The police found an unhoused person's body, not Ajit's. Naren deceived them by luring the man with food, killing him like Maya killed Ajit, and then burning the body to hide the crime.
Naren took the blame as gratitude for Maya saving his life. Despite having a crush on her, his main motivation was to repay her for preventing his suicide.
It symbolizes Naren's return to his love for mathematics and his determination to work on a new math problem during his sentence.
No, Karan never uncovered the truth. He accepted Naren's explanation and failed to apply logic to see the real story.
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