Pvt. Ltd. , EmLabs, eSpark Infotech Pvt. Ltd, I Micro System, Adamya Computing Technologies, Sonata, etc.
Regards.

There are over 13 Distance/Correspondence M.Sc. In Science colleges in Mumbai. Please refer to the link provided below for a detailed list of colleges which offers M.Sc. Courses via distance/correspondence. You should be able to navigate to a college of your choice using the filters on the web page. https://www.shiksha.com/science/colleges/distance-correspondence-m-sc-colleges-mumbai-all.

M.Sc in food Science is offered as a full-time course. Please refer to the link for details. Link: https://www.shiksha.com/science/course/m-sc-in-food-science-and-technology-d-y-patil-university-navi-Mumbai-school-of-biotechnology-and-bioinformatics-124913.

To be eligible for M.Sc in psychology, you need to have Bachelor degree in psychology.