st","extracted_subject":"MATH","extracted_chapter":"PERMUTATIONS AND COMBINATIONS","extracted_topic":"DEFINITON OF COMBINATIONS, CONDITION COMBINATIONS, DIVISION INTO GROUPS, DERANGEMENTS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_2027.png?top_left_x=0&top_left_y=1223&width=532&height=243&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f905","slug":"if-n-7supp4sup5supqsup2sup3sup-is-a-perfect-cube-w","content":"If N = 7^p+4.5^q.2³ is a perfect cube, where 'p' and 'q' are positive integers, the smallest possible value of 'p + q' is-","options":[{"_id":"68a3d0a47f15af4716c474a4","text":"5","sequence":0,"isCorrect":true},{"_id":"68a3d0a47f15af4716c474a5","text":"2","sequence":1,"isCorrect":false},{"_id":"68a3d0a47f15af4716c474a6","text":"8","sequence":2,"isCorrect":false},{"_id":"68a3d0a47f15af4716c474a7","text":"6","sequence":3,"isCorrect":false}],"correct_answer":"5","explanation":"N = 7^{p + 4} . 5^q.2³ is perfect cube.\n\n7, 5, 2 has no common factor except '1'.\n\nLeast value of 'q' is 3 for which 5^q is cube.\n\nLeast value of 'p + 4' is '6' for which 7^p+4 is cube.\n\np + 4 = 6 Ž p = 2\n\n\\\\ Least value of p + q = 2 + 3 = 5.","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.909Z","__v":0,"vector_store_id":"8b23b1cf-2e01-4ac9-871f-61e24aae66a4","updated_at":"2024-08-30T21:49:38.909Z","isStarred":false},"params":{"questionSlug":"if-n-7supp4sup5supqsup2sup3sup-is-a-perfect-cube-w"}}]}]]

Question: If N = 7<sup>p+4</sup>.5<sup>q</sup>.2<sup>3</sup> is a perfect cube, where 'p' and 'q' are positive...

Solution