test","extracted_subject":"MATH","extracted_chapter":"BINOMIAL THEOREM AND MATHEMATICAL INDUCTION","extracted_topic":"MATHEMATICAL INDUCTION AND DIVISIBILITY PROBLEMS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1994.png?top_left_x=532&top_left_y=0&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f382","slug":"if-the-21supstsup-and-22supndsup-terms-in-the-expa","content":"If the 21^st and 22^nd terms in the expansion of (1 –x)⁴⁴ are equal, then x =","options":[{"_id":"68a394ad7f15af4716ba4afd","text":"7/8","sequence":0,"isCorrect":false},{"_id":"68a394ad7f15af4716ba4afe","text":"–8/7","sequence":1,"isCorrect":false},{"_id":"68a394ad7f15af4716ba4aff","text":"–7/8","sequence":2,"isCorrect":true},{"_id":"68a394ad7f15af4716ba4b00","text":"None","sequence":3,"isCorrect":false}],"correct_answer":"–7/8","explanation":"T₂₁ = T₂₂\n\nŽ T₂₀₊₁ = T₂₁₊₁\n\nŽ ⁴⁴C₂₀ x²⁰ = ⁴⁴C₂₁ (–x)²¹\n\nŽ x =\\(\\frac{-^{44}C_{20}}{44C_{21}}\\)= \\(\\frac{(44)!}{(20)!(24)!}\\)× \\(\\frac{(21)!(23)!}{(44)!}\\)\n\n= \\(\\frac{- 21}{24}\\)= \\(\\frac{- 7}{8}\\)","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.557Z","__v":0,"vector_store_id":"7e3d0968-0ad4-4974-9bcb-8723d4719f18","updated_at":"2024-08-30T21:49:38.557Z","isStarred":false},"params":{"questionSlug":"if-the-21supstsup-and-22supndsup-terms-in-the-expa"}}]}]]

Question: If the 21<sup>st</sup> and 22<sup>nd</sup> terms in the expansion of (1 –x)<sup>44</sup> are equal, ...

Solution