Ashmita,

The original meaning of the sentence deals with a contrast - although they look less appetizing, they are more flavorful than their supermarket cousins.

A Although appearing less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year - The first part does not have a verb. Appearing is not a verb. Plus the modifier of the contrast is separated by "grown by seeds". It gives a nonsenical meaning.

B Although heirloom tomatoes, grown from seeds saved during the previous year, appear less appetizing than most of their round and red supermarket cousins - Perfect - grown from seeds... modifies the tomatoes and the modifier of the contrast is close to the verb appear

C Although they appear less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year - The verb is separated from the modifier.

D Grown from seeds saved during the previous year, heirloom tomatoes appear less appetizing than most of their round and red supermarket cousins - This statement says that the tomatoes are less appetizing because they were grown from the seeds saved during the previous year.

E Heirloom tomatoes, grown from seeds saved during the previous year, although they appear less appetizing than most of their round and red supermarket cousins They could refer to the seeds or the tomatoes

das.ashmita wrote:Although appearing less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year--they are often green and striped, or have plenty of bumps and bruises--heirlooms are more flavorful and thus in increasing demand.

A Although appearing less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year
B Although heirloom tomatoes, grown from seeds saved during the previous year, appear less appetizing than most of their round and red supermarket cousins
C Although they appear less appetizing than most of their round and red supermarket cousins, heirloom tomatoes, grown from seeds saved during the previous year
D Grown from seeds saved during the previous year, heirloom tomatoes appear less appetizing than most of their round and red supermarket cousins
E Heirloom tomatoes, grown from seeds saved during the previous year, although they appear less appetizing than most of their round and red supermarket cousins

OA B
Please ans with explanation.

A and C lack main clause - eliminate A and C.

D is illogical without the presence of "although" - infact this is a run on sentence. Eliminate D.

E - "although" is misplaced.

noun, modifier, although .... - wrong. "Although" is a conjunction and has no signification here.
noun, modifier, finite verb.... - correct clause construction.

Hope this helps !!