Let's examine each statement based on the provisions of the Companies Act, 2013.

Companies Act Provisions on Share Purchase

Statement 1: A company cannot purchase its own equity shares.

This statement is incorrect. The Companies Act, 2013 allows a company to purchase its own shares or other specified securities. This process is known as 'Buyback' of shares. Section 68 of the Companies Act, 2013 lays down the conditions under which a company can buy back its shares, such as:

• The buyback is authorised by its articles.
• A special resolution has been passed in the general meeting of the company authorizing the buyback.
• The buyback is within the limits specified in the Act (e.g., not exceeding 25% of the total paid-up capital and free reserves).

Since companies can purchase their own shares under specific conditions, statement 1 is false.

Issuance of Shares at a Discount

Statement 2: A company can issue its shares at a discount by passing a special resolution.

This statement is generally incorrect. Section 53 of the Companies Act, 2013 prohibits a company from issuing shares at a discount, except in the case of sweat equity shares or shares issued under a scheme of reconstruction or amalgamation approved by the Central Government.

• Sweat equity shares can be issued at a discount or for consideration other than cash to directors or employees for providing know-how or making available rights in the nature of intellectual property rights or value additions. This requires a special resolution as per Section 54.
• However, the general issuance of shares to the public or existing shareholders at a discount is prohibited.

The statement implies a general rule for issuing shares at a discount with just a special resolution, which is not accurate for all types of share issues. Therefore, statement 2 is false in a general context.

Interest Rates on Calls-in-Arrear and Calls-in-Advance

Statement 3: The interest rate charged on calls-in-arrear and the interest rate payable on calls-in-advance are the same as per provisions of Table-F of Schedule-I of the Companies Act, 2013.

This statement is incorrect. Table F is a model set of articles of association. As per Table F of Schedule I of the Companies Act, 2013:

• Interest on calls in arrear is charged at a rate not exceeding ten per cent per annum.
• Interest on calls in advance is paid at a rate not exceeding twelve per cent per annum.

Unless the company's own articles specify different rates, the rates provided in Table F apply. According to Table F, the maximum rates for calls-in-arrear (10%) and calls-in-advance (12%) are different. Therefore, statement 3 is false.

Conclusion

Based on the analysis of each statement:

• Statement 1 is false.
• Statement 2 is false (in general context).
• Statement 3 is false.

Since none of the given statements are true, the correct option is "None of the above".