Ideally, NEST for NISER and UM DAE, And IPMAT for IIM Indore IPM have nearly 99% different audiences and hence, the Date doesnt quite become an issue. In case you are applying for both the Tests, you must choose between one, unless their is a change in Date . You may convey your grievances to the Exam Regulatory Authority of IIM Indore or UMDAE, but you should expect any significant reply and action.