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"when it won independence from Britain" - The phrase could be clearer if it includes “in 1947,” for specificity, but this is not a grammatical error.
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"Muslim leaders believed that they deserved their own land where they can follow their religion without fear." - The verb tense should be consistent. "can" should be changed to "could" to match "believed."
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"the differences between Muslims and Hindus grew larger which pushed people to separate them" - A comma should be added before "which" for clarity: "larger, which pushed..."
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"even though they wanted India to stay united." - "even though" could be seen as somewhat informal in this context, but it is not a grammatical error.
Overall, the issues mainly pertain to verb tense consistency and punctuation.