The journal entries are as under-
Incoming partners' current A/c  Dr.
         To Sacrificing partners capital A/c.

What statement among the following is TRUE for the above entry?  

When the new partner does not bring goodwill in cash, partly or fully and goodwill does not exist in the book.

The correct answer is option 2- When the new partner does not bring goodwill in cash, partly or fully and goodwill does not exist in the book.

When the new partner does not bring goodwill in cash, partly or fully and goodwill does not exist in the book is correct for the given journal entry.

When goodwill does not exist in the books, sacrificing partners are credited with their share of goodwill and new partner is debited by the amount of goodwill not brought by him. The journal entry in this case is-
Incoming (New) Partners Current A/c    Dr. 
          To Sacrificing Partners Capital A/c (individually)
(Account of goodwill not brought in by new partner)

Sometimes the new partner brings part of premium for goodwill in cash. In such a situation, new partners  current account will be debited by the amount not brought by new partner.