Science

Because you are not specific about the college, Hence the eligibility criteria of B.Sc. (Design - Interior and Furniture) [Lateral Entry] of LPU Jalandhar is given below. Eligibility criteria : Pass with 60% aggregate marks in Diploma (Interior Design or Architectural Assistantship or Civil engineering. ). [ (3 years after 10th) or (2 years/ 1 year after 10+2)] or equivalent. So from above you are eligible for B.Sc. Interior Design course of LPU. For more details please visit https://www.lpu.in/.

You can easily get admission in top colleges of Du. Colleges that provides B.Sc. Hons. Chemistry are
1. St. Stephen
2. Miranda House
3. Hindu College
4. Sri Venkateswara College
5. Ramjas college
6. Deen Dayal Upadhyay college
7. Kirori mal college
8. Deshbandhu college
And there are many other colleges that provides this course. Depending upon the college tuition fees may vary from 15000 to 35000. Hostel fees vary from college to college. For that you have to check the college website in which you are interested to take admission. Also check which college provides hostel facility or not on DU website.

Yes, you can have chances in 2nd or 3rd cutoff. Don't worry. For more details, check DU's previous year cutoff on DU portal.