st","extracted_subject":"MATH","extracted_chapter":"PROGRESSIONS","extracted_topic":"ARITHMETIC PROGRESSION","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1948.png?top_left_x=0&top_left_y=575&width=532&height=275&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31ecbf","slug":"if-a-b-c-be-the-psupthsup-qsupthsup-and-rsupthsup-","content":"If a, b, c be the p^th, q^th and r^th terms respectively of an AP and GP both, then the product of the roots of the equation a^bb^cc^a x² – abcx + a^cb^ac^b = 0 is equal to-","options":[{"_id":"68a3abea7f15af4716be350f","text":"–1","sequence":0,"isCorrect":false},{"_id":"68a3abea7f15af4716be3510","text":"1","sequence":1,"isCorrect":true},{"_id":"68a3abea7f15af4716be3511","text":"2","sequence":2,"isCorrect":false},{"_id":"68a3abea7f15af4716be3512","text":"(b – c) (c – a) (a – b)","sequence":3,"isCorrect":false}],"correct_answer":"1","explanation":"Product = \\(\\frac{a^{c}b^{a}c^{b}}{a^{b}b^{c}c^{a}}\\)\n\na = mn^p–1, b = mn^q–1, c = mn^r–1\n\nHence product\n\n= \\((mn^{p - 1})^{(r - q)d}\\) \\((mn^{q - 1})^{(p - r)d}(mn^{r - 1})^{(q - p)d}\\)\n\n= 1","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.134Z","__v":0,"vector_store_id":"4eba6459-1ac5-4975-b2a2-53348044627a","updated_at":"2024-08-30T21:49:38.134Z","isStarred":false},"params":{"questionSlug":"if-a-b-c-be-the-psupthsup-qsupthsup-and-rsupthsup-"}}]}]]

Question: If a, b, c be the p<sup>th</sup>, q<sup>th</sup> and r<sup>th</sup> terms respectively of an AP and ...

Solution