i. He succeeded.................perseverance and sheer hard work.
ii. ....................................the power vested in me, I hereby declare these premises sealed.
iii. .................his illness he could not finish his work in time.
iv. .....................need, please contact me at the emergency number indicated.

In i we are given that he succeeded because of his perseverance and hand work and thus, both 'by dint of' or 'by virtue of' can be used.
In ii we are given that the person declares the power he has and thus, both 'by dint of' or 'by virtue of' can be used.
In iii we are given that the illness was the case and thus, 'in consequence of' should be used.
In iv 'in case of' should be clearly used.
Only in option B all of these are correctly used.
Hence, option B is the correct answer.