Right-sided vocal cord palsy seen in -
First I would like to exclude other three options : -


Aortic aneurysm (option b) and mediastinal lymphadenopathy (option c) cause left sided vocal cord paralysis.
Vocal nodules does not cause vocal cord paralysis. 


Now we are left with option 'a' only : -

"Laryngeal carcinoma especially glottic can cause unilateral or bilateral vocal cord paralysis" ─ Conn's current therapy

So, answer of this question is laryngeal carcinoma as it can cause unilateral (right or left) or bilateral vocal cord paralysis.
Larynx carcinoma
Aortic aneurysm
Mediastinal lymphadenopathy
Vocal nodule