M.Tech

Yes they have M.Tech in design engineering course.

https://www.shiksha.com/engineering/course/m-tech-in-automotive-product-engineering-school-of-engineering-ajeenkya-dy-patil-university-lohegaon-pune-244267
Please visit the link above and contact the admissions office for the detailed information.

https://www.shiksha.com/engineering/course/m-tech-in-automotive-product-engineering-school-of-engineering-ajeenkya-dy-patil-university-lohegaon-pune-244267
Please visit the link above and contact the admissions office for the detailed information.

According to me, the best country to do M.Tech is Germany.
You just need visa and residence permit. As an international student, you may need an entry visa for Germany depending on where you come from and how long you plan to stay here.
Proof of financial resources, university entrance qualification, German skills, health insurance and aptitude test.

Hello Akansha,
The answer to your query is not available on the website of this Institute. But other useful information is available that may help you in getting your query solved. I'm attaching a link that will give you all the required information about your query:
http://www.kitmkarnal.com/#

Many universities conduct their own entrance exam also to fill the rest seats. But I am not sure that you will get admission because of your UG degree.