If a partner agrees to take responsibility for carrying out the dissolution process and also agrees to bear all realisation expenses personally, what is the correct journal entry in the firm's books?

No entry is required

The correct answer is option 4- No entry is required.

No entry is required if a partner has agreed to undertake the dissolution work and agreed to pay and bear the realisation expenses himself. 

For payment of realisation expenses-

(a) When some expenses are incurred and paid by the firm in the process of realisation of assets and payment of liabilities:
Realisation A/c Dr.
       To Bank A/c

(b) When realisation expenses are paid by a partner on behalf of the firm:
Realisation A/c Dr.
        To Partner’s Capital A/c

(c) When a partner has agreed to bear the realisation expenses:
(i) if payment of realisation expenses is made by the firm Partner’s Capital A/c Dr. To Bank A/c
(ii) if the partner himself pays the realisation expenses, no entry is required.