Current Affairs 7th Class

  Data Handling   Learning Objectives   ·         Data Collection ·         Graphical Representation of Data ·         Probability   Data Collection             Data collection is important as it helps us to collect, study and record information, make decisions about important issues as well as to pass Information on to others. It enables us to provide information regarding a specific topic or area of study. The data that are collected need to be organised in a proper table, so that it becomes easy to understand and interpret.             Lets understand some important terms: ·         Frequency: The frequency of a particular data value is the number of times the data value occurs. For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f. ·         Variable: The measurable characteristics like age, height. Income etc. are called variables. ·         Mean: The mean or arithmetic mean is the average of the numbers. Average is a number that represents or shows the central tendency of a group of observations or data. It can be calculated by using the formula given below:             Mean =\[\frac{\sum{fixi}}{\sum{fi}}\]. (where f is frequency and x is variable). ·         Mode: It is another form of central tendency or representative value. The mode in a list of numbers refers to the list of numbers that occur most frequently.             For example, to find the mode of 9, 11, 3, 44, 17, 11, 17, 15, 15, 15, 27, 40, 8             Put the numbers in increasing order as shown below:             3, 8, 9, 15, 15, 15, 17, 17, 17, 17, 27, 40, 44 The number which occur most frequently is the mode. In the given data, the mode is 17 which occurs the most at 4 times. ·         The median: The Median is the ?middle value? in your list. It is also a form of representative value. When the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order If a set of n observations is given, more...

  Data Handling   Learning Objectives   ·         Data Collection ·         Graphical Representation of Data ·         Probability   Data Collection             Data collection is important as it helps us to collect, study and record information, make decisions about important issues as well as to pass Information on to others. It enables us to provide information regarding a specific topic or area of study. The data that are collected need to be organised in a proper table, so that it becomes easy to understand and interpret.             Lets understand some important terms: ·         Frequency: The frequency of a particular data value is the number of times the data value occurs. For example, if four students have a score of 80 in mathematics, and then the score of 80 is said to have a frequency of 4. The frequency of a data value is often represented by f. ·         Variable: The measurable characteristics like age, height. Income etc. are called variables. ·         Mean: The mean or arithmetic mean is the average of the numbers. Average is a number that represents or shows the central tendency of a group of observations or data. It can be calculated by using the formula given below:             Mean =\[\frac{\sum{fixi}}{\sum{fi}}\]. (where f is frequency and x is variable). ·         Mode: It is another form of central tendency or representative value. The mode in a list of numbers refers to the list of numbers that occur most frequently.             For example, to find the mode of 9, 11, 3, 44, 17, 11, 17, 15, 15, 15, 27, 40, 8             Put the numbers in increasing order as shown below:             3, 8, 9, 15, 15, 15, 17, 17, 17, 17, 27, 40, 44 The number which occur most frequently is the mode. In the given data, the mode is 17 which occurs the most at 4 times. ·         The median: The Median is the ?middle value? in your list. It is also a form of representative value. When the totals of the list are odd, the median is the middle entry in the list after sorting the list into increasing order If a set of n observations is given, more...

  Image   Learning Objectives  
  • Images
  • Concept of Mirror Image
  • Concept of Water Image
  Images   The reflection of an object as seen in a surface is called Image. Image of an object is similar to the object but it may be inverted or laterally inverted.   Concept of Mirror Image   Image of an object as seen in a mirror is called mirror image or reflection of an object. The left of the object appears right and right appears as left in the image. This phenomenon is called lateral inversion. For example, mirror image of K =                Some English alphabets have identical mirror images. These are - A, H, I, M, O, I, U, V, W, X, Y.   Example Select one alternative which exactly matches with the mirror images of the word in the question given below. EMANATE             (a) ETANAME                   (b)              (c) ENAMEAT                                      (d) EATEMAN                          (e) None of these Ans.     (b) Explanation: Mirror image of the letters E =, M = M, A = A, N =, T = T Therefore mirror image of the word EMANATE will be.   Select one alternative which exactly matches with the mirror image of the word in the question given below. 247593               (a) 395742                     (b)                   (c) 392457                     (d)                     (e) None of these Ans.     (b) Explanation: Mirror image of the digits 2 =, 4 =  7 = , 5 =, 9 = more...

  Number System   Learning Objectives  
  • Number Line
  • Fractions and Decimals
  • Rational Number
    Number Line       Number line is a model that helps us visualise adding and subtracting of integers. A number line is a picture of a straight Sine on which every point is assumed to correspond to a real number and every real number to a point.   Absolute Value Absolute value means to think only about how far a number is from zero.                             For example “6” is 6 away from zero, but” -6” is also 6 away from zero. So the absolute value of 6 is 6 and the absolute value of- 6 is also 6.   Properties of addition of integer
  • Commutative property:  \[\left( A + B \right) = \left( B + A \right)\].
  • Associative property:  \[\operatorname{A} + \left( B + C \right) = \left( A + B \right) +C\].
  • Additive Identity:  Additive identity is any number which when added to a number N will result in the same number, i.e., N + 0 = N. Hence, 0 is the additive identity.
  • Additive Inverse:  Inverse identity is any number which when added to a number M will result in zero. Here, N + (-N) = 0. Hence, in general, additive inverse of N is -N.
  Properties of subtraction of integer  
  • Commutative property does not exist for subtraction, i.e.,  \[2-3~\,\,\ne \,\,3-2\]
  • Associative property also does not exist for subtraction, i.e.,  \[2-\left( 3 - 4 \right)~\ne \left( 2 - 3 \right)  4\]
  • Identity property: Same as that of Additive identity. 0 + (-N) = -N, where N is positive.
  • Inverse property: N is the inverse of a number -N where N is positive, since N - N = 0.
  Properties of multiplication of integers
  • Closure property: Integers are closed under multiplication, i.e. for any two integers, a and b, ab is an integer.
     Example:  \[5~\times 6 = 30; -9~\times -3 = 27\]
  • Commutative property: Division is NOT commutative for integers- For any two integers a and b
           Example: 3/6 = 1/2.
  • Associative property: Multiplication is associative for integers. For any three integers, a, b and c, more...

  Geometry   Learning Objectives  
  •  Line and angles
  •  Triangle
  • Congruency of triangles
  • Symmetry
  Lines and Angles  
  • A is an infinitely thin, infinitely long collection of points extending in two opposite directions. While drawing lines in geometry, an arrow at each end is put up to show that it can extend infinitely.
            A line can be named either using two points on the line (for example\[\overleftrightarrow{AB}\] ) or simply by a letter, usually lowercase (for example, line m).
  • A line segment has two end points. It contains these endpoints and all the points of the line between them. One can measure the length of a segment, but not of a line.
              A segment is named by its two endpoints, for example  \[\overline{AB}\].  
  • A ray is a part of a line that has one endpoint and goes on infinitely in only one direction. You cannot measure the length of a ray.
            A ray is   named using its endpoint first, and then any other point on the ray (for example,\[\overline{BA}\])            
  • An angle is formed when two lines (or rays or line-segments) meet.
             
  • The sum of two complementary angles is equal to\[90{}^\circ \].
  •  The sum of two supplementary angles is equal to\[180{}^\circ \].
  • A right angle measures\[90{}^\circ \].
  • Two adjacent angles have a common vertex and a common arm but no common interior. Linear pair of angles are adjacent and supplementary to each other.
When two lines l and m meet, we say they intersect; the meeting point is called the point of intersection. (i) When two lines intersect (looking like the letter X), two pairs of opposite angles are formed. They are called vertically opposite angles. They are equal in measure. (ii) A transversal is a line that intersects two or more lines at distinct points, it gives rise to several types of angles as shown in the figure.            (iii) In the figure, transversal p intersects the lines I and m.
  •  \[\angle \]3, \[\angle \]4, \[\angle \]5, \[\angle \]6 are interior angles.
  •   \[\angle \]1, \[\angle \]2, \[\angle \]7, \[\angle more...

  Mensuration   Learning Objectives  
  • Mensuration
  • Introduction to Solid Shapes
  • Important Facts
  Mensuration   Mensuration is the branch of mathematics which deals with the study of geometrical shapes, their area, volume and related parameters. Here, we will discuss the areas and perimeter of plane figures.   Some important mensuration formula are listed in the table given below.            
Name Figure Perimeter Area
Rectangle \[2\left( a + b \right)\] \[\operatorname{a}~\,\,\times \,\,b\]
Square 4a \[{{a}^{2}}\]
Right Triangle more...
  Blood Relation   Blood Relation Blood relation is a biological relation. Although husband and wife are not biologically related to each other 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. Blood relations are mainly classified into two categories;   Relations of Paternal Side  
1. Father's father               Grandfather
2. Father's mother              Grandmother
3. Father's brother              Uncle
4. Father's sister                Aunt
5. Children of uncle             Cousin
6. Wife of uncle               Aunt
7. Children of aunt       more...
  Series   Introduction A series is a sequence of many elements following a particular pattern or rule. Such sequence is formed by putting the elements one after another from left to right. There are mainly three types of series - Letter series, Number series and Mixed series.   Letter Series A letter series is a sequence of many elements made of English alphabets. Such sequence is formed by putting the letters one after another from left to right.   Type 1 This type of letter series is a sequence of Setters related to each other by some specific pattern.   Which one of the following letters will come in place of the question mark (?)?             A E I M Q?             (a) T                             (b) U             (c) V                             (d) W             (e) None of these Ans.     (b) Explanation: The letters in the series are moved four steps forward alternatively.                   Replace the question mark (?) in the given letter series with the correct letter.             C E H J M O?             (a) Q                             (b) S             (c) R                              (d) T             (e) None of these Ans.     (c) Explanation: The letters in this series are moved two and three steps forward alternately.                 Commonly Asked Questions Replace the question mark (?) in the given letter series with the correct letter.             U R P M K?             (a) G                             (b) E             (c) H                             (d) F             (e) None of these Ans.     (c) Explanation: The letters in this series are moved three and two steps backward alternately.                             Replace the question mark (?) in the given letter series with the correct letter.             A B F G K L?             (a) P                             (b) M             (c) R                              (d) O             (e) None of these Ans.     (a) Explanation: The letters in this series are moved one and four steps forward alternately.               Type 2             In this type, a group of English alphabets forms a series according to a certain rule.             WV, PO, IH, BA?             (a) ST                           (b) RS             (c) UT                           (d) UV             (e) None of these Ans.     (c) Explanation: Each of the two more...

  Analogy   Introduction Analogy is a similarity between like features of two things on which comparison may be based 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. Analogy plays a significant role in problem solving such as decision making, perception, memory, creativity, emotion, explanation and communication, it lies behind basic tasks such as the identification of places, objects, etc.               Example             Money : Bank : : Book: Library             Explanation: 1st pair- Money: Bank (Thing and a place where it is kept).             2nd pair- Book: Library (Thing and a place where it is kept).             As ‘Money’ is deposited in ‘Bank’, similarly a ‘Book’ is deposited in a ‘Library’.             Clearly, both pairs show similar relationship in a logical way. Hence, both pairs are analogous.               Example             Nose : Smell : : Skin : Feel             Explanation: 1st pair - Nose: Smell (Body part and its utility relationship).             2nd pair – Skin : Feel (Body part and its utility relationship).             We smell (a type of sensation) with nose (a body part); similarly we feel (a type of Sensation something when it touches our skin (a body part),             Clearly, both pairs show similar relationship (body part and its utility relationship). Hence, both pairs exhibit analogy.          Types of Problems             Problems based on analogy may be of different types.               Problems Based on Synonymous Relationship             In such problems, the words given in one pair having same meaning and relationship has to be found in another pair.               Example:             Hard : Tough : : Wrong : Untrue             Explanation; 1st pair-Hard: Tough (Synonymous relationship).             2nd pair-Wrong: Untrue (Synonymous relationship).               Example:             Sad : Sorrow : : Happy : Joy             Explanation: 1st pair – Sad : Sorrow (Synonymous relationship).             2nd pair – Happy : Joy (Synonymous relationship).   Commonly Asked Questions             Select the pair which is related in the same way as the pair of words given in the question:             Baby : Infant : : _________ : ________             (a) Cub : Bear                   (b) Country : Continent             (c) Girl : Woman              (d) Film : Movie             (e) None of these Ans.     (d)             Explanation: Option (d) is correct because “Baby” and ‘Infant’ are synonymous words. In the same manner ‘Film’ and ‘Movie’ are also the synonymous words. Rest of the options is incorrect because words in options (a), (b) and (c) have small- big relationship. Option (e) is useless because of the correctness of option (d).               Select the pair which is related in the same way as the pair of words given in the question.             Catch : Capture : : ________ : more...

                                  Classification   Introduction Classification is a process of grouping various objects on the basis of their common properties. In the Questions that are generally asked on classification we have to assort the items of a given group on the basis of certain common quality they possess and then spot the stranger out. For sample, if we have to separate out the odd one from the group of four animals- lion, tiger, bear and goat, then definitely that animal will be goat because goat is the only animal in the group which is a domestic animal. Rests of the animals (lion, tiger and bear) are wild animals.   Letter Based Classification In these type, a letter or a group of letters is to be sort out from the others on the others on the basis of a specific pattern.   Example Which of the following pair of letters is different from the other three?             (a) JM-KL                      (b) QP-RS             (c) EH-FG                      (d) MP-NO             (e) None of these Ans.     (b) Explanation: In all other groups, the two letters on the right fit between the two letters on the left.   Which one of the following pairs of letters is different from the other three?             (a) AEC                         (b) PTR             (c) FJH                          (d) KPM             (e) None of these Ans.     (d) Explanation: In all other groups, the first, third and second letters are alternate.   Commonly Asked Questions   Which one of the following pairs of letters is different from the other three?             (a) AYT-BZU                  (b) FNG-EMF             (c) RWO-QVN                (d) HJD-GIC             (e) None of these Ans.     (a) Explanation: In all other groups, the letters in the first part are one step forward than the corresponding letters in the second part.   Which one of the following pairs of letters is different from the other tree?             (a) DEVW                      (b) GHMN                                     (c) JKNO                       (d) CBED             (e) None of these Ans.     (d) Explanation: The letters are arranged in increasing order, while in (d) they are not   Word Based Classification In these type of questions/ a word is to be sorted out from the others on the basis of some properties or a particular pattern   Example Choose the word which is not like the other words in the group.                            (a) Paper                       (b) Pencil                                                                        (c) Rubber                      (d) Stationery             (e) None of these Explanation: All others are the various stationery materials.   Choose the word which is not like the other words in the group.             (a) Brinjal                                  (b) Potato             (c) Orange                                  (d) Lady Finger             (e) None of these Ans.     (c) Explanation: Orange is fruit while others are vegetables.   Commonly Asked Questions   Choose the word which is not like the other words in more...



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