You can obtain NOC from the current employer to apply for the proposed new job.

You have done the PG diploma from distant education or open university which do not require physical attendance, hence the course if otherwise qualify for appearing for the post now proposed to apply, you can proceed with the application for the proposed new post, if you are not eligible you will be notified about it while rejecting your application. 

You are eligible to appear for exam as you have done post graduate diploma 

you need not resign to appear for Job

inform your superiors that you are going to appear for UPSC exams during your employment 

- Legally you can appear in any examination without leaving your present job . 

- However , on selection , you will have to inform the present employer . 

1. Even though you are employed in a Government organization, you can still apply for the new job through proper channel. In other words, without leaving the present job, you can apply for another job by obtaining permission from the present employer.

2.  There's no need to resign the present job just for applying to a new job.

Yes you are eligible to appear for the exam without resigning from your first job. 

Hi 

Not sure whether you are a central or state government employee and also not sure whether you have obtained prior permission from your present employer to pursue (PGDUPDL)

Regardless of whether you are a  central or state government employee, the standard procedure is to inform your present employer that you are appearing for a public service exam for another employment opportunity so that there is no problem in case you are selected for interview. 

No need to resign your present job for appearing in exam 
Hope this information is useful

Hi 

As a state government employee, it is mandatory for you to obtain permission from your employer at the time of attending interview for a position with next employer.