Step 1: Admission of a new partner.
Under Section 31 of the Indian Partnership Act, 1932, a new partner can be admitted only with the consent of all existing partners, unless otherwise agreed. This makes (a) correct.
Step 2: Minor’s position.
As per Section 30, a minor cannot enter into a contract, but may be admitted to the benefits of partnership. His share in the profits and property is liable for the firm’s acts. This makes (b) correct.
Step 3: Doctrine of holding out.
Section 28 provides that if a person represents himself as a partner, he may be liable as a partner to third parties — even if no actual partnership exists. This confirms (c) is correct.
Step 4: Conclusion.
Since (a), (b), and (c) are correct, the right answer is (d).
\[
\boxed{(d)}
\]