Funding agencies:
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Department of Science and Technology: Research grants are made through the Science and Engineering Research Council. There are many other programs as well.
A detailed write-up about funding possibilities through DST would be a good idea. Will have to get to it some other day, though!
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Council of Scientific and Industrial Research (CSIR): Research grants are available through its Human Resource Development Group. Application forms may be found here.
Again, there are quite a few other CSIR programs which are of interest to our community. A detailed write-up will have to wait.
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Defence Research and Development Organization (DRDO):
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Aeronautics Research and Development Board (ARDB) has a panel for Materials and Manufacturing. Grant application forms may be downloaded from here.
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Naval Research Board (NRB) has a Materials Panel. Grant application format is here.
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Armaments Research Board (ARB) funds programs in materials and metallurgy.
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Board of Research in Nuclear Sciences (BRNS): The Basic Sciences Committee funds projects in many materials-related areas. Applications can be downloaded from this page.
If there are other agencies that you think ought to be in this list, please leave a comment: Make sure you give the full name, URL of the agency, and the URL from where grant application forms can be downloaded. Thank you for your help.
Materialia Indica 
DRDO has created Aeronautics Research and Development Board, Armour Research Board, Naval Research Board and Life Sciences Research Board. All these boards are involved in approving projects related to materials science in one way or the other. More on this can be found at http://www.drdo.org/academic.html