{"id":93426,"date":"2025-06-01T11:50:17","date_gmt":"2025-06-01T11:50:17","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=93426"},"modified":"2025-06-01T11:50:17","modified_gmt":"2025-06-01T11:50:17","slug":"which-one-among-the-following-digits-can-never-be-at-the-units-place-i","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/","title":{"rendered":"Which one among the following digits can never be at the units place i"},"content":{"rendered":"

Which one among the following digits can never be at the units place in $(273)^n$, where $n$ is a positive integer?<\/p>\n

[amp_mcq option1=”1″ option2=”3″ option3=”5″ option4=”7″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2024<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe correct answer is 5.
\n<\/section>\n
\nThe units digit of a number raised to a power is determined solely by the units digit of the base number and the power. In this case, the base number is 273, and its units digit is 3. So, the units digit of $(273)^n$ is the same as the units digit of $3^n$, where n is a positive integer.
\nLet’s examine the pattern of the units digits of powers of 3:
\n$3^1$: Units digit is 3.
\n$3^2$: Units digit of $3 \\times 3 = 9$.
\n$3^3$: Units digit of $9 \\times 3 = 27$, which is 7.
\n$3^4$: Units digit of $7 \\times 3 = 21$, which is 1.
\n$3^5$: Units digit of $1 \\times 3 = 3$. (The pattern repeats)
\n$3^6$: Units digit of $3 \\times 3 = 9$.
\nThe cycle of the units digits of powers of 3 is 3, 9, 7, 1. This cycle has a length of 4.
\nFor any positive integer n, the units digit of $3^n$ will be one of these four digits: 1, 3, 7, or 9.
\nLet’s check the given options:
\nA) 1: Possible (e.g., for $n=4$)
\nB) 3: Possible (e.g., for $n=1$)
\nC) 5: Not in the cycle {3, 9, 7, 1}
\nD) 7: Possible (e.g., for $n=3$)
\nTherefore, the digit 5 can never be at the units place in $(273)^n$ for any positive integer n.
\n<\/section>\n
\nThe units digits of powers of any single digit follow a repeating pattern (a cycle). For example, powers of 2 have units digits 2, 4, 8, 6, 2, 4, 8, 6, … (cycle length 4). Powers of 7 have units digits 7, 9, 3, 1, 7, 9, 3, 1, … (cycle length 4). Powers of 0, 1, 5, 6 have a cycle length of 1 (always 0, 1, 5, 6 respectively). Powers of 4 and 9 have a cycle length of 2 (4, 6, 4, 6, … and 9, 1, 9, 1, …). The units digit of a number like 273 raised to a power is determined only by the units digit of 273, which is 3.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one among the following digits can never be at the units place in $(273)^n$, where $n$ is a positive integer? [amp_mcq option1=”1″ option2=”3″ option3=”5″ option4=”7″ correct=”option3″] This question was previously asked in UPSC CISF-AC-EXE – 2024 Download PDFAttempt Online The correct answer is 5. The units digit of a number raised to a power … <\/p>\n

Detailed SolutionWhich one among the following digits can never be at the units place i<\/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":[1103,1102],"class_list":["post-93426","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1103","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nWhich one among the following digits can never be at the units place i<\/title>\n<meta name=\"description\" content=\"The correct answer is 5. The units digit of a number raised to a power is determined solely by the units digit of the base number and the power. In this case, the base number is 273, and its units digit is 3. So, the units digit of $(273)^n$ is the same as the units digit of $3^n$, where n is a positive integer. Let's examine the pattern of the units digits of powers of 3: $3^1$: Units digit is 3. $3^2$: Units digit of $3 times 3 = 9$. $3^3$: Units digit of $9 times 3 = 27$, which is 7. $3^4$: Units digit of $7 times 3 = 21$, which is 1. $3^5$: Units digit of $1 times 3 = 3$. (The pattern repeats) $3^6$: Units digit of $3 times 3 = 9$. The cycle of the units digits of powers of 3 is 3, 9, 7, 1. This cycle has a length of 4. For any positive integer n, the units digit of $3^n$ will be one of these four digits: 1, 3, 7, or 9. Let's check the given options: A) 1: Possible (e.g., for $n=4$) B) 3: Possible (e.g., for $n=1$) C) 5: Not in the cycle {3, 9, 7, 1} D) 7: Possible (e.g., for $n=3$) Therefore, the digit 5 can never be at the units place in $(273)^n$ for any positive integer n.\" \/>\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\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which one among the following digits can never be at the units place i\" \/>\n<meta property=\"og:description\" content=\"The correct answer is 5. The units digit of a number raised to a power is determined solely by the units digit of the base number and the power. In this case, the base number is 273, and its units digit is 3. So, the units digit of $(273)^n$ is the same as the units digit of $3^n$, where n is a positive integer. Let's examine the pattern of the units digits of powers of 3: $3^1$: Units digit is 3. $3^2$: Units digit of $3 times 3 = 9$. $3^3$: Units digit of $9 times 3 = 27$, which is 7. $3^4$: Units digit of $7 times 3 = 21$, which is 1. $3^5$: Units digit of $1 times 3 = 3$. (The pattern repeats) $3^6$: Units digit of $3 times 3 = 9$. The cycle of the units digits of powers of 3 is 3, 9, 7, 1. This cycle has a length of 4. For any positive integer n, the units digit of $3^n$ will be one of these four digits: 1, 3, 7, or 9. Let's check the given options: A) 1: Possible (e.g., for $n=4$) B) 3: Possible (e.g., for $n=1$) C) 5: Not in the cycle {3, 9, 7, 1} D) 7: Possible (e.g., for $n=3$) Therefore, the digit 5 can never be at the units place in $(273)^n$ for any positive integer n.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:50:17+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":"Which one among the following digits can never be at the units place i","description":"The correct answer is 5. The units digit of a number raised to a power is determined solely by the units digit of the base number and the power. In this case, the base number is 273, and its units digit is 3. So, the units digit of $(273)^n$ is the same as the units digit of $3^n$, where n is a positive integer. Let's examine the pattern of the units digits of powers of 3: $3^1$: Units digit is 3. $3^2$: Units digit of $3 times 3 = 9$. $3^3$: Units digit of $9 times 3 = 27$, which is 7. $3^4$: Units digit of $7 times 3 = 21$, which is 1. $3^5$: Units digit of $1 times 3 = 3$. (The pattern repeats) $3^6$: Units digit of $3 times 3 = 9$. The cycle of the units digits of powers of 3 is 3, 9, 7, 1. This cycle has a length of 4. For any positive integer n, the units digit of $3^n$ will be one of these four digits: 1, 3, 7, or 9. Let's check the given options: A) 1: Possible (e.g., for $n=4$) B) 3: Possible (e.g., for $n=1$) C) 5: Not in the cycle {3, 9, 7, 1} D) 7: Possible (e.g., for $n=3$) Therefore, the digit 5 can never be at the units place in $(273)^n$ for any positive integer n.","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\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/","og_locale":"en_US","og_type":"article","og_title":"Which one among the following digits can never be at the units place i","og_description":"The correct answer is 5. The units digit of a number raised to a power is determined solely by the units digit of the base number and the power. In this case, the base number is 273, and its units digit is 3. So, the units digit of $(273)^n$ is the same as the units digit of $3^n$, where n is a positive integer. Let's examine the pattern of the units digits of powers of 3: $3^1$: Units digit is 3. $3^2$: Units digit of $3 times 3 = 9$. $3^3$: Units digit of $9 times 3 = 27$, which is 7. $3^4$: Units digit of $7 times 3 = 21$, which is 1. $3^5$: Units digit of $1 times 3 = 3$. (The pattern repeats) $3^6$: Units digit of $3 times 3 = 9$. The cycle of the units digits of powers of 3 is 3, 9, 7, 1. This cycle has a length of 4. For any positive integer n, the units digit of $3^n$ will be one of these four digits: 1, 3, 7, or 9. Let's check the given options: A) 1: Possible (e.g., for $n=4$) B) 3: Possible (e.g., for $n=1$) C) 5: Not in the cycle {3, 9, 7, 1} D) 7: Possible (e.g., for $n=3$) Therefore, the digit 5 can never be at the units place in $(273)^n$ for any positive integer n.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:50:17+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\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/","name":"Which one among the following digits can never be at the units place i","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:50:17+00:00","dateModified":"2025-06-01T11:50:17+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The correct answer is 5. The units digit of a number raised to a power is determined solely by the units digit of the base number and the power. In this case, the base number is 273, and its units digit is 3. So, the units digit of $(273)^n$ is the same as the units digit of $3^n$, where n is a positive integer. Let's examine the pattern of the units digits of powers of 3: $3^1$: Units digit is 3. $3^2$: Units digit of $3 \\times 3 = 9$. $3^3$: Units digit of $9 \\times 3 = 27$, which is 7. $3^4$: Units digit of $7 \\times 3 = 21$, which is 1. $3^5$: Units digit of $1 \\times 3 = 3$. (The pattern repeats) $3^6$: Units digit of $3 \\times 3 = 9$. The cycle of the units digits of powers of 3 is 3, 9, 7, 1. This cycle has a length of 4. For any positive integer n, the units digit of $3^n$ will be one of these four digits: 1, 3, 7, or 9. Let's check the given options: A) 1: Possible (e.g., for $n=4$) B) 3: Possible (e.g., for $n=1$) C) 5: Not in the cycle {3, 9, 7, 1} D) 7: Possible (e.g., for $n=3$) Therefore, the digit 5 can never be at the units place in $(273)^n$ for any positive integer n.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-among-the-following-digits-can-never-be-at-the-units-place-i\/#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":"Which one among the following digits can never be at the units place i"}]},{"@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\/93426","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=93426"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/93426\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=93426"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=93426"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=93426"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}