<?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:blogger='http://schemas.google.com/blogger/2008' xmlns:georss='http://www.georss.org/georss' xmlns:gd="http://schemas.google.com/g/2005" xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-4658064055379609194</id><updated>2024-09-13T13:30:38.738+01:00</updated><category term="Aptitude problems"/><category term="Pandas"/><category term="Computer related"/><category term="Electronics"/><category term="Others"/><category term="Verbal and reasoning"/><title type='text'>KKREDDYS</title><subtitle type='html'></subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><link rel='next' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default?start-index=26&amp;max-results=25'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>36</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>25</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-6150684558071081714</id><published>2020-05-29T18:57:00.003+01:00</published><updated>2021-04-06T14:53:32.754+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Dates &amp; Time - Using Pandas Library</title><content type='html'>Lets see some of methods to deal with dates and time data types using pandas:&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4ew7HMP50RYfRuIFh7nvYMaoON8Oukuj5bGl_2wyrtes84UCcNplRgeNh3GgJ69LrFSSRNwTEb95aiILxEivAXdDheywNReP8AuHQi23eI5JmpU-C4BNQ6ahNCT2gWCoxPo7lprHjn0Rd/&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;778&quot; data-original-width=&quot;500&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4ew7HMP50RYfRuIFh7nvYMaoON8Oukuj5bGl_2wyrtes84UCcNplRgeNh3GgJ69LrFSSRNwTEb95aiILxEivAXdDheywNReP8AuHQi23eI5JmpU-C4BNQ6ahNCT2gWCoxPo7lprHjn0Rd/w413-h640/Capture.JPG&quot; width=&quot;413&quot; /&gt;&lt;/a&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOzEK0Tqj5xGxsdh1P4V-eCnvKYS-1ArOpDByaNwKuyYgb3bGi-q8rPDl_F0M3qduM3z9uUjAXdgZ_oojewxV40dCgaTqRG87mKKZOoX5m2EuDe1E71yDViAUedo-jjhHFboYpDvKo87qz/&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;733&quot; data-original-width=&quot;539&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjOzEK0Tqj5xGxsdh1P4V-eCnvKYS-1ArOpDByaNwKuyYgb3bGi-q8rPDl_F0M3qduM3z9uUjAXdgZ_oojewxV40dCgaTqRG87mKKZOoX5m2EuDe1E71yDViAUedo-jjhHFboYpDvKo87qz/w470-h640/Capture.JPG&quot; width=&quot;470&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/6150684558071081714/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/dates-time-using-pandas-library.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/6150684558071081714'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/6150684558071081714'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/dates-time-using-pandas-library.html' title='Dates &amp; Time - Using Pandas Library'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4ew7HMP50RYfRuIFh7nvYMaoON8Oukuj5bGl_2wyrtes84UCcNplRgeNh3GgJ69LrFSSRNwTEb95aiILxEivAXdDheywNReP8AuHQi23eI5JmpU-C4BNQ6ahNCT2gWCoxPo7lprHjn0Rd/s72-w413-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-4341150572121999549</id><published>2020-05-27T22:35:00.004+01:00</published><updated>2021-04-06T14:53:13.343+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Merging, Joining &amp; Concat of Dataframes using Pandas Library</title><content type='html'>Some of the methods to Join, Merge &amp;amp; Concat DataFrames using Pandas Library:&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiikYOZtFS5m2o7I__to6hc_tKDx36_BrduiBINzdft8Jh3E_vCGPMHrGTbJddOZbTaWMBHIeD8Zii6EqboBnfHHuVMaOCgeBvSj4taLmSwPKIgtxXArVSTJ_cguxOwLafV8kM03rjC6fgK/&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;927&quot; data-original-width=&quot;498&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiikYOZtFS5m2o7I__to6hc_tKDx36_BrduiBINzdft8Jh3E_vCGPMHrGTbJddOZbTaWMBHIeD8Zii6EqboBnfHHuVMaOCgeBvSj4taLmSwPKIgtxXArVSTJ_cguxOwLafV8kM03rjC6fgK/w344-h640/Capture.JPG&quot; width=&quot;344&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/4341150572121999549/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/merging-joining-concat-of-dataframes.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/4341150572121999549'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/4341150572121999549'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/merging-joining-concat-of-dataframes.html' title='Merging, Joining &amp; Concat of Dataframes using Pandas Library'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiikYOZtFS5m2o7I__to6hc_tKDx36_BrduiBINzdft8Jh3E_vCGPMHrGTbJddOZbTaWMBHIeD8Zii6EqboBnfHHuVMaOCgeBvSj4taLmSwPKIgtxXArVSTJ_cguxOwLafV8kM03rjC6fgK/s72-w344-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-2699349951519380261</id><published>2020-05-27T22:33:00.003+01:00</published><updated>2021-04-06T14:52:13.374+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>GroupBy &amp; Aggregations using Pandas</title><content type='html'>Lets see some of the methods to aggregate data using pandas library:&amp;nbsp;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGgp4nXvxnItn_tU86_YWhWwQz_C0suKI9kscg4vSpHKgCP9LvaiilV2jewrK_3Xi8QWqnKFShupEvSdGDk0KVSuWpwfKtklPATfREAkk9KqS9L0P8X_Z-gc5_fl8osXMgkxD6qjBEIUK0/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;780&quot; data-original-width=&quot;524&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGgp4nXvxnItn_tU86_YWhWwQz_C0suKI9kscg4vSpHKgCP9LvaiilV2jewrK_3Xi8QWqnKFShupEvSdGDk0KVSuWpwfKtklPATfREAkk9KqS9L0P8X_Z-gc5_fl8osXMgkxD6qjBEIUK0/w430-h640/Capture.JPG&quot; width=&quot;430&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/2699349951519380261/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/groupby-aggregations-using-pandas.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2699349951519380261'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2699349951519380261'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/groupby-aggregations-using-pandas.html' title='GroupBy &amp; Aggregations using Pandas'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiGgp4nXvxnItn_tU86_YWhWwQz_C0suKI9kscg4vSpHKgCP9LvaiilV2jewrK_3Xi8QWqnKFShupEvSdGDk0KVSuWpwfKtklPATfREAkk9KqS9L0P8X_Z-gc5_fl8osXMgkxD6qjBEIUK0/s72-w430-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-2376611227247466368</id><published>2020-05-25T22:24:00.003+01:00</published><updated>2021-04-06T14:50:49.711+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>MultiIndex in Pandas DataFrame</title><content type='html'>&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSifFK9y6V0PXRPn_2_CJM9Q83M36cabuCOLEmvOIVr0qWccaIrQ5IWNKY9ceVbR64lAtK0r86Mlzv1HnN1LqYYeAJH23ttGCBwmvf59bhc3bJBSea82sMcoKfBW3TRZpt-z-sfwJNfi5i/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;769&quot; data-original-width=&quot;515&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSifFK9y6V0PXRPn_2_CJM9Q83M36cabuCOLEmvOIVr0qWccaIrQ5IWNKY9ceVbR64lAtK0r86Mlzv1HnN1LqYYeAJH23ttGCBwmvf59bhc3bJBSea82sMcoKfBW3TRZpt-z-sfwJNfi5i/w429-h640/Capture.JPG&quot; width=&quot;429&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&amp;nbsp; &amp;nbsp;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-cZ5Ofpc_Or4M82rIDqOAc5Ek3BqyA-54ppqOoXNrMoqz4_pepko-c5pk7A_HcrZaqvRsiDaNirbx11QWn9R3ur-3HAUkETeiNnhW3Ya_rwkxmq1_uDnpA8EVJlZf9GTZFHZHW5fnGfrC/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;720&quot; data-original-width=&quot;513&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj-cZ5Ofpc_Or4M82rIDqOAc5Ek3BqyA-54ppqOoXNrMoqz4_pepko-c5pk7A_HcrZaqvRsiDaNirbx11QWn9R3ur-3HAUkETeiNnhW3Ya_rwkxmq1_uDnpA8EVJlZf9GTZFHZHW5fnGfrC/w456-h640/Capture.JPG&quot; width=&quot;456&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/2376611227247466368/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/multiindex-in-pandas-dataframe.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2376611227247466368'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2376611227247466368'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/multiindex-in-pandas-dataframe.html' title='MultiIndex in Pandas DataFrame'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhSifFK9y6V0PXRPn_2_CJM9Q83M36cabuCOLEmvOIVr0qWccaIrQ5IWNKY9ceVbR64lAtK0r86Mlzv1HnN1LqYYeAJH23ttGCBwmvf59bhc3bJBSea82sMcoKfBW3TRZpt-z-sfwJNfi5i/s72-w429-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-959880985660291515</id><published>2020-05-25T22:22:00.003+01:00</published><updated>2021-04-06T14:48:54.825+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Working with Text data using Pandas</title><content type='html'>Lets see some of methods to work on string columns using Pandas library:&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx22FpGJ128jmMqujoLxPqUtUGwdwY_mTmVw3N9YMdgWlBky1j0xRgPwI3VzceqDoZw0gzS6zBbVMLKqfNMApSCxgCZVlw2gjx-zgsCvpGLDElORgpivR8N_W2e4Y3P0_lNunVlWf9qIJi/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;657&quot; data-original-width=&quot;505&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx22FpGJ128jmMqujoLxPqUtUGwdwY_mTmVw3N9YMdgWlBky1j0xRgPwI3VzceqDoZw0gzS6zBbVMLKqfNMApSCxgCZVlw2gjx-zgsCvpGLDElORgpivR8N_W2e4Y3P0_lNunVlWf9qIJi/w493-h640/Capture.JPG&quot; width=&quot;493&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/959880985660291515/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/working-with-text-data-using-pandas.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/959880985660291515'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/959880985660291515'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/working-with-text-data-using-pandas.html' title='Working with Text data using Pandas'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgx22FpGJ128jmMqujoLxPqUtUGwdwY_mTmVw3N9YMdgWlBky1j0xRgPwI3VzceqDoZw0gzS6zBbVMLKqfNMApSCxgCZVlw2gjx-zgsCvpGLDElORgpivR8N_W2e4Y3P0_lNunVlWf9qIJi/s72-w493-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-2633305277781713092</id><published>2020-05-24T17:16:00.001+01:00</published><updated>2021-04-06T14:47:02.925+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Selection, Filtering &amp; Renaming - Pandas Dataframe</title><content type='html'>Some of the methods to Select/Filter/rename on columns/rows:&amp;nbsp;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp5X7s-abERG83AtWXnd8nwTKJO7bPPzMFuMqNaX3IJM8I6VEbEDCG01V9M_X4a8aML12oE2rnODGXfvYnBh7ux3fCBHR5Qp_Fj3_Dxjr_dEeLRDClc2gOvjokmTnuIYIhFtloWgVZSCiz/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;571&quot; data-original-width=&quot;578&quot; height=&quot;632&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp5X7s-abERG83AtWXnd8nwTKJO7bPPzMFuMqNaX3IJM8I6VEbEDCG01V9M_X4a8aML12oE2rnODGXfvYnBh7ux3fCBHR5Qp_Fj3_Dxjr_dEeLRDClc2gOvjokmTnuIYIhFtloWgVZSCiz/w640-h632/Capture.JPG&quot; width=&quot;640&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj50yaytEvp1jVZG2u7gpdr6JEyxzzppAxGuxjXvINy2w0K2jKvQUVnrVcGbGOZEhgsjeqp_7kcf9frXmTGPHhxpR5CVvguZZ0iyrsAOYYZmhhZ45hyV_THXz508VTZRaR_MVbM4hVuMTBt/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;735&quot; data-original-width=&quot;545&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEj50yaytEvp1jVZG2u7gpdr6JEyxzzppAxGuxjXvINy2w0K2jKvQUVnrVcGbGOZEhgsjeqp_7kcf9frXmTGPHhxpR5CVvguZZ0iyrsAOYYZmhhZ45hyV_THXz508VTZRaR_MVbM4hVuMTBt/s16000/Capture.JPG&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/2633305277781713092/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/selection-filtering-renaming-pandas.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2633305277781713092'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2633305277781713092'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/selection-filtering-renaming-pandas.html' title='Selection, Filtering &amp; Renaming - Pandas Dataframe'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjp5X7s-abERG83AtWXnd8nwTKJO7bPPzMFuMqNaX3IJM8I6VEbEDCG01V9M_X4a8aML12oE2rnODGXfvYnBh7ux3fCBHR5Qp_Fj3_Dxjr_dEeLRDClc2gOvjokmTnuIYIhFtloWgVZSCiz/s72-w640-h632-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-1056475969444404890</id><published>2020-05-24T17:12:00.002+01:00</published><updated>2021-04-06T14:44:44.479+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Continuation on Pandas Data frame</title><content type='html'>lets see some of methods to get familiar with Padas Dataframe:&lt;div&gt;&lt;br /&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbNE7zC8l9TrKnfiaf49lwwYHzbiA-woZ3AZvE1Nbny8JTt0FUGZna3Gdy08PM4jjU6CBVx58tn4fvKUAbETJVcV-PMo-hLouAutPmidn4E6MqgHvPS_UvEUIhtM4SUQTn0AADamEYD-EA/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;935&quot; data-original-width=&quot;498&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbNE7zC8l9TrKnfiaf49lwwYHzbiA-woZ3AZvE1Nbny8JTt0FUGZna3Gdy08PM4jjU6CBVx58tn4fvKUAbETJVcV-PMo-hLouAutPmidn4E6MqgHvPS_UvEUIhtM4SUQTn0AADamEYD-EA/w341-h640/Capture.JPG&quot; width=&quot;341&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;br /&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/1056475969444404890/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/continuation-on-pandas-data-frame.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/1056475969444404890'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/1056475969444404890'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/continuation-on-pandas-data-frame.html' title='Continuation on Pandas Data frame'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjbNE7zC8l9TrKnfiaf49lwwYHzbiA-woZ3AZvE1Nbny8JTt0FUGZna3Gdy08PM4jjU6CBVx58tn4fvKUAbETJVcV-PMo-hLouAutPmidn4E6MqgHvPS_UvEUIhtM4SUQTn0AADamEYD-EA/s72-w341-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-4297008012844618425</id><published>2020-05-19T22:45:00.005+01:00</published><updated>2021-04-06T14:41:06.188+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Introduction to Pandas Dataframe</title><content type='html'>&lt;font size=&quot;2&quot;&gt;Pandas Dataframe and some of its methods:&lt;/font&gt;&lt;br /&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4UvYqYeCPoCi6TGJMKF8HUiEZ4mUapKS1BFMhunXuDbr-qQCsuQu1yJ9zT_WxeS86EEBZ3NRKYN7QFFZDXyG2wtJkz6WndZQ7U-iEIVMMMUnTiZy_w-riHtash-Z0fxxN2fMBP9gT8hj3/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;745&quot; data-original-width=&quot;490&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4UvYqYeCPoCi6TGJMKF8HUiEZ4mUapKS1BFMhunXuDbr-qQCsuQu1yJ9zT_WxeS86EEBZ3NRKYN7QFFZDXyG2wtJkz6WndZQ7U-iEIVMMMUnTiZy_w-riHtash-Z0fxxN2fMBP9gT8hj3/w422-h640/Capture.JPG&quot; width=&quot;422&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;br /&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglB10hkT38HoLpJQ2ws4WuPNKebiFg4nL2g4_7SLCQCtrqzrhO-HVWAOjAtIEOE56QhQK3zNBXshCS95f5jhOzbtwLvOoa5bPIhIZm6JueMNIn3AjU71v5ooi_z6PMtn1tha8Fk2OT4Tfy/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;707&quot; data-original-width=&quot;530&quot; height=&quot;640&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEglB10hkT38HoLpJQ2ws4WuPNKebiFg4nL2g4_7SLCQCtrqzrhO-HVWAOjAtIEOE56QhQK3zNBXshCS95f5jhOzbtwLvOoa5bPIhIZm6JueMNIn3AjU71v5ooi_z6PMtn1tha8Fk2OT4Tfy/w480-h640/Capture.JPG&quot; width=&quot;480&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: left;&quot;&gt;Let me know your comments on this!!&lt;/div&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;br /&gt;&lt;/div&gt;&lt;div&gt;&lt;br /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/4297008012844618425/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2020/05/blog-post.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/4297008012844618425'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/4297008012844618425'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2020/05/blog-post.html' title='Introduction to Pandas Dataframe'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg4UvYqYeCPoCi6TGJMKF8HUiEZ4mUapKS1BFMhunXuDbr-qQCsuQu1yJ9zT_WxeS86EEBZ3NRKYN7QFFZDXyG2wtJkz6WndZQ7U-iEIVMMMUnTiZy_w-riHtash-Z0fxxN2fMBP9gT8hj3/s72-w422-h640-c/Capture.JPG" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-4355976123782095343</id><published>2020-05-17T23:09:00.007+01:00</published><updated>2021-04-06T14:37:54.392+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Pandas"/><title type='text'>Introduction to PANDAS, JUPYTER NOTEBOOK &amp; Series</title><content type='html'>&lt;h3 style=&quot;text-align: left;&quot;&gt;&lt;b style=&quot;font-family: georgia; font-size: small;&quot;&gt;Lets start introduction to Anaconda prompt by looking into below commands which will help in creating environments, installing libraries etc.&amp;nbsp;&lt;/b&gt;&lt;/h3&gt;&lt;div&gt;&lt;font face=&quot;georgia&quot; size=&quot;2&quot;&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTLg2DHjn-uVsaHMoPoqvSaRWWGYpwRxmyjaw2E4ZLDKaj8_y0GuLgoLy-kHIVjG6fOjFEMHEYwcKAUNF5IrvxS_wC7y4Vr3eDOK_eZ-DK-NzgmbE9pmvwTnrjHjnMQMDl_d0GXe7q304H/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;490&quot; data-original-width=&quot;527&quot; height=&quot;373&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiTLg2DHjn-uVsaHMoPoqvSaRWWGYpwRxmyjaw2E4ZLDKaj8_y0GuLgoLy-kHIVjG6fOjFEMHEYwcKAUNF5IrvxS_wC7y4Vr3eDOK_eZ-DK-NzgmbE9pmvwTnrjHjnMQMDl_d0GXe7q304H/w400-h373/Capture.JPG&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;b&gt;Here are some of shortcuts in jupyter notebook:&lt;/b&gt;&lt;/font&gt;&lt;/div&gt;&lt;div&gt;&lt;font face=&quot;georgia&quot; size=&quot;2&quot;&gt;&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxD2FM42z-1OfLdEtIq2jEJly53OTQh48BiCIb_ZDQcHZ7nIDj_jxb_ZqGxuJwSbEyaHMQrgARBMNZuzIMFwwrVzHHK1G0h4O-5vBlNe43SaOYIYB8eALKd4DcIcPUrdC8CelRJ1_0o9yu/&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; data-original-height=&quot;519&quot; data-original-width=&quot;659&quot; height=&quot;315&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgxD2FM42z-1OfLdEtIq2jEJly53OTQh48BiCIb_ZDQcHZ7nIDj_jxb_ZqGxuJwSbEyaHMQrgARBMNZuzIMFwwrVzHHK1G0h4O-5vBlNe43SaOYIYB8eALKd4DcIcPUrdC8CelRJ1_0o9yu/w400-h315/Capture.JPG&quot; width=&quot;400&quot; /&gt;&lt;/a&gt;&lt;/div&gt;&lt;b&gt;Lets start with pandas series with various methods and its uses:&lt;/b&gt;&lt;/font&gt;&lt;/div&gt;&lt;div&gt;&lt;font face=&quot;georgia&quot; 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style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCDa_riAalY466JwR5zdTUqso-ERw9LP0W6jtvQf_bSvlm_zYvmcY2RhQoVHkTl80_NTEFj8mMYZtc8qF6QvJYZNuID__xvIKXtr0ULDb1zpmjt_MpLII2T_yeo4NcbwHd45kTAYyM49Pq/s1600/DSC_0213-1.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCDa_riAalY466JwR5zdTUqso-ERw9LP0W6jtvQf_bSvlm_zYvmcY2RhQoVHkTl80_NTEFj8mMYZtc8qF6QvJYZNuID__xvIKXtr0ULDb1zpmjt_MpLII2T_yeo4NcbwHd45kTAYyM49Pq/s640/DSC_0213-1.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/3562475306018557564/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/ratio-proportion-variation-3.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3562475306018557564'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3562475306018557564'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/ratio-proportion-variation-3.html' title='Ratio proportion variation-3'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiCDa_riAalY466JwR5zdTUqso-ERw9LP0W6jtvQf_bSvlm_zYvmcY2RhQoVHkTl80_NTEFj8mMYZtc8qF6QvJYZNuID__xvIKXtr0ULDb1zpmjt_MpLII2T_yeo4NcbwHd45kTAYyM49Pq/s72-c/DSC_0213-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-7122050272614150116</id><published>2013-08-17T18:10:00.005+01:00</published><updated>2013-08-17T18:14:39.468+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Special calculations-1</title><content type='html'>&lt;div class=&#39;separator&#39; style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW0oUAdLXU9-0j2_iCWZX3IZSudb3FkXUGXAiI8M0Ikyb5WiMSXjwgsnqO4wzRkA5StF7Bgouwk2HgEdI9EBJfowpDNo5xapMbJTB-ZtLztbGY1Tf8gPY3VHiSAm1tJVtxlX_rT4EfsYYq/s1600/DSC_0207-1.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW0oUAdLXU9-0j2_iCWZX3IZSudb3FkXUGXAiI8M0Ikyb5WiMSXjwgsnqO4wzRkA5StF7Bgouwk2HgEdI9EBJfowpDNo5xapMbJTB-ZtLztbGY1Tf8gPY3VHiSAm1tJVtxlX_rT4EfsYYq/s640/DSC_0207-1.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/7122050272614150116/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/special-calculations-1.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7122050272614150116'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7122050272614150116'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/special-calculations-1.html' title='Special calculations-1'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEiW0oUAdLXU9-0j2_iCWZX3IZSudb3FkXUGXAiI8M0Ikyb5WiMSXjwgsnqO4wzRkA5StF7Bgouwk2HgEdI9EBJfowpDNo5xapMbJTB-ZtLztbGY1Tf8gPY3VHiSAm1tJVtxlX_rT4EfsYYq/s72-c/DSC_0207-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-3957731950886653673</id><published>2013-08-17T18:10:00.003+01:00</published><updated>2013-08-17T18:14:39.464+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Multiplying numbers shortcuts -1</title><content type='html'>&lt;div class=&#39;separator&#39; style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilY_0WVUDGbNMvqC3LuTJQnGOUGypkG9aDFz9A0fsa44_3lmeHXQcCYYtOVUDZIe8_iASuaxCv3O-IWtavKAy0NSbgg77mOP-sdZRTbPKNuFyDebYc_2F5O5oZaNqof5JTZXT92hJjClTZ/s1600/DSC_0211-1.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilY_0WVUDGbNMvqC3LuTJQnGOUGypkG9aDFz9A0fsa44_3lmeHXQcCYYtOVUDZIe8_iASuaxCv3O-IWtavKAy0NSbgg77mOP-sdZRTbPKNuFyDebYc_2F5O5oZaNqof5JTZXT92hJjClTZ/s640/DSC_0211-1.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/3957731950886653673/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/multiplying-numbers-shortcuts-1.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3957731950886653673'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3957731950886653673'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/multiplying-numbers-shortcuts-1.html' title='Multiplying numbers shortcuts -1'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEilY_0WVUDGbNMvqC3LuTJQnGOUGypkG9aDFz9A0fsa44_3lmeHXQcCYYtOVUDZIe8_iASuaxCv3O-IWtavKAy0NSbgg77mOP-sdZRTbPKNuFyDebYc_2F5O5oZaNqof5JTZXT92hJjClTZ/s72-c/DSC_0211-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-7312951464700907111</id><published>2013-08-17T18:10:00.001+01:00</published><updated>2013-08-17T18:14:39.469+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Numbers-2 shortcuts</title><content type='html'>&lt;div class=&#39;separator&#39; style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3-ZvdgT9gY0ZuPu9X5vItDzVAgv7MUvP2bVm6OxGQprUbjuASF5044yDbtgQ4uJyen2zciNnc74xhGoTo-nf8JtMTGb7Z1fYCWe74sGsMNp61NM84vtl2yzaxaFL4Yz8fEnc8fAMSYZZp/s1600/DSC_0208-1.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3-ZvdgT9gY0ZuPu9X5vItDzVAgv7MUvP2bVm6OxGQprUbjuASF5044yDbtgQ4uJyen2zciNnc74xhGoTo-nf8JtMTGb7Z1fYCWe74sGsMNp61NM84vtl2yzaxaFL4Yz8fEnc8fAMSYZZp/s640/DSC_0208-1.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/7312951464700907111/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/numbers-2-shortcuts.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7312951464700907111'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7312951464700907111'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/numbers-2-shortcuts.html' title='Numbers-2 shortcuts'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi3-ZvdgT9gY0ZuPu9X5vItDzVAgv7MUvP2bVm6OxGQprUbjuASF5044yDbtgQ4uJyen2zciNnc74xhGoTo-nf8JtMTGb7Z1fYCWe74sGsMNp61NM84vtl2yzaxaFL4Yz8fEnc8fAMSYZZp/s72-c/DSC_0208-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-3042863815768865662</id><published>2013-08-17T17:59:00.001+01:00</published><updated>2013-08-17T18:14:39.463+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Multiplying numbers shortcuts -2</title><content type='html'>&lt;div class=&#39;separator&#39; style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAPpgKLbw0C318OSmMzkqQx8fR8ikH6whsjt2hM7ztNkp8kYdca-LGl8E4cpWlAiBOx-X864Mjik8z2yN1GOVDY9SRsT0j7B5-2rSVTJXrSd8H0M0RlXSugTEw7yhUPrgQJC_P3PzZv_PC/s1600/DSC_0204-1.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAPpgKLbw0C318OSmMzkqQx8fR8ikH6whsjt2hM7ztNkp8kYdca-LGl8E4cpWlAiBOx-X864Mjik8z2yN1GOVDY9SRsT0j7B5-2rSVTJXrSd8H0M0RlXSugTEw7yhUPrgQJC_P3PzZv_PC/s640/DSC_0204-1.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/3042863815768865662/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/multiplying-numbers-shortcuts-2.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3042863815768865662'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3042863815768865662'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/multiplying-numbers-shortcuts-2.html' title='Multiplying numbers shortcuts -2'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhAPpgKLbw0C318OSmMzkqQx8fR8ikH6whsjt2hM7ztNkp8kYdca-LGl8E4cpWlAiBOx-X864Mjik8z2yN1GOVDY9SRsT0j7B5-2rSVTJXrSd8H0M0RlXSugTEw7yhUPrgQJC_P3PzZv_PC/s72-c/DSC_0204-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-8169243182663401550</id><published>2013-08-17T17:57:00.001+01:00</published><updated>2013-08-17T18:14:39.471+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Numbers-1 shortcuts</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqKETa4kNE3KPIogmQo0a7PzK2THKQcSsKaOGOrq1cNSvaHooIzqrR-NxybpxoxTh9F-GFosw8uSwp8wmx5IzgzDjAgT0G-xg9YEvpSfQP7vBMscoKBuK4nklStJDQR07NMv53M_ucID8Z/s1600/DSC_0215-1.jpg&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt; &lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqKETa4kNE3KPIogmQo0a7PzK2THKQcSsKaOGOrq1cNSvaHooIzqrR-NxybpxoxTh9F-GFosw8uSwp8wmx5IzgzDjAgT0G-xg9YEvpSfQP7vBMscoKBuK4nklStJDQR07NMv53M_ucID8Z/s640/DSC_0215-1.jpg&quot; /&gt; &lt;/a&gt; &lt;/div&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/8169243182663401550/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/numbers-shortcuts.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/8169243182663401550'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/8169243182663401550'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/numbers-shortcuts.html' title='Numbers-1 shortcuts'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjqKETa4kNE3KPIogmQo0a7PzK2THKQcSsKaOGOrq1cNSvaHooIzqrR-NxybpxoxTh9F-GFosw8uSwp8wmx5IzgzDjAgT0G-xg9YEvpSfQP7vBMscoKBuK4nklStJDQR07NMv53M_ucID8Z/s72-c/DSC_0215-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-2085831154238846291</id><published>2013-08-17T17:53:00.001+01:00</published><updated>2013-08-17T18:14:39.461+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Ratio proportion variation-2</title><content type='html'>&lt;div class=&#39;separator&#39; style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieQee4v5GRmGBpEfkAWm8beKbWB6jFh-br_f-wjkShnzxqIVkTfgVc5BLXTThusbsIcAytWKyNxmeVdYJf6LWyX02ejd_fA9gFoARX1rnJ4Alsf6e-PCfSXKJBABM21Hs8eS_uL45EhGOM/s1600/IMG_20130817_221328.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieQee4v5GRmGBpEfkAWm8beKbWB6jFh-br_f-wjkShnzxqIVkTfgVc5BLXTThusbsIcAytWKyNxmeVdYJf6LWyX02ejd_fA9gFoARX1rnJ4Alsf6e-PCfSXKJBABM21Hs8eS_uL45EhGOM/s640/IMG_20130817_221328.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/2085831154238846291/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/ratio-proportion-variation-2.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2085831154238846291'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2085831154238846291'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/ratio-proportion-variation-2.html' title='Ratio proportion variation-2'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEieQee4v5GRmGBpEfkAWm8beKbWB6jFh-br_f-wjkShnzxqIVkTfgVc5BLXTThusbsIcAytWKyNxmeVdYJf6LWyX02ejd_fA9gFoARX1rnJ4Alsf6e-PCfSXKJBABM21Hs8eS_uL45EhGOM/s72-c/IMG_20130817_221328.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-6065882205816497472</id><published>2013-08-17T17:50:00.001+01:00</published><updated>2013-08-17T18:14:39.466+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Ratio proportion variation-1 shortcuts</title><content type='html'>&lt;p&gt;Hi...&lt;br&gt;
Find the image&lt;/p&gt;
&lt;div class=&#39;separator&#39; style=&#39;clear: both; text-align: center;&#39;&gt; &lt;a href=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivKnnQJowXZSD5AwWzgckCngfQHJNgI4j0RDTUrvBqSwf8rIkBWlhE8ae-LInarDJdI7e4N6zWcN3kA6NBuC3tCKK8gcGiLLWCt0KbeetMUeOReKOU-l5ChW1l61Lo0AVOcpY_XQwjUvjH/s1600/DSC_0203-1.jpg&#39; imageanchor=&#39;1&#39; style=&#39;margin-left: 1em; margin-right: 1em;&#39;&gt; &lt;img border=&#39;0&#39; src=&#39;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivKnnQJowXZSD5AwWzgckCngfQHJNgI4j0RDTUrvBqSwf8rIkBWlhE8ae-LInarDJdI7e4N6zWcN3kA6NBuC3tCKK8gcGiLLWCt0KbeetMUeOReKOU-l5ChW1l61Lo0AVOcpY_XQwjUvjH/s640/DSC_0203-1.jpg&#39; /&gt; &lt;/a&gt; &lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/6065882205816497472/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2013/08/ratio-proportion-variation-shortcuts.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/6065882205816497472'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/6065882205816497472'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2013/08/ratio-proportion-variation-shortcuts.html' title='Ratio proportion variation-1 shortcuts'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEivKnnQJowXZSD5AwWzgckCngfQHJNgI4j0RDTUrvBqSwf8rIkBWlhE8ae-LInarDJdI7e4N6zWcN3kA6NBuC3tCKK8gcGiLLWCt0KbeetMUeOReKOU-l5ChW1l61Lo0AVOcpY_XQwjUvjH/s72-c/DSC_0203-1.jpg" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-3417727466581642125</id><published>2012-12-23T14:19:00.000+00:00</published><updated>2013-08-17T18:09:52.774+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Computer related"/><title type='text'>How to unhide files in a folder</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;ol style=&quot;text-align: left;&quot;&gt;
&lt;li&gt;Enter into command prompt by clicking into Accessories-&amp;gt;Command Prompt&lt;/li&gt;
&lt;li&gt;Enter into select drive by typing the drive letter:&lt;/li&gt;
&lt;li&gt;Then type &quot;attrib -a -s -h -r /s /d /l&quot; without semicolon.&lt;/li&gt;
&lt;li&gt;Your problem is solved&lt;/li&gt;
&lt;/ol&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/3417727466581642125/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/12/how-to-unhide-files-in-folder.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3417727466581642125'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/3417727466581642125'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/12/how-to-unhide-files-in-folder.html' title='How to unhide files in a folder'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-308154930338148404</id><published>2012-11-27T03:28:00.002+00:00</published><updated>2012-11-27T06:53:25.286+00:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Computer related"/><title type='text'>How to find the IP or MAC address of a computer</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
Every computer has unique IP and MAC address. So let us know how to find the IP and MAC address of a computer.........&lt;br /&gt;
&lt;br /&gt;
In Windows XP&lt;br /&gt;
&lt;ol style=&quot;text-align: left;&quot;&gt;
&lt;li&gt;Click on &lt;span style=&quot;color: blue;&quot;&gt;start&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Click on &lt;span style=&quot;color: blue;&quot;&gt;run&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Type &lt;span style=&quot;color: blue;&quot;&gt;cmd&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Type &lt;span style=&quot;color: blue;&quot;&gt;ipconfig/all&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;&lt;span style=&quot;color: blue;&quot;&gt;IPv4 address&lt;/span&gt; gives the IP address of your computer&lt;/li&gt;
&lt;li&gt;&lt;span style=&quot;color: blue;&quot;&gt;Physical address&lt;/span&gt; gives the MAC address of your computer&lt;/li&gt;
&lt;/ol&gt;
In Windows Vista/7/8&lt;br /&gt;
&lt;ol&gt;
&lt;li&gt;Click on &lt;span style=&quot;color: blue;&quot;&gt;start&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Go to all&lt;span style=&quot;color: blue;&quot;&gt; programs&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Click on &lt;span style=&quot;color: blue;&quot;&gt;accessories&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Click on &lt;span style=&quot;color: blue;&quot;&gt;Command Prompt&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;Type &lt;span style=&quot;color: blue;&quot;&gt;ipconfig/all&lt;/span&gt;&lt;/li&gt;
&lt;li&gt;&lt;span style=&quot;color: blue;&quot;&gt;IPv4 address&lt;/span&gt; gives the IP address of your computer&lt;/li&gt;
&lt;li&gt;&lt;span style=&quot;color: blue;&quot;&gt;Physical address&lt;/span&gt; gives the MAC address of your computer&lt;/li&gt;
&lt;/ol&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/308154930338148404/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/11/how-to-find-ip-or-mac-address-of.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/308154930338148404'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/308154930338148404'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/11/how-to-find-ip-or-mac-address-of.html' title='How to find the IP or MAC address of a computer'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-1888377374355704793</id><published>2012-10-31T05:29:00.000+00:00</published><updated>2012-11-04T11:15:38.787+00:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Computer related"/><title type='text'>c programs asked in interviews</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
Recently I have&amp;nbsp;goggled&amp;nbsp;about programs asked in interview....and I found this website where both questions and answers were given&lt;br /&gt;
&lt;br /&gt;
for c programs asked in interviews&lt;br /&gt;
&lt;br /&gt;
there are several sites &amp;nbsp;1)&amp;nbsp;&lt;a href=&quot;http://www.interview-made-easy.com/2008/06/c-programs-frequently-asked-in.html&quot; target=&quot;_blank&quot;&gt;click here&amp;nbsp;&lt;/a&gt;&lt;br /&gt;
&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; 2) &lt;a href=&quot;http://techforum4u.com/entry.php/1321-Important-C-Programs-Asked-in-Interviews&quot;&gt;click here&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
For complete details on C visit &lt;a href=&quot;http://cwithabhas.blogspot.in/&quot;&gt;here&lt;/a&gt;&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;
&lt;br /&gt;&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/1888377374355704793/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/10/c-programs-asked-in-interviews.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/1888377374355704793'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/1888377374355704793'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/10/c-programs-asked-in-interviews.html' title='c programs asked in interviews'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-7479770988257382924</id><published>2012-10-27T14:09:00.000+01:00</published><updated>2012-10-27T14:54:41.740+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Electronics"/><title type='text'>How resistive Touch Screen Works??</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
A touch screen is an electronic visual display that can detect presence and location of touch within the display area...&lt;br /&gt;
&lt;br /&gt;
It is a two dimensional sensing device that is made of two sheets of material separated by small spacers. There are three main touch screen technologies viz., resistive, capacitive and surface acoustic wave. Here i will discuss about resistive touch screen&lt;br /&gt;
&lt;br /&gt;
Resistive touch screen:&lt;br /&gt;
&lt;br /&gt;
The resistive touch screen consists of flexible top layer made of polythene and rigid bottom layer made of glass. Both the layers are spaced with spacers and are coated with indium tin oxide. When the screen is operating a small current flows in between the space. When a touch is made, the flexible screen presses down to touch the glass layer. A change in current is hence detected and coordinates of the point of touch calculated by the controller and parsed into readable signal for the operating system to react accordingly.&lt;br /&gt;
&lt;br /&gt;
&lt;div class=&quot;separator&quot; style=&quot;clear: both; text-align: center;&quot;&gt;
&lt;a href=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-qDKAmCHPYeJhblIyxUDHb_6uMPX3-KOPeBPBd-ZSA3Rxy_UZkDuyIfXpeYcj0em9cdiRedGvrrDDjhrjh2WdpT_BfCd3A5Rppu4nbTCyouROJXrPSX2TQZdF2Vt3Ih2yZvMJ31skBUjq/s1600/resistive-touch-screen.gif&quot; imageanchor=&quot;1&quot; style=&quot;margin-left: 1em; margin-right: 1em;&quot;&gt;&lt;img border=&quot;0&quot; src=&quot;https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-qDKAmCHPYeJhblIyxUDHb_6uMPX3-KOPeBPBd-ZSA3Rxy_UZkDuyIfXpeYcj0em9cdiRedGvrrDDjhrjh2WdpT_BfCd3A5Rppu4nbTCyouROJXrPSX2TQZdF2Vt3Ih2yZvMJ31skBUjq/s1600/resistive-touch-screen.gif&quot; /&gt;&lt;/a&gt;&lt;/div&gt;
&lt;br /&gt;
&lt;br /&gt;
The four-wire resistive touch screen uses both the layers to calculate the axes information of the touch. Touch measurement is a two-step process. The x-coordinate of the touch point is calculated by creating a voltage&amp;nbsp;gradient on flexible layer, and the y-coordinate is determined by creating a voltage gradient along&amp;nbsp;&amp;nbsp;the bottom layer.&amp;nbsp;&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/7479770988257382924/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/10/how-resistive-touch-screen-works.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7479770988257382924'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7479770988257382924'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/10/how-resistive-touch-screen-works.html' title='How resistive Touch Screen Works??'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><media:thumbnail xmlns:media="http://search.yahoo.com/mrss/" url="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEh-qDKAmCHPYeJhblIyxUDHb_6uMPX3-KOPeBPBd-ZSA3Rxy_UZkDuyIfXpeYcj0em9cdiRedGvrrDDjhrjh2WdpT_BfCd3A5Rppu4nbTCyouROJXrPSX2TQZdF2Vt3Ih2yZvMJ31skBUjq/s72-c/resistive-touch-screen.gif" height="72" width="72"/><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-5926144310897630910</id><published>2012-10-17T03:34:00.001+01:00</published><updated>2012-10-17T03:35:02.206+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Shortcuts in solving aptitude-10</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;br /&gt;
&lt;div align=&quot;center&quot; class=&quot;MsoNormal&quot; style=&quot;background: white; line-height: 150%; text-align: center;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 20pt; line-height: 150%;&quot;&gt;&lt;span style=&quot;color: #0b5394;&quot;&gt;SIMPLE INTEREST COMPOUND INTEREST&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; line-height: 150%;&quot;&gt;Interest&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Interest is the ‘extra’ money
paid by the borrower to the lender for using the money for a specified&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;period of time.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Principal (P) : -&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt; The money lent or borrowed is
called the Principal.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Amount (A) : -&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt; The total money, i.e. Principal
+ Interest is called the amount.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Rate of interest (r) :-&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt; The rate at which interest is
calculated on the Principal is called the rate of interest.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; line-height: 150%;&quot;&gt;Interest is of two kinds&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;1.&amp;nbsp;&amp;nbsp;&amp;nbsp; Simple
interest (I)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;If the interest is calculated for
every time period (generally calculated yearly, half-yearly, quarter-yearly)
only on the original sum (Principal) borrowed, then such interest is called as
the simple interest.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;The interest is same for each qf
the time-periods.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;i.e. if the interest for one
time-period (if taken as a year) is I, then the interest for ‘n’
time-periods(years) is ‘nI’&amp;nbsp;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;line-height: 150%;&quot;&gt;2.&amp;nbsp;&amp;nbsp;&amp;nbsp;
Compound interest&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;In this method, at the end of
each time period, the interest is added to the principal, and this amount
becomes the new Principal for/the next time period. The amount at the end of
the second time period becomes the Principal for the third time period and so
on.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;The interest is not same for all
the time-periods, but the interest for any time period is greater than the
interest for the preceeding time-period. Compound interest (CI) = Final
amount&amp;nbsp; -&amp;nbsp;
initial principal&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;To Exercise some more problems on SI and CI visit &lt;a href=&quot;https://docs.google.com/open?id=0B3pRgpaNbNO7bUVMdHcwRWFRRUU&quot; target=&quot;_blank&quot;&gt;&lt;b&gt;&lt;i&gt;here&lt;/i&gt;&lt;/b&gt;&lt;/a&gt;&lt;/span&gt;&lt;/div&gt;
&lt;br /&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/5926144310897630910/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-10.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/5926144310897630910'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/5926144310897630910'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-10.html' title='Shortcuts in solving aptitude-10'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-2028216863618149854</id><published>2012-10-17T03:31:00.003+01:00</published><updated>2012-10-17T03:35:02.204+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Shortcuts in solving aptitude-9</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;background-color: white; line-height: 150%; text-align: left;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 20pt; line-height: 150%;&quot;&gt;&lt;span style=&quot;color: #0b5394;&quot;&gt;NUMBERS&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 23pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt;Natural numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;The
set of counting numbers 1, 2, 3, 4, …………are called as the natural numbers,
denoted by N. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: 36.0pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;N
= {1, 2, 3, ...}&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt;Whole numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;The
set of natural numbers together with the number ‘0’ is known as the set of
whole numbers, denoted by W.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: 36.0pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;W=
{0, 1,2,3, ...)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt;Integers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;The
negative whole numbers, the number &#39;0&#39; and the natural numbers together form
the set of Integers, denoted by Z.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: 36.0pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Z=
{... ­­-3, -2,– 1, 0, 1.2.3, …..}&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt;Rational numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Numbers
which can be written in the form p/q where p and q are integers and q ≠0 are
called as rational numbers, denoted by Q.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Decimal representation of
rational numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l0 level1 lfo1; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;If
a fraction (rational number) in its lowest terms has no other prime factors
except 2 and 5. we get a terminating decimal.&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l0 level1 lfo1; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;b style=&quot;line-height: 150%;&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraph&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l0 level1 lfo1; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;b style=&quot;line-height: 150%;&quot;&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp;Irrational numbers&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;The
numbers, which cannot be expressed as rational numbers is called as an
irrational number.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Note:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;Every
non-terminating, non-recurring decimal is an irrational number.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Note :&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;A
number may he a rational number or an irrational number, but! it cannot be
both.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot;&gt;Real numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;The
set of all numbers comprising rational numbers and irrational numbers is known
as the set of real numbers, denoted by R.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Note :&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l0 level1 lfo1; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;On
the number line, there is a point corresponding to every real number and to
every point on the number line, there is a real number. Hence the number line
is called the Real Number line. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l0 level1 lfo1; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Real
numbers are so called because they can be seen as points representing them on
the number line.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot;&gt;Complex numbers&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;There
is no real number, whose square is a negative number.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;E.g.
&lt;span style=&quot;mso-text-raise: -5.0pt; position: relative; top: 5.0pt;&quot;&gt;&lt;v:shapetype coordsize=&quot;21600,21600&quot; filled=&quot;f&quot; id=&quot;_x0000_t75&quot; o:preferrelative=&quot;t&quot; o:spt=&quot;75&quot; path=&quot;m@4@5l@4@11@9@11@9@5xe&quot; stroked=&quot;f&quot;&gt;
 &lt;v:stroke joinstyle=&quot;miter&quot;&gt;
 &lt;v:formulas&gt;
  &lt;v:f eqn=&quot;if lineDrawn pixelLineWidth 0&quot;&gt;
  &lt;v:f eqn=&quot;sum @0 1 0&quot;&gt;
  &lt;v:f eqn=&quot;sum 0 0 @1&quot;&gt;
  &lt;v:f eqn=&quot;prod @2 1 2&quot;&gt;
  &lt;v:f eqn=&quot;prod @3 21600 pixelWidth&quot;&gt;
  &lt;v:f eqn=&quot;prod @3 21600 pixelHeight&quot;&gt;
  &lt;v:f eqn=&quot;sum @0 0 1&quot;&gt;
  &lt;v:f eqn=&quot;prod @6 1 2&quot;&gt;
  &lt;v:f eqn=&quot;prod @7 21600 pixelWidth&quot;&gt;
  &lt;v:f eqn=&quot;sum @8 21600 0&quot;&gt;
  &lt;v:f eqn=&quot;prod @7 21600 pixelHeight&quot;&gt;
  &lt;v:f eqn=&quot;sum @10 21600 0&quot;&gt;
 &lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:f&gt;&lt;/v:formulas&gt;
 &lt;v:path gradientshapeok=&quot;t&quot; o:connecttype=&quot;rect&quot; o:extrusionok=&quot;f&quot;&gt;
 &lt;o:lock aspectratio=&quot;t&quot; v:ext=&quot;edit&quot;&gt;
&lt;/o:lock&gt;&lt;/v:path&gt;&lt;/v:stroke&gt;&lt;/v:shapetype&gt;&lt;v:shape id=&quot;_x0000_i1025&quot; o:ole=&quot;&quot; style=&quot;height: 16.5pt; width: 46.5pt;&quot; type=&quot;#_x0000_t75&quot;&gt;
 &lt;v:imagedata o:title=&quot;&quot; src=&quot;file:///C:\Users\kkreddys\AppData\Local\Temp\msohtmlclip1\01\clip_image001.wmz&quot;&gt;
&lt;/v:imagedata&gt;&lt;/v:shape&gt;&lt;!--[if gte mso 9]&gt;&lt;xml&gt;
 &lt;o:OLEObject Type=&quot;Embed&quot; ProgID=&quot;Equation.3&quot; ShapeID=&quot;_x0000_i1025&quot;
  DrawAspect=&quot;Content&quot; ObjectID=&quot;_1411965970&quot;&gt;
 &lt;/o:OLEObject&gt;
&lt;/xml&gt;&lt;![endif]--&gt;&lt;/span&gt;is not a real number.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Such
numbers are called as imaginary numbers.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;The
set of numbers comprising of real numbers and imaginary numbers is known as the
set of complex numbers, denoted by C. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;The
ordered pair (a, b) where a and b are real numbers, when expressed in the form
a + ib, is called a complex number.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-left: 36.0pt; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: 36.0pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;a is called the real part, and b
is called the imaginary part.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Note:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpFirst&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l1 level1 lfo2; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Every
real number a can be represented as a complex number, (a, 0).&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l1 level1 lfo2; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;The
complex numbers a + ib and a - ib are called conjugate complex numbers. Each is
called the conjugate of the other.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpMiddle&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l1 level1 lfo2; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;The
sum and product of two conjugate complex numbers are real.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoListParagraphCxSpLast&quot; style=&quot;line-height: 150%; mso-layout-grid-align: auto; mso-list: l1 level1 lfo2; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: -18.0pt;&quot;&gt;
&lt;!--[if !supportLists]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Wingdings; font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp; v&lt;span style=&quot;font-family: &#39;Times New Roman&#39;; font-size: 7pt; line-height: normal;&quot;&gt;&amp;nbsp; &lt;/span&gt;&lt;/span&gt;&lt;!--[endif]--&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Every
complex number can be represented as a point in the coordinate plane, by taking
real part on the x-axis and the imaginary part on the y-axis. &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;line-height: 150%; margin-left: 72.0pt; mso-layout-grid-align: auto; mso-pagination: widow-orphan; text-autospace: ideograph-numeric ideograph-other; text-indent: 36.0pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Hence, x axis is called real axis&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 9pt;&quot;&gt;y-axis
called imaginary axis.&lt;/span&gt;&lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot;&gt;
&lt;span lang=&quot;EN-US&quot;&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;background-color: white; background-position: initial initial; background-repeat: initial initial; font-family: Verdana, sans-serif; font-size: 9pt; line-height: 150%;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;background-color: white;&quot;&gt;
&lt;b&gt;&lt;span style=&quot;font-family: Verdana, sans-serif;&quot;&gt;&lt;span style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;Some of Mathematical&amp;nbsp;&lt;/span&gt;&lt;span style=&quot;font-size: 12px; line-height: 18px;&quot;&gt;formula&lt;/span&gt;&lt;span style=&quot;font-size: 9pt; line-height: 150%;&quot;&gt;&amp;nbsp;are unable to mention here...so for more visit &lt;a href=&quot;https://docs.google.com/open?id=0B3pRgpaNbNO7bTUzcm11TVlpZTQ&quot; target=&quot;_blank&quot;&gt;&lt;i&gt;here&lt;/i&gt;&lt;/a&gt;&lt;/span&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;br /&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/2028216863618149854/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-9.html#comment-form' title='1 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2028216863618149854'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/2028216863618149854'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-9.html' title='Shortcuts in solving aptitude-9'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>1</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-8856980510619549705</id><published>2012-10-17T03:26:00.001+01:00</published><updated>2012-10-17T03:26:55.698+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Shortcuts in solving aptitude-8</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: left;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 16pt;&quot;&gt;&lt;span style=&quot;color: #0b5394;&quot;&gt;Permutations and Combinations&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Formulae:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Factorial Notation:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Let n be positive integer. Then
,factorial n denoted by n!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;is defined as n! = n(n-1)(n-2).
. . .&amp;nbsp; . . .&amp;nbsp; .3.2.1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Permutations:&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;The different arrangements of a
given number of things by&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;taking some or all at a time,
are called permutations.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;e.g.:- All permutations( or
arrangements)made with the letters&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;a,b,c by taking two at a time
are (ab,ba,ac,ca,bc,cb)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Numbers of permutations:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Number of all permutations of n
things, taken r at a time is&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;given by&amp;nbsp; nPr&amp;nbsp; =
n(n-1)(n-2). .&amp;nbsp; .. . . (n-r+1)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; = n! / (n-r)!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;An Important Result:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;If there are n objects of which
p1 are alike of one kind;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;p2 are alike of another kind ;
p3 are alike of third kind and&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;so on and pr&amp;nbsp; are alike of rth kind, such that&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;(p1+p2+. . . . . . . . pr) = n&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Then, number of permutations of
these n objects is:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; n! / (p1!).(p2!). . . . .(pr!)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Combinations:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Each of different groups or
selections which can be formed by&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;taking some or all of a number
of objects, is called a combination.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp; e.g.:- Suppose we want to select two out of
three boys A,B,C .&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; then ,possible selection are AB,BC
&amp;amp; CA.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Note that AB and BA represent the same
selection.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Number of Combination:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;The number of all combination
of n things taken r at a time is:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp; nCr = n! / (r!)(n-r)!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; = n(n-1)(n-2). . . . . . . tor factors
/ r!&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Note&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;: nCn = 1 and nC0 =1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;An Important Result:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;nCr = nC(n-r)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp; &amp;nbsp;&amp;nbsp;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp; &amp;nbsp;To exercise problems regarding permutations &amp;amp; combinations visit &lt;b&gt;&lt;i&gt;&lt;a href=&quot;https://docs.google.com/open?id=0B3pRgpaNbNO7T1RleWU0b2lOMHM&quot; target=&quot;_blank&quot;&gt;here&lt;/a&gt;&lt;/i&gt;&lt;/b&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot;&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; text-align: left;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 22pt;&quot;&gt;&lt;span style=&quot;color: #0b5394;&quot;&gt;Probability&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Introduction:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Experiment:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;An operation which can produce
some well-defined outcome is called an experiment.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Random Experiment:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;An experiment in which all
possible out comes are known and the exact output cannot be predicted in
advance is called a random experiment. EX:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;1) Rolling an unbiased dice.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;2) Tossing a fair coin.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;3) Drawing a card from a pack
of well-shuffled cards .&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;4)Picking up a ball of certain color
from a bag containing balls of different colors.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Details:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;1) When we thrown a coin ,then
either a Head(H) or a Tail(T)appears.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;2)A dice is a solid cube
,having 6 faces, marked 1,2,3,4,5,6respectively. When we throw a die ,the
outcome is the number that appears on its upper face.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;3)A pack of cards has 52 cards.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;It has 13 cards of each suit, namely
spades, clubs, hearts and diamonds.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&amp;nbsp;Cards of spades and clubs are black cards.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Cards of hearts and diamonds
are red cards.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;There are four honors of each
suit.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;These are Aces, Kings, queens
and Jacks.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;These are called Face cards.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Sample Space:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;When we perform an experiment
,then the set of S of all possible outcomes is called the Sample space .&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Event: &lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Any subset of a sample space is
called an Event.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Probability of occurrence of an
Event:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Let S be the sample space.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Let E be the Event.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Then E c S i.e. E is subset of
S then&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;probability of E &amp;nbsp;p(E) =n(E)/n(S).&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Results on Probability:&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;1)P(S) =1.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;2)0 &amp;lt; P(E) &amp;lt; 1&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;probability of an event lies
between 0 and 1.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Max value of probability of an
event is one.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;3)For any events A and B we
have .&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;P(AUB) =P(A) +P(B) -P(A n B ).&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;4)If A denotes (not -A) then&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&amp;nbsp; P (A) =1-P(A)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&amp;nbsp; P(A)+P(A) =1.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt; margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot;&gt;&lt;span style=&quot;font-family: Verdana, sans-serif; font-size: x-small;&quot;&gt;To Exercise problems in&amp;nbsp;probability visit &lt;a href=&quot;https://docs.google.com/open?id=0B3pRgpaNbNO7OGRwamtWVDZmZ1E&quot; target=&quot;_blank&quot;&gt;here&lt;/a&gt;&amp;nbsp;&lt;/span&gt;&lt;/span&gt;&lt;/div&gt;
&lt;br /&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/8856980510619549705/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-8.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/8856980510619549705'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/8856980510619549705'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-8.html' title='Shortcuts in solving aptitude-8'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-4658064055379609194.post-7557607328939793017</id><published>2012-10-16T18:11:00.001+01:00</published><updated>2012-10-16T18:11:21.303+01:00</updated><category scheme="http://www.blogger.com/atom/ns#" term="Aptitude problems"/><title type='text'>Shortcuts in solving aptitude-7</title><content type='html'>&lt;div dir=&quot;ltr&quot; style=&quot;text-align: left;&quot; trbidi=&quot;on&quot;&gt;
&lt;br /&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: left;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 24pt;&quot;&gt;&lt;span style=&quot;color: #0b5394;&quot;&gt;Allegation or Mixtures&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 12pt;&quot;&gt;Important&lt;/span&gt;&lt;/b&gt;&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt; Facts and Formulae:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif;&quot;&gt; &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;1. Allegation: It is the rule
that enables us to find the Ratio in which two of more ingredients at the given
price must be mixed to produce a mixture of a desired price.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;2. Mean Price: The cost price
of a unit quantity of the mixture is called the mean price.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;3. Rule of Allegation: If two
ingredients are mixed then &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;Quantity of Cheaper / Quantity
of Dearer = (C.P of Dearer – Mean Price) /(Mean Price–C.P of Cheaper).&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;C.P of a unit quantity of
cheaper(c)&amp;nbsp;&amp;nbsp;&amp;nbsp; C.P of unit quantity of
dearer (d)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
Mean Price (m)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; (d-m)&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;
(m-c) &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp;&amp;nbsp; Cheaper quantity: Dearer quantity =
(d-m):(m-c)&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;4. Suppose a container contains
x units of liquid from which units are taken out and replaced by water. After n
Operatations the quantity of pure liquid = x (1 – y/x)n units.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;To exercise some problems on allegation or mixtures visit &lt;b&gt;&lt;i&gt;&lt;a href=&quot;https://docs.google.com/open?id=0B3pRgpaNbNO7NmNXQ29PMTlsbVU&quot; target=&quot;_blank&quot;&gt;here&lt;/a&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;b&gt;&lt;br /&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-family: Verdana, sans-serif; font-size: 10pt;&quot;&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;text-align: left;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 18pt;&quot;&gt;&lt;span style=&quot;color: #0b5394;&quot;&gt;Boats and Streams&lt;/span&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/b&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Important facts: &lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&amp;nbsp;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;1)In water, the direction along
the stream is called downstream.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;2)Direction against the stream
is called upstream.&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;3)The speed of boat in still
water is U km/hr and the speed of &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;stream is V km/hr then &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;speed downstream =U + V km/hr&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;speed up stream = U – V km/hr&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;Formulae:&lt;/span&gt;&lt;/b&gt;&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;br /&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;If the speed downstream is A
km/hr and the speed up stream is &lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;B km/hr then speed in still
water = ½(A+B) km/hr&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;rate of stream =1/2(A-B) km/hr&lt;o:p&gt;&lt;/o:p&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;&lt;br /&gt;&lt;/span&gt;&lt;/div&gt;
&lt;div class=&quot;MsoNormal&quot; style=&quot;margin-bottom: 0.0001pt;&quot;&gt;
&lt;span lang=&quot;EN-US&quot; style=&quot;font-size: 10pt;&quot;&gt;To exercise some problems on Boats and streams visit &lt;b&gt;&lt;i&gt;&lt;a href=&quot;https://docs.google.com/open?id=0B3pRgpaNbNO7b25rUG1xR0pMOTg&quot; target=&quot;_blank&quot;&gt;here&lt;/a&gt;&lt;/i&gt;&lt;/b&gt;&lt;/span&gt;&lt;/div&gt;
&lt;br /&gt;
&lt;/div&gt;
</content><link rel='replies' type='application/atom+xml' href='https://kkreddys.blogspot.com/feeds/7557607328939793017/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-7.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7557607328939793017'/><link rel='self' type='application/atom+xml' href='https://www.blogger.com/feeds/4658064055379609194/posts/default/7557607328939793017'/><link rel='alternate' type='text/html' href='https://kkreddys.blogspot.com/2012/10/shortcuts-in-solving-aptitude-7.html' title='Shortcuts in solving aptitude-7'/><author><name>Kkreddys</name><uri>http://www.blogger.com/profile/18307873945648892703</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='https://img1.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry></feed>