CBSE has introduced two levels of Maths paper for class X students: Basic and Standard, for the board exam.
Basic for those who do not wish to opt for Maths in class XI-XII and standard for those who will opt for Maths in XI-XII. The syllabus for the examination will remain the same only the difficulty level of the question paper varies.
For DU JAT, NPAT aspirants, one should advise Standard Maths as the same will lead to studying Maths in XI and XII which is mandatory for these two exams.
While most other exams don't need Maths as a prerequisite subject but that is based on the assumption of no change in future by the colleges. Eg., DU had once removed Maths as a criterion and later reintroduced it.
To be safe, one should go for Standard Maths. A conscious call must be taken by Students and Parents in this regard.