{"id":93248,"date":"2025-06-01T11:45:51","date_gmt":"2025-06-01T11:45:51","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93248"},"modified":"2025-06-01T11:45:51","modified_gmt":"2025-06-01T11:45:51","slug":"the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is\/","title":{"rendered":"The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :"},"content":{"rendered":"

The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :<\/p>\n

[amp_mcq option1=”9″ option2=”1″ option3=”7″ option4=”3″ correct=”option4″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2023<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is D.
\n<\/section>\n
\nTo find the unit digit of a product, we need to find the unit digit of each number being multiplied and then find the unit digit of their product. The unit digit of a number raised to a power depends only on the unit digit of the base and the exponent. The unit digits follow cycles.
\nFor (347)\u00b9\u2079\u00b2: The unit digit of the base is 7. The cycle of unit digits for powers of 7 is 7, 9, 3, 1 (length 4). Divide the exponent 192 by the cycle length 4: 192 \u00f7 4 = 48 with a remainder of 0. When the remainder is 0 (or the power is a multiple of the cycle length), the unit digit is the last digit in the cycle, which is 1 (corresponding to 7\u2074). So, the unit digit of (347)\u00b9\u2079\u00b2 is 1.
\nFor (143)\u00b2\u2070\u2075: The unit digit of the base is 3. The cycle of unit digits for powers of 3 is 3, 9, 7, 1 (length 4). Divide the exponent 205 by the cycle length 4: 205 \u00f7 4 = 51 with a remainder of 1. The unit digit is the first digit in the cycle, which is 3 (corresponding to 3\u00b9). So, the unit digit of (143)\u00b2\u2070\u2075 is 3.
\nThe unit digit of (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is the unit digit of the product of the individual unit digits: unit digit of (1 * 3) = unit digit of 3, which is 3.
\n<\/section>\n
\nThe unit digit cycles for powers of digits 0-9 are:
\n0: 0 (length 1)
\n1: 1 (length 1)
\n2: 2, 4, 8, 6 (length 4)
\n3: 3, 9, 7, 1 (length 4)
\n4: 4, 6 (length 2)
\n5: 5 (length 1)
\n6: 6 (length 1)
\n7: 7, 9, 3, 1 (length 4)
\n8: 8, 4, 2, 6 (length 4)
\n9: 9, 1 (length 2)
\nFor a power ‘n’, divide ‘n’ by the cycle length. If the remainder is ‘r’ (r > 0), the unit digit is the r-th digit in the cycle. If the remainder is 0, the unit digit is the last digit in the cycle.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is : [amp_mcq option1=”9″ option2=”1″ option3=”7″ option4=”3″ correct=”option4″] This question was previously asked in UPSC CISF-AC-EXE – 2023 Download PDFAttempt Online The correct answer is D. To find the unit digit of a product, we need to find the unit digit of each … <\/p>\n

Detailed SolutionThe digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1089],"tags":[1105,1102],"class_list":["post-93248","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1105","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nThe digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :<\/title>\n<meta name=\"description\" content=\"The correct answer is D. To find the unit digit of a product, we need to find the unit digit of each number being multiplied and then find the unit digit of their product. The unit digit of a number raised to a power depends only on the unit digit of the base and the exponent. The unit digits follow cycles. For (347)\u00b9\u2079\u00b2: The unit digit of the base is 7. The cycle of unit digits for powers of 7 is 7, 9, 3, 1 (length 4). Divide the exponent 192 by the cycle length 4: 192 \u00f7 4 = 48 with a remainder of 0. When the remainder is 0 (or the power is a multiple of the cycle length), the unit digit is the last digit in the cycle, which is 1 (corresponding to 7\u2074). So, the unit digit of (347)\u00b9\u2079\u00b2 is 1. For (143)\u00b2\u2070\u2075: The unit digit of the base is 3. The cycle of unit digits for powers of 3 is 3, 9, 7, 1 (length 4). Divide the exponent 205 by the cycle length 4: 205 \u00f7 4 = 51 with a remainder of 1. The unit digit is the first digit in the cycle, which is 3 (corresponding to 3\u00b9). So, the unit digit of (143)\u00b2\u2070\u2075 is 3. The unit digit of (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is the unit digit of the product of the individual unit digits: unit digit of (1 * 3) = unit digit of 3, which is 3.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347\u00b9\u2079\u00b2-x-143\u00b2\u2070\u2075-is\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :\" \/>\n<meta property=\"og:description\" content=\"The correct answer is D. To find the unit digit of a product, we need to find the unit digit of each number being multiplied and then find the unit digit of their product. The unit digit of a number raised to a power depends only on the unit digit of the base and the exponent. The unit digits follow cycles. For (347)\u00b9\u2079\u00b2: The unit digit of the base is 7. The cycle of unit digits for powers of 7 is 7, 9, 3, 1 (length 4). Divide the exponent 192 by the cycle length 4: 192 \u00f7 4 = 48 with a remainder of 0. When the remainder is 0 (or the power is a multiple of the cycle length), the unit digit is the last digit in the cycle, which is 1 (corresponding to 7\u2074). So, the unit digit of (347)\u00b9\u2079\u00b2 is 1. For (143)\u00b2\u2070\u2075: The unit digit of the base is 3. The cycle of unit digits for powers of 3 is 3, 9, 7, 1 (length 4). Divide the exponent 205 by the cycle length 4: 205 \u00f7 4 = 51 with a remainder of 1. The unit digit is the first digit in the cycle, which is 3 (corresponding to 3\u00b9). So, the unit digit of (143)\u00b2\u2070\u2075 is 3. The unit digit of (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is the unit digit of the product of the individual unit digits: unit digit of (1 * 3) = unit digit of 3, which is 3.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347\u00b9\u2079\u00b2-x-143\u00b2\u2070\u2075-is\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:45:51+00:00\" \/>\n<meta name=\"author\" content=\"rawan239\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"rawan239\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"1 minute\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :","description":"The correct answer is D. To find the unit digit of a product, we need to find the unit digit of each number being multiplied and then find the unit digit of their product. The unit digit of a number raised to a power depends only on the unit digit of the base and the exponent. The unit digits follow cycles. For (347)\u00b9\u2079\u00b2: The unit digit of the base is 7. The cycle of unit digits for powers of 7 is 7, 9, 3, 1 (length 4). Divide the exponent 192 by the cycle length 4: 192 \u00f7 4 = 48 with a remainder of 0. When the remainder is 0 (or the power is a multiple of the cycle length), the unit digit is the last digit in the cycle, which is 1 (corresponding to 7\u2074). So, the unit digit of (347)\u00b9\u2079\u00b2 is 1. For (143)\u00b2\u2070\u2075: The unit digit of the base is 3. The cycle of unit digits for powers of 3 is 3, 9, 7, 1 (length 4). Divide the exponent 205 by the cycle length 4: 205 \u00f7 4 = 51 with a remainder of 1. The unit digit is the first digit in the cycle, which is 3 (corresponding to 3\u00b9). So, the unit digit of (143)\u00b2\u2070\u2075 is 3. The unit digit of (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is the unit digit of the product of the individual unit digits: unit digit of (1 * 3) = unit digit of 3, which is 3.","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347\u00b9\u2079\u00b2-x-143\u00b2\u2070\u2075-is\/","og_locale":"en_US","og_type":"article","og_title":"The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :","og_description":"The correct answer is D. To find the unit digit of a product, we need to find the unit digit of each number being multiplied and then find the unit digit of their product. The unit digit of a number raised to a power depends only on the unit digit of the base and the exponent. The unit digits follow cycles. For (347)\u00b9\u2079\u00b2: The unit digit of the base is 7. The cycle of unit digits for powers of 7 is 7, 9, 3, 1 (length 4). Divide the exponent 192 by the cycle length 4: 192 \u00f7 4 = 48 with a remainder of 0. When the remainder is 0 (or the power is a multiple of the cycle length), the unit digit is the last digit in the cycle, which is 1 (corresponding to 7\u2074). So, the unit digit of (347)\u00b9\u2079\u00b2 is 1. For (143)\u00b2\u2070\u2075: The unit digit of the base is 3. The cycle of unit digits for powers of 3 is 3, 9, 7, 1 (length 4). Divide the exponent 205 by the cycle length 4: 205 \u00f7 4 = 51 with a remainder of 1. The unit digit is the first digit in the cycle, which is 3 (corresponding to 3\u00b9). So, the unit digit of (143)\u00b2\u2070\u2075 is 3. The unit digit of (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is the unit digit of the product of the individual unit digits: unit digit of (1 * 3) = unit digit of 3, which is 3.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347\u00b9\u2079\u00b2-x-143\u00b2\u2070\u2075-is\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:45:51+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"1 minute"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is\/","url":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is\/","name":"The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:45:51+00:00","dateModified":"2025-06-01T11:45:51+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is D. To find the unit digit of a product, we need to find the unit digit of each number being multiplied and then find the unit digit of their product. The unit digit of a number raised to a power depends only on the unit digit of the base and the exponent. The unit digits follow cycles. For (347)\u00b9\u2079\u00b2: The unit digit of the base is 7. The cycle of unit digits for powers of 7 is 7, 9, 3, 1 (length 4). Divide the exponent 192 by the cycle length 4: 192 \u00f7 4 = 48 with a remainder of 0. When the remainder is 0 (or the power is a multiple of the cycle length), the unit digit is the last digit in the cycle, which is 1 (corresponding to 7\u2074). So, the unit digit of (347)\u00b9\u2079\u00b2 is 1. For (143)\u00b2\u2070\u2075: The unit digit of the base is 3. The cycle of unit digits for powers of 3 is 3, 9, 7, 1 (length 4). Divide the exponent 205 by the cycle length 4: 205 \u00f7 4 = 51 with a remainder of 1. The unit digit is the first digit in the cycle, which is 3 (corresponding to 3\u00b9). So, the unit digit of (143)\u00b2\u2070\u2075 is 3. The unit digit of (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is the unit digit of the product of the individual unit digits: unit digit of (1 * 3) = unit digit of 3, which is 3.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/the-digit-in-the-unit-place-of-the-number-347%c2%b9%e2%81%b9%c2%b2-x-143%c2%b2%e2%81%b0%e2%81%b5-is\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CISF-AC-EXE","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-cisf-ac-exe\/"},{"@type":"ListItem","position":3,"name":"The digit in the unit place of the number (347)\u00b9\u2079\u00b2 x (143)\u00b2\u2070\u2075 is :"}]},{"@type":"WebSite","@id":"https:\/\/exam.pscnotes.com\/mcq\/#website","url":"https:\/\/exam.pscnotes.com\/mcq\/","name":"MCQ and Quiz for Exams","description":"","potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/exam.pscnotes.com\/mcq\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Person","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209","name":"rawan239","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/761a7274f9cce048fa5b921221e7934820d74514df93ef195a9d22af0c1c9001?s=96&d=mm&r=g","caption":"rawan239"},"sameAs":["https:\/\/exam.pscnotes.com"],"url":"https:\/\/exam.pscnotes.com\/mcq\/author\/rawan239\/"}]}},"amp_enabled":true,"_links":{"self":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93248","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/comments?post=93248"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93248\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=93248"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=93248"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=93248"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}