{"id":90682,"date":"2025-06-01T10:33:36","date_gmt":"2025-06-01T10:33:36","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=90682"},"modified":"2025-06-01T10:33:36","modified_gmt":"2025-06-01T10:33:36","slug":"which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/","title":{"rendered":"Which one of the following is the difference of the sum of cubes of fi"},"content":{"rendered":"

Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers?<\/p>\n

[amp_mcq option1=”2400″ option2=”2640″ option3=”2880″ option4=”2000″ correct=”option2″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CAPF – 2022<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
The sum of the first ten natural numbers’ cubes is calculated using the formula $[\\frac{n(n+1)}{2}]^2$ with n=10, giving $[\\frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers’ squares is calculated using the formula $\\frac{n(n+1)(2n+1)}{6}$ with n=10, giving $\\frac{10(11)(21)}{6} = \\frac{2310}{6} = 385$. The difference is $3025 – 385 = 2640$.<\/section>\n
The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first ‘n’ natural numbers and applying them for n=10.<\/section>\n
The formula for the sum of the first n natural numbers is $\\frac{n(n+1)}{2}$. The sum of cubes of the first n natural numbers is the square of the sum of the first n natural numbers: $(\\sum_{k=1}^n k)^2 = (\\frac{n(n+1)}{2})^2$. The sum of squares of the first n natural numbers is $\\sum_{k=1}^n k^2 = \\frac{n(n+1)(2n+1)}{6}$.<\/section>\n","protected":false},"excerpt":{"rendered":"

Which one of the following is the difference of the sum of cubes of first ten natural numbers and the sum of squares of first ten natural numbers? [amp_mcq option1=”2400″ option2=”2640″ option3=”2880″ option4=”2000″ correct=”option2″] This question was previously asked in UPSC CAPF – 2022 Download PDFAttempt Online The sum of the first ten natural numbers’ … <\/p>\n

Detailed SolutionWhich one of the following is the difference of the sum of cubes of fi<\/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":[1085],"tags":[1108,1102],"class_list":["post-90682","post","type-post","status-publish","format-standard","hentry","category-upsc-capf","tag-1108","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nWhich one of the following is the difference of the sum of cubes of fi<\/title>\n<meta name=\"description\" content=\"The sum of the first ten natural numbers' cubes is calculated using the formula $[frac{n(n+1)}{2}]^2$ with n=10, giving $[frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers' squares is calculated using the formula $frac{n(n+1)(2n+1)}{6}$ with n=10, giving $frac{10(11)(21)}{6} = frac{2310}{6} = 385$. The difference is $3025 - 385 = 2640$. The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first 'n' natural numbers and applying them for n=10.\" \/>\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-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Which one of the following is the difference of the sum of cubes of fi\" \/>\n<meta property=\"og:description\" content=\"The sum of the first ten natural numbers' cubes is calculated using the formula $[frac{n(n+1)}{2}]^2$ with n=10, giving $[frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers' squares is calculated using the formula $frac{n(n+1)(2n+1)}{6}$ with n=10, giving $frac{10(11)(21)}{6} = frac{2310}{6} = 385$. The difference is $3025 - 385 = 2640$. The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first 'n' natural numbers and applying them for n=10.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T10:33:36+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 of the following is the difference of the sum of cubes of fi","description":"The sum of the first ten natural numbers' cubes is calculated using the formula $[frac{n(n+1)}{2}]^2$ with n=10, giving $[frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers' squares is calculated using the formula $frac{n(n+1)(2n+1)}{6}$ with n=10, giving $frac{10(11)(21)}{6} = frac{2310}{6} = 385$. The difference is $3025 - 385 = 2640$. The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first 'n' natural numbers and applying them for n=10.","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-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/","og_locale":"en_US","og_type":"article","og_title":"Which one of the following is the difference of the sum of cubes of fi","og_description":"The sum of the first ten natural numbers' cubes is calculated using the formula $[frac{n(n+1)}{2}]^2$ with n=10, giving $[frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers' squares is calculated using the formula $frac{n(n+1)(2n+1)}{6}$ with n=10, giving $frac{10(11)(21)}{6} = frac{2310}{6} = 385$. The difference is $3025 - 385 = 2640$. The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first 'n' natural numbers and applying them for n=10.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T10:33:36+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-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/","url":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/","name":"Which one of the following is the difference of the sum of cubes of fi","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T10:33:36+00:00","dateModified":"2025-06-01T10:33:36+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The sum of the first ten natural numbers' cubes is calculated using the formula $[\\frac{n(n+1)}{2}]^2$ with n=10, giving $[\\frac{10(11)}{2}]^2 = 55^2 = 3025$. The sum of the first ten natural numbers' squares is calculated using the formula $\\frac{n(n+1)(2n+1)}{6}$ with n=10, giving $\\frac{10(11)(21)}{6} = \\frac{2310}{6} = 385$. The difference is $3025 - 385 = 2640$. The problem requires knowing the formulas for the sum of cubes and the sum of squares of the first 'n' natural numbers and applying them for n=10.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/which-one-of-the-following-is-the-difference-of-the-sum-of-cubes-of-fi\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/exam.pscnotes.com\/mcq\/"},{"@type":"ListItem","position":2,"name":"UPSC CAPF","item":"https:\/\/exam.pscnotes.com\/mcq\/category\/upsc-capf\/"},{"@type":"ListItem","position":3,"name":"Which one of the following is the difference of the sum of cubes of fi"}]},{"@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\/90682","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=90682"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/90682\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=90682"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=90682"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=90682"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}