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Hello Ashutosh,
Honestly speaking be practical rather than emotional. Analyse the reason for the shortcoming in Math and also reason out whether you can cope up with the subject in future. Since engineering is all about Math. Another point here is that suppose you clear 12th math and entrance exam in whatever ways you can, but please note if Math is something you do not understand or enjoy and you get a KT (Keep term) then yes, it would affect your placements. So think and then take a call.
Coming to the diploma part, again if Math does not interest you or you do not enjoy it, you may begin with a diploma and then leave it midway. Then you would be nowhere as such. Waste of years and efforts and lack of confidence.
Hence would suggest, think practically and then only take a decision. Engineering is not the only stream. You could opt for BCA too.
Wish you good luck..
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