I currently have a Standard Chartered Unlimited Cashback Credit card, However, it did not take into account the premium paid for my annual Personal Accident Insurance policy. Are all online transactions not eligible for cashback?

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On the back end, the card associations will assign merchants a code that summarizes their line of business (this is called the merchant category code - MCC)
Banks generally have exclusions for certain classes of transactions (insurance, topups to prepaid accounts, stock trading accounts are common ones). However, practice is different by each bank so you need to look at the T&C for your particular card on what is excluded.