Current Affairs 10th Class

Mensuration   We are familiar with some of the basic solids like cuboid/ cone, cylinder and sphere. In this chapter we will discuss about how to find the surface area and volume of these figures. In our daily life, we come across number of solids made up of combinations of two or more of the basic solids.   Surface Area of Solids We may get the solids which may be combinations of cylinder and cone or cylinder and hemisphere or cone and hemisphere and so on. In such cases we find the surface area of each part separately and add them to get the surface area of entire solid.   Cylinder If 'r' is the radius and 'h1 is the height of a cylinder, then Curved surface area of the cylinder = \[2\pi rh\] Total surface area of the cylinder = \[2\pi r(r+h)\]   Cone If 'r' be the radius and 'h' be the height of a cone, then Curved surface area of the cone = \[\pi rl\] Total surface area of the cone = \[\pi r(r+l)\]   Where, I is the slant height of the cone and is given by \[l=\sqrt{{{r}^{2}}+{{h}^{2}}}\]   Sphere If 'r' be the radius of a sphere, then Surface area of the sphere \[4\pi {{r}^{2}}\]   Hemisphere If 'r' be the radius of a hemisphere, then Curved surface area of the hemisphere = \[2\pi {{r}^{2}}\] Total Surface area of the hemisphere =\[3\pi {{r}^{2}}\]                                        Volume of Solids The volume of the combined figures is obtained by finding the volume of each part separately and then adding them together.   Cylinder If 'r' be the radius and 'h' be the height of a cylinder, then Volume of the cylinder = \[\pi {{r}^{2}}h\]   Cone If 'r' be the radius and 'h' be the height of a cone, then Volume of the cone =\[\frac{1}{3}\pi {{r}^{2}}h\]   Sphere If 'r' be the radius of a sphere, then Volume of a the sphere = \[\frac{4}{3}\pi {{r}^{2}}h\]   Hemisphere If 'r' be the radius of a hemisphere, then Volume of the hemisphere = \[\frac{2}{3}\pi {{r}^{2}}h\]  

•       Example:

A toy is in the form of a cone of radius 77 cm and height 36 cm. Find the area of the cardboard required to make the toy. (a) 18720\[c{{m}^{2}}\]                                               (b) 20570\[c{{m}^{2}}\]    (c) 21426\[c{{m}^{2}}\]                                               (d) 22480\[c{{m}^{2}}\] (e) None of these Ans.     (b) Explanation: Area of the cardboard required = curved surface area of the toy = \[\pi rl\] Here, \[I{{=}^{+}}\sqrt{{{r}^{2}}+{{h}^{2}}}=\sqrt{{{77}^{2}}+{{36}^{2}}}=85\] \[\therefore ~Curve\text{ }surface\text{ }area\text{ }=\text{ }\frac{22}{7}\text{ }\times \text{ }77\text{ }\times \text{ }85\text{ }=\text{ }22\text{ }\times \text{ }11\text{ }\times \text{ }85\text{ }=\text{ }20570\text{ }c{{m}^{2}}\]    

Statistics and Probability   Statistics Statistics is the branch of Mathematics which deals with the collection and interpretation of data. The data may be represented in different graphical forms such as bar graphs, histogram, ogive curve, and pie chart. This representation of data reveals certain salient features of the data. These values of the data are called measure of central tendency. The various measures of central tendencies are mean, median and mode. A measure of central tendency gives us the rough idea of where data points are centered. But in order to make more accurate interpretation of central values of the data, we should also have an idea of how the data are scattered around the measure of central tendency.   Mean Deviation about Mean of an Ungrouped Data Let \[{{x}_{1}},\text{ }{{x}_{2}},\text{ }{{x}_{3}},\text{ }---,\text{ }{{x}_{n}}\]be the n observations, then the mean of the data is given by: \[\overline{x}=\frac{{{x}_{1}}+{{x}_{2}}+{{x}_{3}}+---+{{x}_{n}}}{n}\]\[\Rightarrow \overline{x}=\frac{1}{n}\sum\limits_{k\,=\,1}^{n}{{{X}_{k}}}\] Then the deviation of the data from the mean is given by: \[|{{x}_{1}}-\overline{x}|,|{{x}_{2}}-\overline{x}|,|{{x}_{3}}-\overline{x}|,---|{{x}_{n}}-\overline{x}|\] Now the mean deviation of the data is given by \[\frac{1}{n}\sum\limits_{k=1}^{n}{|{{X}_{k}}-\overline{x}|}\]   Mean Deviation about Mean of a Grouped Data Let \[{{x}_{1}},\text{ }{{x}_{2}},\text{ }{{x}_{3}},\text{ }---,\text{ }{{x}_{n}}\]be the n - observations and \[{{f}_{1}},\text{ }{{f}_{2}},\text{ }{{f}_{3}},---,\text{ }{{f}_{n}}\]be the corresponding frequencies of the data. Then the mean of the data is given by: \[\overline{x}=\frac{{{x}_{1}}{{f}_{1}}+{{x}_{2}}{{f}_{2}}+---+{{x}_{n}}{{f}_{n}}}{{{f}_{1}}+{{f}_{2}}+---+{{f}_{n}}}\] or, \[\overline{x}=\frac{\sum\limits_{k\,=\,1}^{n}{{{X}_{k}}}{{f}_{k}}}{\sum\limits_{k\,=\,1}^{n}{{{f}_{k}}}}\] Then the mean deviation about mean is given by \[\frac{\sum\limits_{k\,=\,1}^{n}{{{f}_{k}}|{{x}_{k}}-\overline{x}|}}{\sum\limits_{k\,=\,1}^{n}{{{f}_{k}}}}\]   Mean Deviation About Median of an Ungrouped Data The median of an ungrouped data is obtained by arranging the data in the ascending order. If the data contains odd number of terms, then the median is \[{{\left( \frac{n+1}{2} \right)}^{th}}\]I term of the data and if the data contains even number of terms, then the median is the average of \[{{\left( \frac{n}{2} \right)}^{th}}\]and\[{{\left( \frac{n}{2}+1 \right)}^{th}}\]terms i.e., \[\frac{{{\left( \frac{n}{2} \right)}^{th}}term+{{\left( \frac{n}{2}+1 \right)}^{th}}term}{2}\].   If M is the median of the data, then mean deviation about M is given by \[\frac{1}{n}\sum\limits_{k\,=\,1}^{n}{|{{x}_{k}}-M}|\] Mean Deviation About Median of a Grouped Data Let \[{{x}_{1}},\text{ }{{x}_{2}},\text{ }{{x}_{3}},\text{ }---,\text{ }{{x}_{n}}\] be the n -observations and \[{{f}_{1}},\text{ }{{f}_{2}},\text{ }{{f}_{3}},---,\text{ }{{f}_{n}}\] be the corresponding frequencies of the data. Then the mean deviation about the median of the data is given by: \[\frac{\sum\limits_{k\,=\,1}^{n}{{{f}_{k}}|{{x}_{k}}-M|}}{\sum\limits_{k\,=\,1}^{n}{{{f}_{k}}}}\] For the grouped data the median can be obtained by \[l+\left( \frac{\frac{N}{2}-C}{f} \right)\times h\] Where,  I = lower limit of the median class N = sum of all frequencies c = cumulative frequency of preceding median class h = class width f = frequency of the median class   Standard Deviation and Variance Standard deviation is the square root of the arithmetic mean of the squares of deviations of the terms from their arithmetic mean and it is denoted by o. The square of standard deviation is called the variance. Thus for simple distribution, \[\sigma =\sqrt{\frac{\sum\limits_{i\,=\,1}^{n}{{{({{x}_{1}}-\overline{x})}^{2}}}}{n}}\]   Note: (i) The standard deviation of any arithmetic progression is \[\sigma =\,\,|d|\sqrt{\frac{{{n}^{2}}-1}{12}}\]where d = common difference and n = number of terms of the A.P. (ii) Coefficient of variation (C.V.) =\[\frac{\sigma }{x}\]\[\times \]100   Probability We have studied about the probability more...

Verbal and Non-verbal Reasoning   In this chapter, we will solve problems related to reasoning and aptitudes as we know that Reasoning and logic skills are an integral part of Mathematics.   Find the Missing Number In such types of problems, we have to choose a missing number (or character) in the figure out of the given options.  

•                   Example:

Find the missing number in the following figure.             (a) 1728                                                (b) 1331 (c) 729                                                              (d) 512 (e) None of these Ans.     (b) Explanation: Here the pattern is ________ \[{{(18+10+8)}^{\frac{3}{2}}}=216,\] \[{{(15+12+22)}^{\frac{3}{2}}}=343,\] \[{{(57+43+21)}^{\frac{3}{2}}}=1331\]   Direction Sense Problems In such types of problems, we draw a diagram by using the given information. The following diagram shows all the directions in a proper manner.  

•             Example:

If P is to the north of Q and R is to the west of Q, then in which direction is P with respect to R? (a) North-east                                                     (b) South-west    (c) North                                                               (d) South (e) None of these Ans.     (a)        Explanation: Clearly from the diagram it is clear that P is in north-east direction with respect to R.                          Blood-Relations Problems In such types of problems, we should first be clear on the relations given in the following table: Mother's father \[\to \] Maternal grand father Mother's mother \[\to \] Maternal grand mother Husband of aunt \[\to \]Uncle Wife of maternal uncle \[\to \] Maternal aunt Mother's brother \[\to \] Maternal uncle Mother's sister \[\to \] Maternal aunt Children of maternal uncle/aunt \[\to \]Cousins Father's father \[\to \]Paternal grand father Father's mother \[\to \]Paternal grand mother Father's brother \[\to \] Uncle Father's sister \[\to \] Aunt Children of uncle \[\to \]Cousins  

•             Example:

Pointing at a photo, A man said, "His father is the only son of my mother". The man has a relation from the person in the photo is of _____ (a) Uncle                                                           (b) Grandfather (c) Father                                                           (d) Cousin (e) None of these Ans.     (c) Explanation:             Clearly the photo belongs to man's son/so the man is the father of the person shown in the photo.   Figure Based Problems In such types of problems, a series of figures is given which proceeds with a certain rule or pattern.  

•              Example:

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Real Numbers   In the previous classes, we have learnt about rational and irrational numbers. In this chapter we will learn about real numbers. A real number can be any positive or negative numbers. All the rational and irrational numbers are real numbers. In other words we can say that real numbers are the set of rational and irrational numbers.             Important Points Related to Real Numbers

•                 A rational number is a real number which can be written as a simple fraction (i.e., in a ratio of two integers). In other words, a number r is called  a rational number when it can be written in the form \[\frac{p}{q}\]where p and q are integers and q is not equal to zero. For example\[\frac{3}{5}\], 0, 3, \[\frac{\mathrm{1}}{\mathrm{100}}\] are rational numbers
•            The decimal expansion of a rational number is either terminating or non-terminating recurring. For example \[\frac{\mathrm{12}}{\mathrm{5}}=2.4\] and \[\frac{13}{9}=1.44444\]???are decimal expansion of rational numbers.
•                  An irrational number is a real number which cannot be written as a simple fraction. In other words, a number s is called an irrational number when it cannot be written in the form\[\frac{\mathrm{p}}{\mathrm{q}}\], where p and q are integers and q is not equal to zero.

        For example, \[\sqrt{\mathrm{2}}\mathrm{=1}\mathrm{.41421356}.........\mathrm{,}\sqrt{\mathrm{3}}\mathrm{=1} \mathrm{.7320508075}.........\mathrm{,  }\!\!\pi\!\!\text{ =3}\mathrm{.14159265}........\] are irrational numbers since they cannot be written in the form\[\frac{\mathrm{p}}{\mathrm{q}}\]. Note: (i)         We use  \[\pi =\frac{22}{7}\], which is its approximate value but not accurate. (ii)         The decimal expansion of irrational number is non-terminating non-recurring. For example 1.002000200002 ??. is an irrational number.   more...

Introduction to Trigonometry             As we know, the trigonometry is the branch of Mathematics in which we study about the relationship between angles and its sides. In this chapter, we will discuss about trigonometric ratios which are defined in a right-angled triangle.   Trigonometrical Ratios In the given triangle ABC, \[\angle B=90{}^\circ \] and let angle C is\[\theta \]. Then the trigonometrical ratios are defined as follows:

•            \[\sin \theta \text{ }=\text{ }\frac{Perpendicular}{Hypotenuse}\text{ }=\frac{AB}{AC}\]
•            \[\cos \theta \text{ }=\text{ }\frac{Base}{Hypotenuse}\text{ }=\frac{BC}{AC}\]
•           \[\tan \theta \text{ }=\text{ }\frac{Perpendicular}{Hypotenuse}\text{ }=\frac{AB}{BC}\]
•           \[\cot \theta \text{ }=\text{ }\frac{Base}{Perpendicular}\text{ }=\frac{BC}{AB}\]
•          \[\sec \theta \text{ }=\text{ }\frac{Hypotenuse}{Base}\text{ }=\frac{AC}{BC}\]
•          \[cosec\theta \text{ }=\text{ }\frac{Hypotenuse}{Perpendicular}\text{ }=\frac{AC}{AB}\]

  Relationship between T-ratios             \[\sin \theta =\frac{1}{\cos ec\text{ }\theta },\text{ cos }\theta =\frac{1}{\sec \text{ }\theta \,}\text{ and cot }\theta =\frac{1}{\tan \text{ }\theta }\] From more...

  More About Logic Gates   Introduction The internal architecture of computer performs operations like, mathematical as well as logical operations. Logical and arithmetic operations in the microprocessor of a computer is done by comparing the inputs in which output is depend on the state of input. Combination of logic circuit can be used for addition, logical functions, etc. Combination of logic gates is used to make half adder, full adder in the form of flip flop which is used for the manufacturing of microprocessor. The logic gate is made of logic circuits perform the Boolean function. A basic logic gate obtains one or two input but it produces one output at a time. Logic gates is made of transistors and other devices which supports the function of the transistor, such as, resister. All types of logic circuits are divided into two groups, Basic logic gates and Derived logic gates. The following picture illustrates the application of logic circuits in the microprocessor.     Basic Logic Gates Basic logic gates are logic circuits which are made of a single logic gate. It is made of transistor and capacitors. The output of the basic logic gate is depend on the switching of transistor.   AND Gate AND gate has two input and one output. The output of the AND gate is also written as, Y = A.B. Output of the AND gate is obtained by multiplying both the input. The input of the AND gate is given as logic high and logic low or 0 and 1. Every logic gate has a truth table which is the statement of input given to the logic gate and output obtained by that logic gate.                                                                    Look at the following symbol of the AND gate:     Look at the following truth table of the AND gate:      

Input		Output
A	B	Y = A.B
0	0	0
0	1	0
1	0	0
1	1	1

    From the truth table of AND gate, the output is low or 0 if any one of input A or B is low or high and also output is low if both input are low. In the case of both input high, the output of the AND gate is high.   OR more...

  Working With MS-Access 2013   Introduction MS-Access 2013 is an application software integrated with Microsoft Office package which is used for database management applications. Data is the raw fact. It can be character, number or symbols which are processed by a computer. In terms of computer science you can say data may be characters, facts or number, which can be processed by a computer. A group of meaningful data is called information. Information may be broken down further.   In computerize system, you can store the data in spreadsheets or in database. An organized collection of data, which can be updated, accessed and managed in a systematic order is called database. With the help of computers, one can works on huge volume of data. It allows the user to access data conveniently and data can also be easily updated whenever it is required.   Need of Database Without database you cannot maintain data in proper way. You can face a lot of problem, such as data duplicity and security. Using database you can manage your data in proper and secure way.   Database provides the following advantages:   v  Sharing Data. v  Avoiding data redundancy. v  Maintaining integrity of data. v  Avoiding inconsistency of data. v  Securing data.   Disadvantages Database maintenance increases the cost because it requires special database software and hardware. Database systems are complex, difficult and time-consuming to design. It requires initial training for all users and programmers.   Getting started with Access   Click on Start All Apps  Microsoft Office  Access 2013   In the left pane, the template categories?including the featured local templates?are listed, as well as the categories on Office Online. Templates are prebuilt databases focused on a specific task that you can download and use immediately.       In the example below, the featured templates are selected, and the template options are displayed in the center area of the screen. Featured templates include database template options that are available online, as well as templates available as part of the local version Access.   Opening a database You have three main options on the Getting Started page. You can open a template database stored locally or online, an existing database, or a blank database. To view templates included with Access:   v  Click on Blank desktop database and click on create option. v  Now the screen will change to main screen of the database.     more...

  Working With HTML     Introduction HTML is defined as the hypertext markup language used for creating web pages. It is also defined as the text which links to the other text and allows 3you to format, arrange and group text, display text as links, and add images and multimedia to a webpage. There are many version of HTML such as, HTML 1.0, HTML 2.0, HTML 3, HTML 4, HTML 5. HTML 5 is the latest version released in 2009 that includes a number of new elements and attributes and removes some elements and attributes that was the part of its earlier version. A text editor can be used for creating the HTML webpages. Some specialized HTML editors are also available.  There are number of HTML editors available for creating Web pages. The followings are the HTML editors.   Gedit: It is designed as general purpose text editor for Mac OS X and Windows has tools to edit source codes for creating webpage.  TinyMCE: It is an open source HTML editor offers HTML formatting tools such as, bold, italics, underline, TinyMCE is compatible with Internet Explorer, Mozilla firefox, Opera, Google Chrome.  CKEditor: It is an open source text editor can be used to create web pages. It is compatible with most of the popular internet browser such as, Internet explorer, Google chrome, Opera.  Adobe Dreamwaver: It is the web development application or HTML editor available for both Mac and Windows operating system.   Hypertext Markup Language (HTML) HTML language is developed by Tim Berner-Lee at CERN (Consiel European pour la Research Nuclear) to enable permit the researchers to share their research papers with the help of the Internet. Generally all the browsers are supporting HTML but basically the HTML was used by Mosaic Browser. The HTML 1.0 is the first version of HTML, whereas continuous growth of Web extended HTML growth in several other ways. World Wide Web (W3C) is the organization which did not specify the fir version of HTML. This organization maintains the language and keeps involving it proper direction. Latest version of HTML is HTML 4.01 which is in general uses are is the sub version of HTML4.0. The errors which are occurring in HTML4.0 have been fixed in this version.  The whole HTML document comes under the <html>tag which is used as a container. The entire content of the HTML page comes under the opening and closing of the <html>tags. This <html>tag indicates the browser this is the starting of the document and the closing </html>tag indicates that it's the ending of an HTML document.   The following is the syntax:   <html>  …………….  Contents mentioned in the page  </html>   For the Heading of the HTML document the tag <head> is used. The information contains some certain headings regarding documents that come under this. There are only few tags which are valid under the heading section. These are the following:   <HTML dir = rtl>: Specifies more...

  Working With CSS   Introduction CSS is defined as the Cascading Style Sheets (CSS) is a text document or Style sheet. A style sheet is a set of style rules that tell a browser how to present a document. HTML's STYLE element is the simplest ways of linking these style rules to your HTML documents. These elements are placed in the document HEAD, and it contains the style rules for the page. Same CSS document can be used to define multiple HTML document. CSS document has the .css extension. The CSS syntax can be divided into two parts, selector and declaration. The selector is defined as the HTML element to which the CSS style is applied and declaration contains the CSS properties, such as colour, font size, and values of these properties.   CSS Syntax A CSS rule divides into two parts. Selector (Head1; Head2 ;) and declaration (property1: value1; property2: value2). Basically selector is the HTML element you want to style and property is the style attribute. CSS declaration always ends with a semicolon and declaration group is surrounded by middle or curly bracket. The following is the simple example of CSS:   Mystyle { color:green; text-align:center; }   CSS Background CSS allows changing background colour of a page. It enables background-colour property that specifies the background colour of an element. The following code snippet shows how to change background:   body {background-color: # ff0000;}   CSS enables background-image property that allows changing background image of a page. The following code snippet shows how to change background image for a page:   body {background-image: url ('imgl.gif');}   To repeat the image only horizontally you need to use repeat-x property.   The following code snippet shows how to use repeat-x property:   body { background-image: uri ('img 1.gif'); background-repeat: repeat-x; }   Background property allows following values declaration:   Background-Color Allows setting background colour of an element. You can pass the following values:   v  color-rgb v  color-hex v  color-name v  transparent   Background-Image Allows setting background image for an element. You can pass the following values:   v  url v  inherit v  none   Background-Repeat Allows setting background image will be repeated. You can pass the following values:   v  repeat v  repeat-x v  repeat-y v  no-repeat v  inherit   Background-Attachments Allows making a background image is fixed or scroll. You can pass the following values:   v more...

  Working With Internet Application   Introduction Nothing has revolutionized modern life the way rapid progress of computer has. For better or worse computers have infiltrated every aspect of our society. Today, computers do much more than simply compute. They make airline or railway reservation and teach on-line, some super store scanners Calculate our grocery bills while keeping the store inventory computerized telephone switching has greatly improved the telephone system and automatic teller machines (ATM).   As a computers become more widespread in the workplace, new ways to harness their potential developed. As smaller computers become more powerful, they could be linked together, or network to share memory space, software and information and communication with each other.   In Education Computer applications in education is a broad and changing term due to the breadth of the area of study and the rapid and ever ? changing naturo of technology. Computer applications includes, but are not limited to, desktop publishing and presentations, computer use in classrooms, telecommunications and distance education, computer hardware and software, networking, tab administration, multimedia presentations and publishing.   v  Online Education: Many web sites provide online education. You can read or download educational material and books. v  Research: Computers are also used for research work. Internet is a huge source of information on any topic. v  Preparing time - table: Computers help in preparing time - tables, schedules etc. v  Tutorial and dialogue: Computer can play effectively the role of the tutor. It helps the teachers in engaging students in tutorial work: v  Maintenance of progress cards: Computers maintain progress cards and preserve them efficiently and confidentially. v  Computers are being used to perform many tasks in educational institutions, easily and quickly.   ·         Keeping Records of students. ·         Storing Records of employees of school/college. ·         Managing Accounts of the institution. ·         Fee collection' and maintains of fees records. ·         Circulation of instruction / notices and getting it in printed form. ·         Preparation of school / college magazine etc.         In Healthcare The use of information and communication technologies has become widespread in the health care sector. Computer plays very important role in medical science. Today, more and more members of the medical profession are embracing social media for sharing helpful medical information and providing patient care.   Computers can be used to perform research in the health sector. Research studies can be done more...