st","extracted_subject":"MATH","extracted_chapter":"BINOMIAL THEOREM AND MATHEMATICAL INDUCTION","extracted_topic":"GENERAL TERM, COEFFICIENT OF ANY POWER OF x","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1979.png?top_left_x=532&top_left_y=1293&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f139","slug":"number-of-rational-terms-in-the-expansion-7sup13su","content":"Number of rational terms in the expansion (7^1/3 + 11^1/9) ⁶⁵⁶¹","options":[{"_id":"68a397a47f15af4716bacf69","text":"729","sequence":0,"isCorrect":false},{"_id":"68a397a47f15af4716bacf6a","text":"730","sequence":1,"isCorrect":true},{"_id":"68a397a47f15af4716bacf6b","text":"731","sequence":2,"isCorrect":false},{"_id":"68a397a47f15af4716bacf6c","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"730","explanation":"T_r+1 = ⁶⁵⁶¹C_r (7^1/3)^{6561 – r} (11^1/9)^r\n\n= ⁶⁵⁶¹C_r 7²¹⁸⁷. 7^–r/3. 11^r/9\n\n0 £ r £ 6561\n\nFor rational terms r is multiple of 9 0, 9, 81, 27,……6561\n\nT_n = 6561 = a +(n – 1) d = 0 + (n – 1) 9\n\nn = 1 + \\(\\frac{6561}{9}\\) = 1 + 729 = 730.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.409Z","__v":0,"vector_store_id":"14613328-5f71-4692-8579-96eee3161a46","updated_at":"2024-08-30T21:49:38.409Z","isStarred":false},"params":{"questionSlug":"number-of-rational-terms-in-the-expansion-7sup13su"}}]}]]

Question: Number of rational terms in the expansion (7<sup>1/3</sup> + 11<sup>1/9</sup>) <sup>6561</sup>...

Solution