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Mathematics · 2024

JEE Main · 27 January 2024, Shift 1 · Q21

If α satisfies the equation x^2+x+1=0 and (1+α)^7= A + B α+ C α^2, A, B, C ≥ 0, then 5(3 A -2 B - C ) is equal to ____.

If $\displaystyle \alpha$ satisfies the equation $\displaystyle x^2+x+1=0$ and $\displaystyle (1+\alpha)^7=\mathrm{A}+\mathrm{B} \alpha+\mathrm{C} \alpha^2, \mathrm{~A}, \mathrm{~B}, \mathrm{C} \geqslant 0$, then $\displaystyle 5(3 \mathrm{~A}-2 \mathrm{~B}-\mathrm{C})$ is equal to $\displaystyle \_\_\_\_$.
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JEE Main 2024 Mathematics question, with the answer from NTA’s final answer key. Where our answers come from.