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=1064&top_left_y=1201&width=532&height=246&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f37f","slug":"if-sum-of-all-the-coefficients-in-the-expansion-of","content":"If sum of all the coefficients in the expansion of (x^3/2 + x^–1/3)ⁿ is 128, then the coefficient of x⁵ is –","options":[{"_id":"68a9364b7f15af4716d3937c","text":"35","sequence":0,"isCorrect":true},{"_id":"68a9364b7f15af4716d3937d","text":"45","sequence":1,"isCorrect":false},{"_id":"68a9364b7f15af4716d3937e","text":"7","sequence":2,"isCorrect":false},{"_id":"68a9364b7f15af4716d3937f","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"35","explanation":"Sum of all coefficients,\n\nPut x = 1, 2ⁿ = 128 0 Ž n = 7\n\nNow in (x^3/2 + x^–1/3)⁷, r = \\(\\frac{\\frac{21}{2}–5}{\\frac{3}{2} + \\frac{1}{3}}\\) = \\(\\frac{\\frac{11}{2}}{\\frac{11}{6}}\\) = 3\n\nT₄ = ⁷C₃ = 35","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.557Z","__v":0,"vector_store_id":"5d040a15-2bb3-4103-bc9d-7321162fe6a8","updated_at":"2024-08-30T21:49:38.557Z","isStarred":false},"params":{"questionSlug":"if-sum-of-all-the-coefficients-in-the-expansion-of"}}]}]]

Question: If sum of all the coefficients in the expansion of (x<sup>3/2</sup> + x<sup>–1/3</sup>)<sup>n</sup> ...

Solution