The answer I got is that variables and subqueries will not work and we have to user dynamic SQL script. The following works:
DECLARE @SQL VARCHAR(4000)
SET @SQL = 'ALTER TABLE dbo.Student DROP CONSTRAINT |ConstraintName| '
SET @SQL = REPLACE(@SQL, '|ConstraintName|', ( SELECT name
FROM sysobjects
WHERE xtype = 'PK'
AND parent_obj = OBJECT_ID('Student')))
EXEC (@SQL)