5}}{{(x+1)}^{5}}\] \[={{[}^{5}}{{C}_{0}}{{x}^{5-5}}{{C}_{1}}{{x}^{4}}\times 2+...]\]\[{{[}^{5}}{{C}_{0}}{{+}^{5}}{{C}_{1}}x+...]\] \[\RIGHTARROW \]COEFFICIENT of\[{{x}^{5}}\]\[{{=}^{5}}{{C}_{0}}^{5}{{C}_{5}}{{-}^{5}}{{C}_{1}}\times 2{{\times }^{5}}{{C}_{4}}{{+}^{5}}{{C}_{2}}\times {{2}^{2}}{{\times }^{5}}{{C}_{3}}{{-}^{5}}{{C}_{3}}\times {{2}^{3}}{{\times }^{5}}{{C}_{2}}\]\[{{+}^{5}}{{C}_{4}}\times {{2}^{4}}{{\times }^{5}}{{C}_{1}}{{-}^{5}}{{C}_{5}}\times {{2}^{5}}{{\times }^{5}}{{C}_{0}}\]\[=1-5\times 5\times 2+10\times 10\times 4-10\times 10\times 8+5\times 5\times 16-32\]\[=-81\]

"> 5}}{{(x+1)}^{5}}\] \[={{[}^{5}}{{C}_{0}}{{x}^{5-5}}{{C}_{1}}{{x}^{4}}\times 2+...]\]\[{{[}^{5}}{{C}_{0}}{{+}^{5}}{{C}_{1}}x+...]\] \[\RIGHTARROW \]COEFFICIENT of\[{{x}^{5}}\]\[{{=}^{5}}{{C}_{0}}^{5}{{C}_{5}}{{-}^{5}}{{C}_{1}}\times 2{{\times }^{5}}{{C}_{4}}{{+}^{5}}{{C}_{2}}\times {{2}^{2}}{{\times }^{5}}{{C}_{3}}{{-}^{5}}{{C}_{3}}\times {{2}^{3}}{{\times }^{5}}{{C}_{2}}\]\[{{+}^{5}}{{C}_{4}}\times {{2}^{4}}{{\times }^{5}}{{C}_{1}}{{-}^{5}}{{C}_{5}}\times {{2}^{5}}{{\times }^{5}}{{C}_{0}}\]\[=1-5\times 5\times 2+10\times 10\times 4-10\times 10\times 8+5\times 5\times 16-32\]\[=-81\]

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The coefficient of \[{{x}^{5}}\]in the expansion of \[{{({{x}^{2}}-x-2)}^{5}}\]is

Joint Entrance Exam - Main (JEE Main) Mathematics in Joint Entrance Exam - Main (JEE Main) 11 months ago

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[d] \[{{(x-2)}^{5}}{{(x+1)}^{5}}\] \[={{[}^{5}}{{C}_{0}}{{x}^{5-5}}{{C}_{1}}{{x}^{4}}\times 2+...]\]\[{{[}^{5}}{{C}_{0}}{{+}^{5}}{{C}_{1}}x+...]\] \[\RIGHTARROW \]COEFFICIENT of\[{{x}^{5}}\]\[{{=}^{5}}{{C}_{0}}^{5}{{C}_{5}}{{-}^{5}}{{C}_{1}}\times 2{{\times }^{5}}{{C}_{4}}{{+}^{5}}{{C}_{2}}\times {{2}^{2}}{{\times }^{5}}{{C}_{3}}{{-}^{5}}{{C}_{3}}\times {{2}^{3}}{{\times }^{5}}{{C}_{2}}\]\[{{+}^{5}}{{C}_{4}}\times {{2}^{4}}{{\times }^{5}}{{C}_{1}}{{-}^{5}}{{C}_{5}}\times {{2}^{5}}{{\times }^{5}}{{C}_{0}}\]\[=1-5\times 5\times 2+10\times 10\times 4-10\times 10\times 8+5\times 5\times 16-32\]\[=-81\]

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Posted on 07 Aug 2024, this text provides information on Joint Entrance Exam - Main (JEE Main) related to Mathematics in Joint Entrance Exam - Main (JEE Main). Please note that while accuracy is prioritized, the data presented might not be entirely correct or up-to-date. This information is offered for general knowledge and informational purposes only, and should not be considered as a substitute for professional advice.

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