st","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_1992.png?top_left_x=532&top_left_y=1159&width=532&height=263&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f369","slug":"if-coefficient-of-asup2supbsup3supcsup4sup-in-a-b-","content":"If coefficient of a²b³c⁴ in (a + b + c)^m, (where mĪN) is L (L ≠ 0) then in same expansion coefficient of a⁴b⁴c¹ will be","options":[{"_id":"68a376897f15af4716b529b8","text":"L","sequence":0,"isCorrect":false},{"_id":"68a376897f15af4716b529b9","text":"\$\\frac{L}{3}\$","sequence":1,"isCorrect":false},{"_id":"68a376897f15af4716b529ba","text":"\$\\frac{mL}{4}\$","sequence":2,"isCorrect":false},{"_id":"68a376897f15af4716b529bb","text":"\$\\frac{L}{2}\$","sequence":3,"isCorrect":true}],"correct_answer":"$$\\frac{L}{2}$","explanation":"as L ¹ 0 \\\\ m = 2 + 3 + 4 = 9\n\n\\\\ L = \$\\frac{9!}{2!3!4!}\$\n\nNow coefficient of a⁴b⁴c = \$\\frac{9!}{4!4!1!} = \\frac{L}{2}\$","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.555Z","__v":0,"vector_store_id":"b32160df-ec51-42a9-8bb1-430746061993","updated_at":"2024-08-30T21:49:38.555Z","isStarred":false},"params":{"questionSlug":"if-coefficient-of-asup2supbsup3supcsup4sup-in-a-b-"}}]}]]

Question: If coefficient of a<sup>2</sup>b<sup>3</sup>c<sup>4</sup> in (a + b + c)<sup>m</sup>, (where mĪN) is...

Solution