Anjali, if you hold the domicile of Rajasthan but want to secure admission in Himachal Pradesh, you should try for admission under All India Counselling. . Under All India Quota, All the 15% of All India Quota Seats except for Jammu and Kashmir, 100% Seats at Deemed and Central Universities, IP Quota seats in ESIC Colleges, Seats at AFMC, AIIMS and JIPMER  are filled by DGHS. This is for Government Medical Colleges. But Maharshi Markandeswar Medical College is a Private Medical College. Private Medical Colleges do not participate in All India Counselling and the seats are filled through State Counselling alone. And for appearing for State Counselling you need to hold the domicile of that particular State. If you do not hold the domicile of HP,  you might not be able to secure Government Quota seat in MMU, Solan. You only opt for B Category seats which are also called Management Quota Seats and they are filled through State Counselling. In 2018, the cut offs for MMU Solan under various Categories have been as follows:

General Category: 408

OBC: 396

SC: 296

ST: 343

Now you haven't mentioned your Category. Nevertheless, this is 2018 data and cut offs change every year. Cut offs change every year depending on various factors such as no.of Candidates appearing for the exam, no.of Candidates qualified, top NEET score and difficulty of the exam. So you have to aim for atleast 50 marks more than those mentioned against your Category here.