test","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_2023.png?top_left_x=1064&top_left_y=1347&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f852","slug":"the-number-of-odd-proper-divisors-of-3suppsup-6sup","content":"The number of odd proper divisors of 3^p. 6^m.21ⁿ is-","options":[{"_id":"68a936257f15af4716d38a71","text":"(p+1) (m+1) (n+1) – 2","sequence":0,"isCorrect":false},{"_id":"68a936257f15af4716d38a72","text":"(p + m + n + 1) (n + 1) –1","sequence":1,"isCorrect":true},{"_id":"68a936257f15af4716d38a73","text":"(p + 1) (m+1) (n+1) – 1","sequence":2,"isCorrect":false},{"_id":"68a936257f15af4716d38a74","text":"None of these","sequence":3,"isCorrect":false}],"correct_answer":"(p + m + n + 1) (n + 1) –1","explanation":"3^p. 6^m.21ⁿ = 2^m.3^p+m+n.7ⁿ\n\n\\\\ the required number of proper divisors\n\n= Number of selections of any number of 3’sand 7’s\n\n[Q for odd divisors 2 must not be selected]\n\n= (p + m + n + 1) (n + 1) –1","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.861Z","__v":0,"vector_store_id":"472c4b65-e2e7-4754-95ab-ac3af20eb6a1","updated_at":"2024-08-30T21:49:38.861Z","isStarred":false},"params":{"questionSlug":"the-number-of-odd-proper-divisors-of-3suppsup-6sup"}}]}]]

Question: The number of odd proper divisors of 3<sup>p</sup>. 6<sup>m</sup>.21<sup>n</sup> is-...

Solution