The correct option is C The student having been absent, the teacher gave him a negative marking.
The absolute construction is a grammatical construction where the absolute (including a participle) modifies an entire sentence.
A
nominative absolute is a free standing part of a sentence that describes
the main subject and verb of that sentence. It can be placed before or
after the sentence, and is usually a non-finite clause that does not
express the tense of the sentence.
Option B contains the absolute construction, "The student having been absent" modifies the clause that follows. (In an absolute construction, the participle 'having' does not modify any noun, but the construction as a whole modifies the sentence.) Hence option B is correct.
Option A does not use an absolute construction, it uses the conjunction 'so'. Hence A is incorrect.
Option C also doesn't use an absolute construction, it uses the subordinating conjunction, 'even though'. Hence C is incorrect.
Option D is incorrect because the answer lies in B.