Why can’t a bank be a broker-dealer, or an investment adviser? I thoug...

You are correct that many well-known banks are also in the brokerage and investment advisory businesses. The point of these exam questions is that the bank is a separate entity from either the related broker-dealer or investment adviser.  Typically, well-known banks are bank holding companies, with stock trading on the secondary market. Under the bank holding company, we find a bank, a broker-dealer, and a wealth manager/investment adviser. The three entities are related yet separate. Therefore, a bank is not a broker-dealer or an investment adviser, even when related to them under a common parent company.