{"id":21079,"date":"2025-02-13T11:59:17","date_gmt":"2025-02-13T06:29:17","guid":{"rendered":"https:\/\/cracku.in\/blog\/?p=21079"},"modified":"2025-02-21T15:09:17","modified_gmt":"2025-02-21T09:39:17","slug":"cat-questions-on-factorial-pdf","status":"publish","type":"post","link":"https:\/\/cracku.in\/blog\/cat-questions-on-factorial-pdf\/","title":{"rendered":"CAT Questions on Factorial PDF"},"content":{"rendered":"<blockquote>\n<h1><span style=\"text-decoration: underline; font-size: 18pt;\"><strong>CAT Questions on Factorial PDF:<\/strong><\/span><\/h1>\n<\/blockquote>\n<p>Download CAT Questions on Factorial of a number PDF. Practice important problems with detailed explanations for CAT.<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/downloads\/1446\" target=\"_blank\" class=\"btn btn-danger  download\">Download CAT Questions on Factorial PDF<\/a><\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\" target=\"_blank\" class=\"btn btn-info \">CAT Online Coaching<\/a><\/p>\n<p>Download All <a href=\"https:\/\/cracku.in\/blog\/quantitative-aptitude-for-cat\/\" target=\"_blank\" rel=\"noopener noreferrer\">Quantitative Aptitude important Questions PDF<\/a><\/p>\n<p>Take <a href=\"https:\/\/cracku.in\/cat-mock-test\" target=\"_blank\" rel=\"noopener noreferrer\">Free Mock Test for CAT<\/a><\/p>\n<p><strong>Question 1:\u00a0\u00a0<\/strong>What is the remainder when 96! is divided by 291 ?<\/p>\n<p>a) 86<br \/>\nb) 96<br \/>\nc) 76<br \/>\nd) 66<\/p>\n<p><strong>Question 2:<\/strong> What is the remainder when $120!$ is divided by $120^{24}$ ? \u00a0?<\/p>\n<p>a) 2<br \/>\nb) 1<br \/>\nc) 0<br \/>\nd) 3<\/p>\n<p><strong>Question 3:<\/strong>\u00a0Which digit from the right end of 933! is the first non-zero digit?<\/p>\n<p>a) 300<br \/>\nb) 232<br \/>\nc) 400<br \/>\nd) 320<\/p>\n<p><strong>Question 4:<\/strong>\u00a0In which position from the right is the first non-zero digit present in 334!?<\/p>\n<p>a) 81st<br \/>\nb) 82nd<br \/>\nc) 83rd<br \/>\nd) 84th<\/p>\n<p><strong>Question 5:\u00a0<\/strong>Find the number of zeroes at the end of 179!.<\/p>\n<p>a) 32<br \/>\nb) 51<br \/>\nc) 43<br \/>\nd) 28<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/cat-mock-test\" target=\"_blank\" class=\"btn btn-danger \">CAT Mock Tests<\/a><\/p>\n<p class=\"text-center\"><a href=\"https:\/\/cracku.in\/cat-previous-papers\" target=\"_blank\" class=\"btn btn-primary \">CAT Previous year papers<\/a><\/p>\n<p><span style=\"font-size: 14pt;\"><u><strong>Answers &amp; Solutions<\/strong>:<\/u><\/span><\/p>\n<p><strong>1) Answer (B)<\/strong><\/p>\n<p>Using Wilson&#8217;s theorem, 96! + 1 is divisible by 97.<br \/>\nLet 96! + 1 be equal to 97k for some natural number k.<br \/>\nNote that 291 = 97*3.<br \/>\nHence, 96! + 1 is either 291p or 291p + 97 or 291p + 194 for some natural number p. This is because 96! + 1 is a multiple of 97.<br \/>\nWe know that 96! is divisible by 3. So, 96! + 1 leaves a remainder of 1 when divided by 3. Using this, we can conclude that 96! + 1 is of the form 291p + 96.<br \/>\nHence, 96! leaves a remainder of 96 when divided by 291.<\/p>\n<p><strong>2) Answer (C)<\/strong><\/p>\n<p>The product of any five consecutive numbers is divisible by 5!<br \/>\nSo, 1*2*3*4*5 is divisible by 120.<br \/>\nSimilarly, 6*7*8*9*10 is also divisible by 120.<br \/>\n120! can be written as (1*2*3*4*5)*(6*7*8*9*10)*&#8230;*(116*117*118*119*120)<br \/>\nEach of the 24 terms is divisible by 120<br \/>\nHence, the product is divisible by<br \/>\nSo, the remainder when 120!120! is divided by<br \/>\nis 0.<\/p>\n<p><strong>3) Answer (B)<\/strong><\/p>\n<p>Number of zeros in 933! = $\\left \\lfloor \\frac{933}{5} \\right \\rfloor + \\left \\lfloor \\frac{933}{25} \\right \\rfloor + \\left \\lfloor \\frac{933}{125} \\right \\rfloor + \\left \\lfloor \\frac{933}{625} \\right \\rfloor + \\left \\lfloor \\frac{933}{3125} \\right \\rfloor + ..$<\/p>\n<p>where $\\left \\lfloor x \\right \\rfloor$ means greatest integer less than or equal to x<\/p>\n<p>= 186 + 37 + 7 + 1 + 0<br \/>\n= 231<br \/>\n=&gt; 232nd digit from right end is the first non-zero digit.<\/p>\n<p><strong>4) Answer (B)<\/strong><\/p>\n<p>Number of zeros = $\\left \\lfloor \\frac{334}{5} \\right \\rfloor$ + $\\left \\lfloor \\frac{334}{25} \\right \\rfloor$ + $\\left \\lfloor \\frac{334}{125} \\right \\rfloor$ + $\\left \\lfloor \\frac{334}{625} \\right \\rfloor$<br \/>\n= 66 + 13 + 2 + 0<br \/>\n= 81<br \/>\n=&gt; 82nd digit is the first non-zero digit<\/p>\n<p><strong>5) Answer (C)<\/strong><\/p>\n<p>Number of zeroes in 179! = $\\left \\lfloor \\frac{179}{5} \\right \\rfloor + \\left \\lfloor \\frac{179}{5^2} \\right \\rfloor + \\left \\lfloor \\frac{179}{5^3} \\right \\rfloor + \\left \\lfloor \\frac{179}{5^4} \\right \\rfloor$<br \/>\n= 35 + 7 + 1 + 0<br \/>\n= 43<\/p>\n<p class=\"text-center\"><a href=\"https:\/\/play.google.com\/store\/apps\/details?id=in.cracku.app&amp;hl=en\" target=\"_blank\" class=\"btn btn-primary \">Top Rated APP for CAT Preparation<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>CAT Questions on Factorial PDF: Download CAT Questions on Factorial of a number PDF. Practice important problems with detailed explanations for CAT. Download All Quantitative Aptitude important Questions PDF Take Free Mock Test for CAT Question 1:\u00a0\u00a0What is the remainder when 96! is divided by 291 ? a) 86 b) 96 c) 76 d) 66 [&hellip;]<\/p>\n","protected":false},"author":34,"featured_media":21086,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"om_disable_all_campaigns":false,"_mi_skip_tracking":false,"footnotes":""},"categories":[3,169,125],"tags":[6,6106],"class_list":{"0":"post-21079","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-cat","8":"category-downloads","9":"category-featured","10":"tag-cat","11":"tag-cat-2023"},"better_featured_image":{"id":21086,"alt_text":"CAT Questions on Factorial PDF","caption":"CAT Questions on Factorial PDF","description":"CAT Questions on Factorial 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