I know that you ___ pass the exam with flying colors.

The correct option is B. will. 'Will' is used to express future certainty, prediction, or a strong expectation. In this sentence, 'I know that you will pass the exam with flying colors' conveys a confident prediction about the future.

• A. shall: While 'shall' can indicate the future, it is less common in modern English for general predictions and is often used for offers, suggestions, or formal statements with 'I' or 'we'.
• C. would: 'Would' is typically used for conditional sentences, polite requests, or to refer to the past future (e.g., 'He said he would come'). It doesn't fit a direct future prediction here.
• D. will have: 'Will have' is the future perfect tense, indicating an action that will be completed by a certain time in the future (e.g., 'By next year, you will have passed the exam'). It doesn't fit the simple future prediction.