If a new partner does not bring his share of goodwill in cash, the fo…

The correct answer is Option (2) → Crediting old partners capital A/c in sacrificing ratio and debiting new partner current A/c

The new partner owes the old partners for the share of goodwill he takes, and the old partners are paid for it in the ratio in which they give up their shares. When he does not bring it in cash, the amount is charged to him through his current account and credited to the sacrificing partners’ capital accounts.

New Partner’s Current A/c     Dr.
    To Sacrificing Partners’ Capital A/cs (in sacrificing ratio)

“No entry” would leave the old partners uncompensated for the goodwill they have built, which is the very point of the adjustment.