Current Affairs 6th Class

  Algebraic Expressions   In an algebraic expression constant and variables are linked with arithmetic operations. The value of unknown variable is obtained by simplification of the given expression.   Terms of an algebraic Expression   Variables Alphabetical symbols used in algebraic expressions are called variables a, b, c, d, m, n, x, y, z ........... etc. are some common letters which are used for variables.   Constant Terms The symbol which itself indicate a permanent value is called constant. All numbers are constant. \[6,10,\frac{10}{11},15,-6,\sqrt{3}....\]etc. are constants because, their values are fixed.   Variable Terms A term which contains various numerical values is called variable term. For example. Product of \[\text{X=4 }\!\!\times\!\!\text{ }\,\text{X=4X}\]Product of \[\text{2,X,}{{\text{Y}}^{2\,}}\] and \[\text{Z=}\,\text{2 }\!\!\times\!\!\text{ X }\!\!\times\!\!\text{ }{{\text{Y}}^{\text{2}}}\text{ }\!\!\times\!\!\text{ Z=2X}{{\text{Y}}^{\text{2}}}\text{Z}\] Thus, 4X and \[\text{2X}{{\text{Y}}^{\text{2}}}\text{Z}\] are variable terms   Types of Terms There are two types of terms, like and unlike. Terms are classified by similarity of their variables.   Like and unlike Terms The terms having same variables are called like terms and the terms having different variables are called unlike terms. For example, \[6x,\,x,\,-2x,\,\frac{4}{9}x,\]are like terms and \[6x,\,2{{y}^{2}},\,-9{{x}^{2}}yz,4xy,\]are unlike terms.   Coefficient A number or a symbol multiplied with a variable in an algebraic expression is called its coefficient. In\[-6{{m}^{2}}np\], coefficient of\[n{{m}^{2}}p\] is \[-6\] because \[{{\text{m}}^{\text{2}}}np\]is multiplied with \[-6\] to from \[-6{{m}^{2}}np\]. The variable part of the term is called its variable or literal coefficient. In\[-\frac{5}{4}abc\], variable coefficients are a, b and c. The constant part of the term is called constant coefficient. In term\[-\frac{5}{4}abc\], constant coefficient is\[-\frac{5}{4}\].   Example: Sign of resulting addition of two like terms depends on which one of the following? (a) Sign of biggest term (b) Sign of smallest term (c) Sign of positive term (d) Sign of negative term (e) None of these Answer (a)   Operations on Algebraic Expressions When constant and variables are linked with any of the following fundamental arithmetic operations i.e. addition, subtraction, multiplication and division, then the solution of the expression is obtained by simplification of the expression.   Addition and Subtraction of Terms The addition of two unlike terms is not possible and their addition is obtained in the same form. Addition of \[2x+3x\] is \[5x\] but the addition of \[2x+3y\] is\[2x+3y\]. Subtraction of two like terms is same as the subtraction of whole numbers. For example,\[4x-2x=2x\]   Example: Simplify: \[(2{{x}^{2}}+{{x}^{2}})-(5{{x}^{2}}+11{{x}^{2}})\] (a) \[15{{x}^{3}}\]                   (b) \[15{{x}^{2}}\]      (c) \[-3{{x}^{2}}\]                    (d) \[13{{x}^{2}}\] (e) None of these   Answer (c) Explanation:\[(2{{x}^{2}}+{{x}^{2}})-(5{{x}^{2}}+11{{x}^{2}})\] = \[3{{x}^{2}}-16{{x}^{2}}=-13{{x}^{2}}\]   Example: Evaluate: \[[\{({{x}^{2}}+3{{x}^{2}})-({{x}^{2}}+{{x}^{2}})5\}\div x]\] (a) \[-10x\]                     (b) \[-15x\] (c) \[-6x\]                                   (d) \[10x\] (e) None of these Answer (c) Explanation:\[(4{{x}^{2}}-5\times 2{{x}^{2}})\div x=\]\[\frac{4{{x}^{2}}-10{{x}^{2}}}{x}\] \[=\frac{-6{{x}^{2}}}{x}=-6x\]   Equation An equation is a condition on a variable. For example, the expression \[10x+3=13\] is an equation which describe that the variable is equal to a fixed number. This value itself is called the solution of the equation. Thus,\[10x+3=\]\[13\Rightarrow 10x\]\[=13-3=\]\[10\Rightarrow x=1\] Here the definite value of the variable x in the equation \[10x+3=13\]   Note: (i) An equation has two sides, LHS and RHS, between them more...

  Geometry and Symmetry   Basic Geometrical Shapes Lines and angles are the main geometrical concept and every geometrical figure is made up of lines and angles. Triangles are also constructed by using lines and angles.   Point A geometrical figure which indicates position but not the dimension is called a point. A point does not have length, breadth and height. A point is a fine dot. P is a point on a plane of paper as shown below.   Line A set of points which can be extended infinitely in both directions is called a line.     Line Segment A line of fix length is called a line segment.                                                    In the above figure RS is a line segment and the length of RS is fixed.   Ray A ray is defined as the line that can be extended infinitely in one direction.     In the above figure AB can be extended towards the direction of B. Hence, called a ray.   Note: A line segment has two end points, a ray has only one end point and a line has no end points.   Angle Angle is formed between two rays which have a common point.   Vertex or common end point is O. OA and OB are the arms of \[\angle AOB\] The name of the above angle can be given as \[\angle AOB\]or \[\angle BOA\] The unit of measurement of an angle is degree\[({}^\circ )\]   Types of Angles Acute Angle The angle between \[0{}^\circ \] and \[90{}^\circ \] is called an acute angle. For example, \[10{}^\circ ,\,\,30{}^\circ ,\,\,60{}^\circ ,\,\,80{}^\circ \]are acute angles.   Right Angle An angle of measure \[90{}^\circ \] is called a right angle.   Obtuse Angle An angle whose measure is between \[90{}^\circ \] and \[180{}^\circ \] is called an obtuse angle. Straight Angle An angle whose measure is \[180{}^\circ \,\,\text{is}\]called a straight angle.                                                  Reflex Angle An angle whose measure is more than \[180{}^\circ \] and less than \[360{}^\circ \]is called a reflex angle.   Complementary Angle Two angles whose sum is \[90{}^\circ \,\,\text{is}\] called the complimentary angle. Complementary angle of any angle \[\theta \] is\[90{}^\circ -\theta \].   Supplementary Angle Two angles whose sum is \[180{}^\circ \,\,\text{is}\] called supplementary angles. Supplementary angle of any angle \[\theta \] is\[180{}^\circ -\theta \].   Adjacent Angle Two angles are said to be adjacent if they have a common vertex and one common arm. In the following figure \[\angle AOC\] and \[\angle COB\]are adjacent angles.   Vertically more...

  Mensuration   Perimeter and Area of Plane Figures Perimeter of geometrical figure is the sum of its sides. There are different types of geometrical figures. Figures are classified by their shapes and sizes. Area of a geometrical figure is its total surface area.   Perimeter and Area of a Triangle
  • Perimeter of a triangle = Sum of the length of all sides.
  • Area of a right triangle \[\text{=}\frac{\text{1}}{\text{2}}\times \text{Base}\times \text{Height}\]
  • Perimeter of an equilateral triangle \[\text{=3}\times \text{Side}\]
  • Area of an equilateral triangle \[\text{=}\frac{\sqrt{\text{3}}}{\text{4}}\times {{\text{(Side)}}^{\text{2}}}\]
  Perimeter and Area of a Parallelogram Parallelogram is a quadrilateral whose opposite sides are equal and parallel to each other. In the given figure ABCD is a Parallelogram in which \[\text{AB}\parallel \text{CD,}\,\,\text{BC}\parallel \text{AD,}\,\,\text{AB}=\text{CD}\] and \[\text{AD=BC}\]   Perimeter of a Parallelogram = 2 (sum of two adjacent sides) Hence, perimeter of a parallelogram \[\text{ABCD=2(AB+BC)}\]Area of a parallelogram = Base \[\text{ }\!\!\times\!\!\text{ }\] Height Therefore, the area of a parallelogram \[\text{ABCD=AB }\!\!\times\!\!\text{ CE}\]   Perimeter and Area of a Rectangle A rectangle has four right angles and its opposite sides are equal. Longer side of a rectangle is called length and shorter side is called width.     Perimeter of rectangle  \[ABCD=AB+BC+CD+DA\] = length + width + length + width = 2(length + width) Hence, perimeter of a rectangle = 2(length + width) Area of a rectangle = length \[\times \]width   Perimeter and Area of a Rhombus A rhombus is a parallelogram with four equal sides. Therefore, perimeter of rhombus\[=4\times side\]. In the figure given below ABCD is a rhombus.   Perimeter of a rhombus, \[=4\times side\] Area of a rhombus = base \[\times \] height Also area of a rhombus \[\text{=}\frac{1}{2}\times \] product of length of diagonals. Perimeter and Area of a Square A square has four equal sides and each angle of\[90{}^\circ \]. In the picture given below, ABCD is a square because its all sides are equal and each angle is a right angle.     Perimeter of square = side + side + side + side\[=4\times side\] Area of a Square = side \[\times \]side = \[{{(side)}^{2}}\]   Perimeter and Area of a Trapezium A quadrilateral whose one pair of sides are parallel is called a trapezium. The given figure is a trapezium in which parallel sides are AB and CD and non-parallel sides are AD and BC     Perimeter of a trapezium = Sum of the length of all sides Area of a trapezium \[=\frac{1}{2}\times \] (Sum of lengths of parallel sides) \[\times \]distance between parallel sides.   Cirumference and Area of a circle A round plane figure whose all points are equidistant from a fixe point is called a circle and the fixed point is called centre of the circle more...

  Data Handling   In this chapter we will learn about pictograph and bar graph.   Data Data is a collection of facts, such as numbers, observations, words or even description things.   Observation Each numerical figure in a data is called observation.   Frequency The number of times a particular observation occurs is called its frequency.   Statistical Graph The information provided by a numerical frequency distribution is easy to understand when we represent it in terms of diagrams or graphs. To represent statistical data, we use different types of diagrams or graphs. Some of them are:   (i)  Pictograph (ii) Bar graph   Pictograph A pictograph represents the given data through pictures of objects. It helps to answer the questions on the data at a glance.   Example: The following pictograph, shows the number of cakes sold at a bakery over five days.              
Day Number of cakes = 10 cakes
Monday
Tuesday
Wednesday
Thursday
more...
                                                                                            Analogy   Learning Objectives  
  • What is Analogy
  • Types of Problems
  Analogy Simple meaning of analogy is similarity. But, in terms of reasoning, the meaning of analogy is logical similarity in two or more things. This similarity may be on the basis of properties, kinds, traits, shapes etc.   Example: (i) Student : School : : Patient : Hospital Explanation: A 'Student' goes to ‘School’ in the same way a 'Patient' goes to 'Hospital', In other words, school (place to take education) is a proper place for a student arid in the same way hospital (place to get treatment) is a proper place for a patient. 1st pair- Student: School (person and proper place relationship). 2nd pair - Patient: Hospital (person and proper place relationship). Clearly, both pairs show similar relationship in a logical way. Hence, both pairs are analogous or it is said that both pairs exhibit analogy.   (ii) Good : Bad : : Tall : Short Explanation: 1st pair - Good: Bad (opposite relationship). 2nd pair - Tall: Short (opposite relationship). Clearly, both pairs show similar relationship (opposite relationship). Hence, both pairs exhibit analogy.   Types of Problems Problems Based on Synonymous Relationship In such problems, the words given in one pair have same meaning and the same relationship that is found in another pair of words.   Example 1 Right: Correct:: Fat: Bulky Explanation: 1st pair - Right: Correct (synonymous relationship). 2nd pair - Fat: Bulky (synonymous relationship).   Example 2 Brave : Bold :: Wrong : Incorrect Explanation: 1st pair - Brave: Bold (synonymous relationship). 2nd pair - Wrong: Incorrect (synonymous relationship).   Commonly Asked Questions   Select the pair which is related in the same way as the pair of words given in the question. Tough : Hard \[::\text{ }\_\_\_\_\_\_\text{ }:\text{ }\_\_\_\_\_\_\_\_\] (a) Rich : Wealthy           (b) Rich : Poor (c) Tall : Short                (d) True : False (e) None of these   Answer (a) Explanation: Option (a) is correct because ‘Tough’ and 'Hard' are synonymous words. In the same manner 'Rich’ and ‘Wealthy' are synonymous words. Rest of the options is incorrect because words in option (b), (c) and (d) have opposite meanings and option (e) is useless because of the correctness of option (a).   'Start' is related to ‘Begin’ in the same way as ‘Joy’ is related to………….. (a) Right                        (b) False (c) True                                     (d) Delight (e) None of these Answer (d) Explanation: Option (d) is correct because ‘Start’ and ‘Begin’ have same meaning. Similarly, ‘Joy’ and ‘Delight' have same meaning. Rest of the options is incorrect because of the correctness of option (d).   Problems Based on Opposite Relationship In such more...

                                                                         Blood Relation   Learning Objectives  
  • What is Blood Relation
  • Type of Blood Relations
  • Some Important Blood Relations
  • Types of Problems  
  What is Blood Relation?   Blood relation is biological relation. Remember a wife and husband are not biologically related but they are biological parents of their own children. Similarly, brother, sister, paternal grandfather, paternal grandmother, maternal grandfather, maternal grandmother, grandson, grandmother, niece, cousin etc. are our blood relatives.   Types of Blood Relations   There are mainly two types of blood relations:             (i) Blood relation from paternal side             (ii) Blood relation from maternal side Now, we will discuss both kind of relations one by one.               Blood Relation From Paternal Side This type of blood relation can be further subdivided into three types:
  • Past generations of father
Example: Great grandfather, great grandmother, grandfather, grandmother etc.
  • Parallel generations of father
Examples: Uncles (brothers of father), aunts (sisters of father) etc.
  • Future generations of father
Examples: Sons, daughters, grandsons, granddaughters etc.               Blood Relation From Maternal Side This type of blood relations can also be subdivided into three types:"
  • Past generations of mother
Examples: Maternal great grandfather, maternal great grandmother, maternal grandfather, maternal grandmother etc.
  • Parallel generations of mother
Examples: Maternal uncles, maternal aunts etc.
  • Future generations of mother
Examples: Sons, daughters, grandsons, granddaughters etc.   Some Important Blood Relations  
1. Son of father or mother \[\to \] Brother
2. Daughter of father or mother \[\to \] more...
                                                                                        Direction Test   Learning Objectives
  • Concept of Direction
  • Concept of Turn
  • Concept of Minimum Distance
  Concept of Direction In our day to day life we make our concept of direction after seeing the position of the sun. In fact, this is truth that sun rises in the East and goes down in the West. Thus, when we stand facing sunrise then our front is called East while our back is called West. At this position, our left hand is in the northward and the right hand is in the southward. Let us see the following direction map that will make your concept more clear.   Direction Map:   Note: On paper North is always on the top while South is always at the bottom.   Concept of Turn Left turn            =   Anti clockwise turn Right turn           =   Clockwise turn   Let us understand it through pictorial presentation:"   (i)          (ii) (iii)           (iv)   Important Points Regarding Directions  
  • If our face is towards North, then after left turn our face will be towards West while after right turn it will be towards East.
  • If our face is towards South, then after left turn our face will be towards East and after right turn it will be towards West.
  • If our face is towards East, then after left turn our face will be towards North and after right turn it will be towards South.
  • If our face is towards West, then after left turn our face will be towards South and after right turn it will be towards North.
  • If our face is towards North West, then after left turn our face will be towards South West and after right turn it will be towards North East.
  • If our face is towards South West, then after left turn our face will be towards South East and after right turn it will be towards North West.
  • If our face is towards South East, then after left turn our face will be towards North East and after right turn it will be towards South West.
  • If our face is towards North East, then after left turn our face will be towards North West and after right turn it will be towards South East.
  Concept of Minimum Distance   Minimum distance between initial and last point   \[{{h}^{2}}={{b}^{2}}+{{p}^{2}},\] where h   =  Hypotenuse b   =  Base p   =  perpendicular Remember this important rule is known as 'Pythagoras Theorem'.   Example 1 Pinki starts moving from a point P towards East. After walking some distance she turns her left. Now, her direction is definitely towards North. more...

                                                                                           Coding-Decoding   Learning Objectives
  • What is Coding-Decoding
  • How to Decode
  What is coding-Decoding? Let us start it with an interesting story. Suppose you and your father like ice-cream very much. But your mother does not want you two to have it because you both catch cold very easily. Then you and your father make a secret plan to use the word 'Chocolate' for ice-cream. Now, whenever you feel like eating ice-cream you say to your father that you want to eat chocolates. Mother hears it and thinks that you are really demanding chocolates. Therefore, she gives you permission to go out with father and enjoy chocolates. Then you and your father go out, eat ice-cream and comeback.   What do you think happens here? Here, you coded the word Ice-cream' with another word 'Chocolate'. Only you and father know about this code, when you say that you want to eat 'Chocolate', your father hears and easily decodes it that you want to eat ice-cream. This can be presented as below. \[Ice-cream\xrightarrow{Coded\,as}Chocolate\xrightarrow{Decoded\,as}Ice-cream\]   How to Decode?   In reasoning, words, letters and numbers are coded according to a certain rule. While solving problems, student has to identify that particular rule first and then the same rule is applied to decode other coded words, letters, number etc. The types of coding decoding problems will give you more clear concept about it. But before coming to the actual problems, we must remember the positions of letters in English alphabet in forward order that will help you in solving problems of coding-decoding, Let us see the positions:     Types of Problems               Coding-Decoding in Forward Sequence In such problems, letters are coded in forward alphabetical sequence.   Example 1 If 'AB' is coded as ‘BC’, then ‘EF’ will definitely be coded as ‘FG’. Explanation: Here, letters of ‘AB’ shift one place in forward alphabetical sequence. Let us see:               Similarly, letters of 'EF' shift one place in forward alphabetical order. Let us see:               Clearly, code for ‘AB’ is ‘BC’ and code for ‘EF’ is ‘FG’   Example 2 If 'GO' is coded as 'IQ', then 'TO' will definitely be coded as 'VQ'. Explanation: Here, letters of the word 'GO' shift two places in forward alphabetical sequence. Let us see:               Similarly, both letters of the word 'TO' will move two places forward Let us see:              Note: In forward sequence coding-decoding ‘Table 1’ is used.   Commonly Asked Questions   If code of ‘LMN’= 'MNO’, then find the code for 'PQR'. (a) QRS                        more...

                                                                                 Letter Series   Learning Objectives
  • What is a Letter Series
  • Properties of Letter Series
  • Types of Problems
  What is a Letter Series? A letter series is a sequence of many elements made of letters of English alphabet only. Such sequence is formed by putting the letters one after another from left to right.   Example: (i) A BCD (ii)  DCB A (iii) AL BL CB DE   Note: An element of a series is a single member (identity) of that particular series. For example, in a letter series 'A B C D', each A, B, C and D is a single element. Point to be noted that an element can be made with more than one letter. In a series of 'AB LE BE’, each AB, LE and BE is a single element.   Properties of Letter Series A letter series can be in forward order Look at the following:
  • A BCD
  • BCDE
  Commonly Asked Questions   Find the next letter in the series given below. L M N….......... (a) A                                (b) O (c) D                                (d) B (e) None of these               Answer (b) Explanation: Option (b) is correct because this is a forward order series of English alphabet in which M comes just after L, N comes just after M and O comes just after N. Rest of the options is incorrect because of the correctness of option (b).   Which of the following options is the next element of the given series? L N P   ........ (a) Q                             (b) A (c) S                                (d) R (e) None of these                         Answer (d) Explanation; Option (d) is correct because every next letter takes place skipping one letter in forward alphabetical order. Let us see:                 Rest of the options is incorrect because of the correctness of option (d).   A letter series can be in reverse order. Look at the following:
  • C B A
  • D C B A
  Commonly Asked Questions   Find the next letter in the following series. E D C ……… (a) A                             (b) B (c) F                              (d) G (e) None of these Explanation: Option (b) is correct because this is a reverse order series of English .alphabet. This series starts with E and then comes D, the next letter in reverse order. Just after D, C will be the next letter in the reverse order. Similarly, B comes just after C to fill the blank space. Rest of the options is incorrect because of the correctness of option (b).   Find the next element in more...

                                                                                     Number Series   Learning Objectives
  • What is a Number Series
  • Types of Problems
  What is a Number Series? A number series is a sequence of numbers which follow a particular rule. Each element of a series is called a 'term'. In this chapter, we will analyse the pattern of different kind of number series that a particular series follow and find the missing term to continue the pattern.   Example Find the missing term in the given series. 2, 8, 32, 128, __. (a) 512                          (b) 510 (c) 516                          (d) 520 (e) None of these   Answer (a) Explanation: Option (a) is correct. The relationship between the terms or the pattern that the given series follows is as below. Therefore, the next term or missing term of the given series will be   Find the missing term in the following number series. 2, 3, 5, 7, 11, 13__. (a) 15                            (b) 19 (c) 17                            (d) 14 (e) None of these   Answer (c) Explanation: Option (c) is correct. The given number series is the sequence of consecutive prime number. So, the next number or the missing term will be 17,   Commonly Asked Questions   Find the next number. 64, 32, 16, 8, __ (a) 2                                          (b) 4 (c) 6                                           (d) 0 (e) None of these                         Answer (b) Explanation: Option (b) is correct because in the given number series, each number is half of its previous number. So the required number or the missing term will be 4. Rest of the options is incorrect because of the correctness of option (b).   What comes in place of question mark (?) in the series given below? 1, 4, 10, 19, ? (a) 30                            (b) 31 (c) 32                            (d) 33 (e) None of these   Answer: (b) Explanation: Option (b) is correct because the series goes as following- So the required next term in the series will be Rest of the options is incorrect because of the correctness of option (b)   A single number series can have more than one series.             Example Look at the following: (i) 1  4  2  5  3  6   Clearly, 1st series:    1      2          3 2nd series:   4      5          5 (ii) 4 9 5 3 6 8 7 2 8 7 9 1 Let us see:                           Here, 1st series:   4 5 6 7 8 9 2nd series:   9 8 7 3rd series:   3 2 1   Commonly Asked Questions   Find the missing number in the following series 8 2 9 1 10 0………….. (a) 12                            (b) 11 (c) 3                                (d) 5 (e) None of these   Answer (b) Explanation: Option (b) is correct. Let us see:   more...


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