1.You should declare your first LINQ expression, but not to execute it, like below:
var firstQuery= from sd in students
from m in query1
where sd.Student_ID != m.Student_ID
select sd.Student_ID;
2.Then use the above first query in the second one like below:
var finalResult = (from sd in dbcDefaulter.Student_Details
from r in firstQuery where r.Student_ID == sd.Student_ID
orderby sd.Student_ID
select new { sd.Student_ID, sd.Name, sd.Class, sd.Section, sd.F_Name, sd.F_Mobile }).Distinct().ToList();