Step 1: Understanding the Concept:
The question asks which of the listed powers can be exercised by the Board of Directors through a 'resolution by circulation' instead of at a formal Board Meeting. The Companies Act, 2013, specifies certain important matters that must be decided only at a duly convened Board Meeting.
Step 2: Detailed Explanation:
Section 179(3) of the Companies Act, 2013, lists the powers which the Board of Directors \textit{must} exercise only by means of resolutions passed at meetings of the Board. This list includes:
- Power to issue securities, including debentures. (Matches option A)
- Power to invest the funds of the company. (Matches option B)
- Power to grant loans or give guarantee or provide security in respect of loans. (Matches option C)
Other powers listed in this section include making calls on shares, authorizing buy-back, approving financial statements, diversifying the business, etc.
The power to appoint an additional director (under Section 161) is \textit{not} included in the restrictive list of Section 179(3). Therefore, this power can be exercised by passing a resolution by circulation as per Section 175 of the Act, provided the Articles of Association do not prohibit it.
Step 3: Final Answer:
The powers to issue debentures, invest funds, and make loans are restricted matters that must be decided at a Board meeting. The power to appoint an additional director is not on this restrictive list and can be exercised through a resolution by circulation. Therefore, option (D) is correct.