st","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_1992.png?top_left_x=1064&top_left_y=1159&width=532&height=252&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f36c","slug":"if-it-is-known-that-the-third-term-of-the-binomial","content":"If it is known that the third term of the binomial expansion \\(\\left( x + x^{\\log_{10}x} \\right)^{5}\\)is 10⁶ then x is equal to-","options":[{"_id":"68dfd6718c3e555ae9e70639","text":"10","sequence":0,"isCorrect":true},{"_id":"68dfd6718c3e555ae9e7063a","text":"10^–5/2","sequence":1,"isCorrect":false},{"_id":"68dfd6718c3e555ae9e7063b","text":"100","sequence":2,"isCorrect":false},{"_id":"68dfd6718c3e555ae9e7063c","text":"5","sequence":3,"isCorrect":false}],"correct_answer":"10","explanation":"In \\((x + x^{\\log_{10}x})^{5}\\)3^rd term is 10⁶\n\nŽ T₃ = ⁵C₂ (x)²[\\((x)^{\\log_{10}x}\\)]³ = 10⁶\n\nx² (\\((x)^{3\\log_{10}x}\\)) = 10⁵\n\nŽ x = 10","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.556Z","__v":0,"vector_store_id":"7f3fa7ad-6aec-41ba-bb9a-f028d08c1e90","updated_at":"2024-08-30T21:49:38.556Z","isStarred":false},"params":{"questionSlug":"if-it-is-known-that-the-third-term-of-the-binomial"}}]}]]

Question: If it is known that the third term of the binomial expansion \(\left( x + x^{\log_{10}x} \right)^{5}...

Solution