If $ \alpha, \beta $ are natural numbers such that $ (100)^{\alpha}- $ $ 199 \beta=(100)(100)+(99)(101)+(98)(102) $ $ +\ldots \ldots . .+(1)(199) $, then the slope of the line passing through $ (\alpha, \beta) $ and origin is: [JEE Main 2021, 18 Mar (Shift 1)]

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If \( \alpha, \beta \) are natural numbers such that \( (100)^{\alpha}- \) \( 199 \beta=(100)(100)+(99)(101)+(98)(102) \…

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