st","extracted_subject":"MATH","extracted_chapter":"CIRCLE AND SYSTEM OF CIRCLES","extracted_topic":"CHORD OF CONTACT OF TANGENT, POLE AND POLAR","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2252.png?top_left_x=1064&top_left_y=0&width=532&height=278&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e74425d76b7ab321658","slug":"if-sum-of-coefficients-in-expansion-of-1-2xsupmsup-1","content":"If sum of coefficients in expansion of (1 + 2x)^m and (2 + x)ⁿ are respectively 6561 and 243. Then position of point (m, n) w.r.t. circle x² + y² – 4x – 6y – 32 = 0 is-","options":[{"_id":"68a3e1107f15af4716c62a52","text":"Outside the circle","sequence":0,"isCorrect":false},{"_id":"68a3e1107f15af4716c62a53","text":"Inside the circle","sequence":1,"isCorrect":true},{"_id":"68a3e1107f15af4716c62a54","text":"On the circle","sequence":2,"isCorrect":false},{"_id":"68a3e1107f15af4716c62a55","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"Inside the circle","explanation":"Q sum of coefficients in (1 + 2x)^m is 3^m = 6561\n\nm = 8\n\nsum of coefficients in (2 + x)ⁿ is 3ⁿ = 243; n = 5\n\n\\\\ (8, 5) lies inside as s₁ \\< 0","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:40.814Z","__v":0,"vector_store_id":"6dfa26bf-b548-42d5-942d-6243d490aceb","updated_at":"2024-08-30T21:49:40.814Z","isStarred":false},"params":{"questionSlug":"if-sum-of-coefficients-in-expansion-of-1-2xsupmsup-1"}}]}]]

Question: If sum of coefficients in expansion of (1 + 2x)<sup>m</sup> and (2 + x)<sup>n</sup> are respectively...

Solution