Yes, Manipal University, Jaipur is approved for Engineering and technology by both AICTE and UGC.
But for Engineering in Computer Science, Mechanical or Computer Communication and Mechatronics, it's better that you consider taking admission at the main campus of Manipal University which is in Karnataka rather than Jaipur campus as the fee is almost the same at both the campus and teaching are not up to the mark at Jaipur campus. For the fee, the ROI will be very low if you opt for Jaipur Campus.
Even though Manipal University Jaipur is AICTE approved, make your decision wisely as it is a matter of your future.