test","extracted_subject":"MATH","extracted_chapter":"BINOMIAL THEOREM AND MATHEMATICAL INDUCTION","extracted_topic":"PROPERTIES OF BINOMIAL COEFFICIENTS","questionPreviewUrl":"https://cdn.pureessence.tech/question-previews/packed_canvases/canvas_1985.png?top_left_x=532&top_left_y=1361&width=532&height=215&app=solveeit"},"seo_metadata":{"keywords":[]},"doubt_solver_data":{"concept_summary":[]},"embeddings":[],"is_hidden":false,"_id":"66d23e72425d76b7ab31f27d","slug":"if-7sup103sup-is-divided-by-25-then-find-the-remai","content":"If 7¹⁰³ is divided by 25 then find the remainder –","options":[{"_id":"68a41dd97f15af4716ca5d75","text":"1","sequence":0,"isCorrect":false},{"_id":"68a41dd97f15af4716ca5d76","text":"7","sequence":1,"isCorrect":false},{"_id":"68a41dd97f15af4716ca5d77","text":"10","sequence":2,"isCorrect":false},{"_id":"68a41dd97f15af4716ca5d78","text":"18","sequence":3,"isCorrect":true}],"correct_answer":"18","explanation":"Since 7¹⁰³ = 7(49)⁵¹ = 7(50 – 1)⁵¹\n\n= 7 {50⁵¹ – ⁵¹C₁ 50⁵⁰ + ⁵¹C₂ 50⁴⁹ – ....–1}\n\n=7{50⁵¹ – ⁵¹C₁ 50⁵⁰+⁵¹C₂50⁴⁹ –...} – 7+18– 18\n\n= 7 (50⁵¹ – ⁵¹C₁ 50⁵⁰ + ⁵¹C₂ 50⁴⁹ – ....) – 25 + 18","question_type":"single_choice","appeared_in":[],"created_at":"2024-08-30T21:49:38.502Z","__v":0,"vector_store_id":"ced7770f-9e40-44fb-a467-ece25ffa245a","updated_at":"2024-08-30T21:49:38.502Z","isStarred":false},"params":{"questionSlug":"if-7sup103sup-is-divided-by-25-then-find-the-remai"}}]}]]

Question: If 7<sup>103</sup> is divided by 25 then find the remainder –...

Solution