{"id":92520,"date":"2025-06-01T11:27:15","date_gmt":"2025-06-01T11:27:15","guid":{"rendered":"https:\/\/exam.pscnotes.com\/mcq\/?p=92520"},"modified":"2025-06-01T11:27:15","modified_gmt":"2025-06-01T11:27:15","slug":"how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal","status":"publish","type":"post","link":"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/","title":{"rendered":"How many times in a day are the hour hand and the minute hand of a wal"},"content":{"rendered":"

How many times in a day are the hour hand and the minute hand of a wall clock straight (i.e., the angle between them is 180\u00b0)?<\/p>\n

[amp_mcq option1=”20″ option2=”21″ option3=”22″ option4=”24″ correct=”option3″]<\/p>\n

\n
\n
This question was previously asked in<\/div>\n
UPSC CISF-AC-EXE – 2018<\/div>\n<\/div>\n
Download PDF<\/a>Attempt Online<\/a><\/div>\n<\/div>\n
\nThe hour hand and the minute hand of a wall clock are straight (180\u00b0 apart) 22 times in a day (24 hours).
\n<\/section>\n
\nIn a 12-hour period, the minute hand completes 12 revolutions while the hour hand completes 1 revolution. The minute hand gains 11 full revolutions over the hour hand. During this process, the hands coincide (0\u00b0 apart) 11 times and are opposite (180\u00b0 apart) 11 times.
\nThe hands are 180\u00b0 apart once in every hour interval, except for the interval between 6 o’clock and 7 o’clock, where they are 180\u00b0 apart exactly at 6 o’clock. The 6 o’clock position is counted in both the 5-6 interval and the 6-7 interval if we consider specific time points, but considering distinct occurrences in a 12-hour cycle, it happens 11 times.
\nFor example, between 12 pm and 12 am, the hands are opposite at approximately 12:33, 1:38, 2:44, 3:49, 4:55, 6:00, 7:05, 8:11, 9:16, 10:22, 11:27. (These are approximate times, the exact times are fractions). This is 11 distinct times in a 12-hour period.
\nA full day is 24 hours, which consists of two 12-hour periods.
\nTherefore, in 24 hours, the hands will be straight (180\u00b0 apart) 11 times + 11 times = 22 times.
\n<\/section>\n
\nThe general formula for the time t (in minutes past H o’clock) when the hands are at an angle $\\theta$ is $t = \\frac{2}{11} (30H \\pm \\theta)$.
\nFor the hands to be straight, $\\theta = 180^\\circ$.
\n$t = \\frac{2}{11} (30H \\pm 180)$.
\nLet’s check for H from 1 to 12.
\nFor H=6, $t = \\frac{2}{11} (180 \\pm 180)$. $t = \\frac{2}{11} (360) \\approx 65.45$ min (past 6) or $t = \\frac{2}{11} (0) = 0$ min (past 6). This confirms 6:00 is one time.
\nFor H=5, $t = \\frac{2}{11} (150 \\pm 180)$. $t = \\frac{2}{11} (330) = 60$ min (past 5, which is 6:00) or $t = \\frac{2}{11} (-30)$ (not valid in this hour).
\nThe hands are exactly opposite at 6:00. This instance is the boundary point that is counted only once in a 12-hour period when counting the intervals between hours.
\nThe number of times the hands are 180\u00b0 apart is 11 in 12 hours, and 22 in 24 hours.
\n<\/section>\n","protected":false},"excerpt":{"rendered":"

How many times in a day are the hour hand and the minute hand of a wall clock straight (i.e., the angle between them is 180\u00b0)? [amp_mcq option1=”20″ option2=”21″ option3=”22″ option4=”24″ correct=”option3″] This question was previously asked in UPSC CISF-AC-EXE – 2018 Download PDFAttempt Online The hour hand and the minute hand of a wall … <\/p>\n

Detailed SolutionHow many times in a day are the hour hand and the minute hand of a wal<\/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":[1114,1102],"class_list":["post-92520","post","type-post","status-publish","format-standard","hentry","category-upsc-cisf-ac-exe","tag-1114","tag-quantitative-aptitude-and-reasoning","no-featured-image-padding"],"yoast_head":"\nHow many times in a day are the hour hand and the minute hand of a wal<\/title>\n<meta name=\"description\" content=\"The hour hand and the minute hand of a wall clock are straight (180\u00b0 apart) 22 times in a day (24 hours). In a 12-hour period, the minute hand completes 12 revolutions while the hour hand completes 1 revolution. The minute hand gains 11 full revolutions over the hour hand. During this process, the hands coincide (0\u00b0 apart) 11 times and are opposite (180\u00b0 apart) 11 times. The hands are 180\u00b0 apart once in every hour interval, except for the interval between 6 o'clock and 7 o'clock, where they are 180\u00b0 apart exactly at 6 o'clock. The 6 o'clock position is counted in both the 5-6 interval and the 6-7 interval if we consider specific time points, but considering distinct occurrences in a 12-hour cycle, it happens 11 times. For example, between 12 pm and 12 am, the hands are opposite at approximately 12:33, 1:38, 2:44, 3:49, 4:55, 6:00, 7:05, 8:11, 9:16, 10:22, 11:27. (These are approximate times, the exact times are fractions). This is 11 distinct times in a 12-hour period. A full day is 24 hours, which consists of two 12-hour periods. Therefore, in 24 hours, the hands will be straight (180\u00b0 apart) 11 times + 11 times = 22 times.\" \/>\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\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"How many times in a day are the hour hand and the minute hand of a wal\" \/>\n<meta property=\"og:description\" content=\"The hour hand and the minute hand of a wall clock are straight (180\u00b0 apart) 22 times in a day (24 hours). In a 12-hour period, the minute hand completes 12 revolutions while the hour hand completes 1 revolution. The minute hand gains 11 full revolutions over the hour hand. During this process, the hands coincide (0\u00b0 apart) 11 times and are opposite (180\u00b0 apart) 11 times. The hands are 180\u00b0 apart once in every hour interval, except for the interval between 6 o'clock and 7 o'clock, where they are 180\u00b0 apart exactly at 6 o'clock. The 6 o'clock position is counted in both the 5-6 interval and the 6-7 interval if we consider specific time points, but considering distinct occurrences in a 12-hour cycle, it happens 11 times. For example, between 12 pm and 12 am, the hands are opposite at approximately 12:33, 1:38, 2:44, 3:49, 4:55, 6:00, 7:05, 8:11, 9:16, 10:22, 11:27. (These are approximate times, the exact times are fractions). This is 11 distinct times in a 12-hour period. A full day is 24 hours, which consists of two 12-hour periods. Therefore, in 24 hours, the hands will be straight (180\u00b0 apart) 11 times + 11 times = 22 times.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/\" \/>\n<meta property=\"og:site_name\" content=\"MCQ and Quiz for Exams\" \/>\n<meta property=\"article:published_time\" content=\"2025-06-01T11:27:15+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=\"2 minutes\" \/>\n<!-- \/ Yoast SEO Premium plugin. -->","yoast_head_json":{"title":"How many times in a day are the hour hand and the minute hand of a wal","description":"The hour hand and the minute hand of a wall clock are straight (180\u00b0 apart) 22 times in a day (24 hours). In a 12-hour period, the minute hand completes 12 revolutions while the hour hand completes 1 revolution. The minute hand gains 11 full revolutions over the hour hand. During this process, the hands coincide (0\u00b0 apart) 11 times and are opposite (180\u00b0 apart) 11 times. The hands are 180\u00b0 apart once in every hour interval, except for the interval between 6 o'clock and 7 o'clock, where they are 180\u00b0 apart exactly at 6 o'clock. The 6 o'clock position is counted in both the 5-6 interval and the 6-7 interval if we consider specific time points, but considering distinct occurrences in a 12-hour cycle, it happens 11 times. For example, between 12 pm and 12 am, the hands are opposite at approximately 12:33, 1:38, 2:44, 3:49, 4:55, 6:00, 7:05, 8:11, 9:16, 10:22, 11:27. (These are approximate times, the exact times are fractions). This is 11 distinct times in a 12-hour period. A full day is 24 hours, which consists of two 12-hour periods. Therefore, in 24 hours, the hands will be straight (180\u00b0 apart) 11 times + 11 times = 22 times.","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\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/","og_locale":"en_US","og_type":"article","og_title":"How many times in a day are the hour hand and the minute hand of a wal","og_description":"The hour hand and the minute hand of a wall clock are straight (180\u00b0 apart) 22 times in a day (24 hours). In a 12-hour period, the minute hand completes 12 revolutions while the hour hand completes 1 revolution. The minute hand gains 11 full revolutions over the hour hand. During this process, the hands coincide (0\u00b0 apart) 11 times and are opposite (180\u00b0 apart) 11 times. The hands are 180\u00b0 apart once in every hour interval, except for the interval between 6 o'clock and 7 o'clock, where they are 180\u00b0 apart exactly at 6 o'clock. The 6 o'clock position is counted in both the 5-6 interval and the 6-7 interval if we consider specific time points, but considering distinct occurrences in a 12-hour cycle, it happens 11 times. For example, between 12 pm and 12 am, the hands are opposite at approximately 12:33, 1:38, 2:44, 3:49, 4:55, 6:00, 7:05, 8:11, 9:16, 10:22, 11:27. (These are approximate times, the exact times are fractions). This is 11 distinct times in a 12-hour period. A full day is 24 hours, which consists of two 12-hour periods. Therefore, in 24 hours, the hands will be straight (180\u00b0 apart) 11 times + 11 times = 22 times.","og_url":"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/","og_site_name":"MCQ and Quiz for Exams","article_published_time":"2025-06-01T11:27:15+00:00","author":"rawan239","twitter_card":"summary_large_image","twitter_misc":{"Written by":"rawan239","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"WebPage","@id":"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/","url":"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/","name":"How many times in a day are the hour hand and the minute hand of a wal","isPartOf":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#website"},"datePublished":"2025-06-01T11:27:15+00:00","dateModified":"2025-06-01T11:27:15+00:00","author":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/#\/schema\/person\/5807dafeb27d2ec82344d6cbd6c3d209"},"description":"The hour hand and the minute hand of a wall clock are straight (180\u00b0 apart) 22 times in a day (24 hours). In a 12-hour period, the minute hand completes 12 revolutions while the hour hand completes 1 revolution. The minute hand gains 11 full revolutions over the hour hand. During this process, the hands coincide (0\u00b0 apart) 11 times and are opposite (180\u00b0 apart) 11 times. The hands are 180\u00b0 apart once in every hour interval, except for the interval between 6 o'clock and 7 o'clock, where they are 180\u00b0 apart exactly at 6 o'clock. The 6 o'clock position is counted in both the 5-6 interval and the 6-7 interval if we consider specific time points, but considering distinct occurrences in a 12-hour cycle, it happens 11 times. For example, between 12 pm and 12 am, the hands are opposite at approximately 12:33, 1:38, 2:44, 3:49, 4:55, 6:00, 7:05, 8:11, 9:16, 10:22, 11:27. (These are approximate times, the exact times are fractions). This is 11 distinct times in a 12-hour period. A full day is 24 hours, which consists of two 12-hour periods. Therefore, in 24 hours, the hands will be straight (180\u00b0 apart) 11 times + 11 times = 22 times.","breadcrumb":{"@id":"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/exam.pscnotes.com\/mcq\/how-many-times-in-a-day-are-the-hour-hand-and-the-minute-hand-of-a-wal\/#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":"How many times in a day are the hour hand and the minute hand of a wal"}]},{"@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\/92520","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=92520"}],"version-history":[{"count":0,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/posts\/92520\/revisions"}],"wp:attachment":[{"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/media?parent=92520"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/categories?post=92520"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/exam.pscnotes.com\/mcq\/wp-json\/wp\/v2\/tags?post=92520"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}