6. to mesmerize someone is to have a distinct memory of that person.\n7. equilibrium is a state of…

Brief Explanations:

6. "To mesmerize" means to attract or hold the attention of someone, not to have a distinct memory of them. So this is False.
7. Equilibrium is a state of balance or stability, not unrest. So this is False.
8. An illusory goal is based on illusion, something that seems real but isn't, and often cannot be attained. So this is True.
9. "Gratuitous" means given or done free of charge, so a gratuitous service is not paid for. This is True.
10. A precedent is an earlier event or action that is regarded as an example or guide to be considered in subsequent similar circumstances. So this is True.
11. To adjudicate means to make a formal judgment or decision on a disputed matter. So this is True.
12. A manifesto is a public declaration of policy and aims, not a list for record - keeping. So this is False.
13. "Spurious" means false or fake, so a spurious claim is fraudulent. This is True.
14. "To gird" a tree means to encircle it with something. So this is True.
15. "To expedite" means to make (an action or process) happen sooner or be accomplished more quickly, i.e., to help advance it. So this is True.

Answer:

6. False
7. False
8. True
9. True
10. True
11. True
12. False
13. True
14. True
15. True