Current Affairs 8th Class

  Synthetic Fibres and Plastics   ·                     Fibres that are obtained by chemical processing of petrochemicals are called synthetic fibres. Like natural fibres, these fibres can also be woven into fabrics. ·                     Synthetic fibres and plastics are made of very large units called polymers. ·                     Polymers are made up of many smaller units called monomers. ·                     Synthetic fibres have various uses in our day to day life. They are used in household articles like ropes, buckets, furniture, containers, etc. Apart from items of household uses, they are also used in aircrafts, ships, spacecraft?s, healthcare, etc. ·                     Rayon, nylon, polyester and acrylic are some of the main types of synthetic fibres. ·                     The properties of rayon are similar to that of silk. Due to this rayon is also called as artificial silk. ·                     The different types of fibres differ from one another in their strength, water absorbing capacity, nature of burning, cost, durability, etc. ·                     The material which gets decomposed through natural processes, such as action by bacteria, is called biodegradable. ·                     The material which is not easily decomposed by natural processes is termed as non-biodegradable. ·                     Plastic becomes one of the most important things of our life. We can see lots of things made up of plastics at home, or outside, everywhere. ·                     Plastics can be classified mainly into two types ?
(i) Thermoplastics and
(ii) Thermosetting plastics.
·                     Thermoplastics are the plastics that do not undergo chemical change in their composition when heated and can be molded again and again. Polyethylene, polypropylene, polystyrene and polyvinyl chloride are some of the examples of thermoplastics. ·                     Thermosetting plastics are the plastics that can melt and take shape once; after they have solidified, they stay solid. They undergo chemical change in their composition when heated and cannot be molded again and again. Polystyrene, polyisoprene, rubber are examples of thermosetting polymers. ·                     Plastics release poisonous gases on burning. On dumping in the ground they may take years to get decomposed. They are non-biodegradable in nature. ·                     We need to use synthetic fibres and plastics in such a manner that we can enjoy their good qualities and at the same time minimise their environmental hazards. ·                     Be a responsible citizen and always remember the 4 R principle - Reduce, Reuse, Recycle and Recover to minimise the pollution which more...

  Crop Production and Management   ·                     Crop production and management plays a key role in our country's economy. By adopting advanced and latest technologies in agriculture, enough yields of crops can be grown to provide food to our growing population. ·                     The plants of same kind grown and cultivated at one place on a large scale are called a crop. ·                     There are mainly two types of crops grown in India - rabi and kharif crops. ·                     Rabi crops are the agricultural crops that are sown in winter and harvested in the spring. Wheat, Gram, Pea, Mustard, Linseed, Barley, Peas are the examples of rabi crop. ·                     Kharif crops are referred to those crops that are sown in the rainy (monsoon) season. These crops are planted for autumn harvest and may also be called the summer or monsoon crop. Paddy, cotton, maize, sugarcane are some examples of the kharif crops. ·                     For growing a good crop, it is necessary to prepare soil by tilling and livelong before sowing the seeds. Ploughs and levellers are used for this purpose. ·                     Selection of good quality seeds is another important step of growing a good crop. The seeds should be sown at appropriate depth and at enough distance from one another to avoid competition for nutrients. ·                     The use of organic manure and fertilizers helps in replenishing the quality of soil. Use of chemical fertilizers is commonly used in present time. The use of chemical fertilizers in excessive amount is also harmful for environment. ·                     Water is important for proper growth and development of plants. The supply of water to crops at different intervals is called irrigation. Plant roots absorb water and mineral from the soil. Along with water, minerals and fertilisers are also absorbed. The time and frequency of irrigation varies from crop to crop, soil to soil and season to season. ·                     Moat, Chain pump, Rahat and Dhekli are the traditional methods of irrigation. At present irrigation is done by pumps and tube wells run on electricity, by sprinkler system and by drip system. ·                     Sprinkler system and drip irrigation methods also minimise the loss of water. ·                     Some unwanted plants called weeds also need to be removed from the field from time to time as they compete with the main crops for nutrients. The practice of removing of weeds is also called weeding. It can be done by using weedicides like 2, 4 -D. ·                     The cutting of the mature crop manually or by machines is called harvesting. ·                     The process of separating out grains more...

  Number System   Learning Objectives
  • Properties of Rational Numbers
  • Square and Square Roots
  • Cube and Cube Roots
  • Playing with Numbers
  • Divisibility Test
  Properties of Rational Numbers Rational numbers are the numbers that can be expressed in the form \[\frac{p}{q}\], where p and q are integers and \[q\ne ~0\] . The collection of rational numbers is denoted by Q. These rational numbers satisfy following laws or properties
  •  Rational numbers are closed under addition, subtraction and multiplication. If a, b are any two rational numbers, then the sum, difference and product of these rational numbers is also a rational number, thus we can say that rational numbers satisfy the closure law.
  • Rational numbers are commutative under addition and multiplication. If a, b are rational numbers, then:
  • Commutative law under addition: \[\mathbf{a}+\mathbf{b}=\mathbf{b}+\mathbf{a}\]
  • Commutative law under multiplication: \[\mathbf{a}\times \mathbf{b}=\mathbf{b}\times \mathbf{a}\]
  • Rational numbers are associative under addition and multiplication. If a, b, c are rational numbers, then:
  • Associative law under addition: \[\mathbf{a}+\left( \mathbf{b}+\mathbf{c} \right)=\left( \mathbf{a}+\mathbf{b} \right)+\mathbf{c}\]
  • Associative law under multiplication: \[\mathbf{a}\left( \mathbf{bc} \right)=\left( \mathbf{ab} \right)\mathbf{c}\]
  • 0 is the additive identity for rational numbers.
  • 1 is the multiplicative identity for rational numbers.
  • The additive inverse of a rational number \[\frac{p}{q}\] is \[\left( -\frac{p}{q} \right)\], and the additive inverse of \[\left( -\frac{p}{q} \right)\] is\[\frac{p}{q}\].
  • If \[\frac{a}{b}\times \frac{p}{q}=1\], then \[\frac{a}{b}\] is the reciprocal or multiplicative inverse of \[\frac{p}{q}\] and vice versa.
  • For all rational numbers p, q and r; p (q + r) = pq + pr and p (q - r) = pq - pr is known as the distributive property.
  Example 1. Find the multiplicative identity of the rational number \[\frac{\mathbf{455}}{\mathbf{1024}}\] (a) \[\frac{1024}{455}\]                (b) \[\frac{1}{455}\] (c) \[\frac{1}{1024}\]                (d) 1 (e) None of these Answer: (a)   2. Which one of the following rational numbers lies between \[\frac{\mathbf{45}}{\mathbf{78}}\] and \[\frac{\mathbf{26}}{\mathbf{52}}\]? (a) \[\frac{75}{156}\]               (b) \[\frac{84}{156}\] (c) \[\frac{95}{156}\]               (d) \[\frac{105}{156}\] (e) None of these Answer: (b) Explanation: On equating the denominator, the given rational number reduce to \[\frac{90}{156}\] and \[\frac{78}{156}\] and the rational number lying between these two is \[\frac{84}{156}\].   Square and Square Roots If a natural number m can be expressed as \[{{n}^{2}}\], where n is also a natural number, then m is called the square root of a square number, \[{{n}^{2}}\]. For example, 1, 4, 9, 16, 25 are the square numbers. Some interesting properties of square numbers are as follows:
  • All square numbers end with 0, 1, 4, 5, 6 or 9 at unit's place.
  • No square number ends with 2, 3, 7 or 8 at unit's place.
  • When a square number ends with 6 at unit's place, the number whose square it is, will have either 4 or 6 in unit's place.
  • There are 2n non perfect square numbers between the squares of the numbers n and (n + 1).
  • If a natural number cannot be expressed as a sum of successive odd natural numbers starting with 1, then it is not a more...

  Geometry   Learning Objectives  
  • Understanding Polygons
  • Parallelogram
  • Rhombus
  • Trapezium
  • Kite
  • Rectangle
  • Square
  • Practical Geometry
  Understanding Polygons  
  • A polygon is a simple closed curve made up of only line segments.
  • A line segment that connects the two non-consecutive vertices of a polygon is called a diagonal.
  • A convex polygon is defined as a polygon with all its interior angles less than \[180{}^\circ \]. This means that all the vertices of the polygon will point outwards, away from the interior of the shape.
  • A concave polygon is defined as a polygon with one or more interior angles greater than \[180{}^\circ \]. It looks like a vertex has been 'pushed in' towards the inside of the polygon.
  • A regular polygon is both 'equiangular' and ?equilateral?. For example, a square has sides of equal length and angles of equal measure and thus it is a regular polygon. A rectangle is equiangular but not equilateral, so it is a irregular polygon.
  Properties of Polygon  
  • The sum of the measures of the external angles of any polygon is \[360{}^\circ \].
  • For a regular polygon,
  • Number of sides \[\left( n \right)=360{}^\circ \]/ (measure of an exterior angle)
  • Number of sides \[\left( n \right)=360{}^\circ \]/ (\[180{}^\circ \]- measure of an interior angle)
  • For a regular polygon,
  • Measure of interior angle \[(\theta )=180{}^\circ -\left( 360{}^\circ /n \right)\]
  • Measure of interior angle \[(\theta )=180{}^\circ \left( \left( n-2 \right)/n \right)\]
  • A polygon having three sides is called a triangle. Similarly a polygon having four sides is called quadrilateral, a polygon having five sides is called pentagon, a polygon having six sides is called hexagon.
  • A triangle can never be concave.
  • The sum of all interior angles of a triangle is \[180{}^\circ \].
  • The sum of all interior angles of a quadrilateral is \[360{}^\circ \].
  Parallelogram A parallelogram is a quadrilateral whose opposite sides are parallel. Properties of a parallelogram
  • Opposite angles of a parallelogram are equal.
  • Adjacent angles of a parallelogram are supplementary i.e. their sum is equal to \[180{}^\circ \].
  •  The sum of all interior angles of a parallelogram is \[360{}^\circ \].
  • Opposite sides of a parallelogram are parallel (by definition) and so will never intersect.
  • Diagonals of a parallelogram bisect each other.
  Rhombus A rhombus is a quadrilateral whose all sides are equal and opposite sides are parallel.   Properties of a Rhombus  
  •  Opposite angles of a rhombus are equal.
  •  Adjacent angles of a rhombus are supplementary i.e. their sum is more...

  Mensuration   Learning Objectives  
  • Mensuration
  • Visualizing Solid Shapes
  Mensuration   Mensuration is the branch of mathematics which deal with the study of geometric shapes, their area, volume and related parameters. Some important formulae of area and volume are listed below.   Area of some plane figures:   more...
  Algebra             Learning Objectives  
  • Liner equation in one variable
  • Algebraic expression and identities
  • Factorisation 
  • Exponents and Powers
  • Direct and Indirect Proportion
  • Comparing Quantities
  Linear Equations in one Variable  
  • An algebraic equation is an equality involving variables and an equality sign. The expression on the left of the equality sign is the Left Hand Side (LHS). The expression on the right of the equality sign is the Right Hand Side (RHS).
  • An algebraic equation involving only one variable with its highest power 1 is called a linear equation.
  • The values of the expressions on the LHS and RHS are equal. This happens to be true only for certain values of the variable. These values are the solutions of the equation.
  Example 1. Solve the equation: \[\frac{\mathbf{0}\mathbf{.5}\left( \mathbf{z-0}\mathbf{.4} \right)}{\mathbf{3}\mathbf{.5}}\mathbf{-}\frac{\mathbf{0}\mathbf{.6}\left( \mathbf{z-2}\mathbf{.7} \right)}{\mathbf{4}\mathbf{.2}}\mathbf{=z+6}\mathbf{.1}\] (a) \[-\frac{202}{35}\]    (b) \[\frac{202}{35}\] (c) \[\frac{35}{202}\]      (d) \[-\frac{35}{202}\] (e) None of these Answer: (a) Explanation: \[\frac{5\left( z-0.4 \right)}{35}-\frac{6\left( z-2.7 \right)}{42}=z+6.1\Rightarrow \frac{30z-12-30z+81}{210}=z+6.1\Rightarrow \frac{69}{210}=z+6.1\Rightarrow z=-\frac{202}{35}\]   2. David cuts a bread into two equal pieces and cuts one half into smaller pieces of equal size. Each of the small pieces is twenty gram in weight. If he has seven pieces of the bread all with him, how heavy is the original cake. (a) 120 gm                     (b) 180 gm (c) 300 gm                     (d) 240 gm (e) None of these Answer: (d) Explanation: There are total of seven pieces, so number of smaller pieces is six. Weight of each smaller piece is 20 gm Therefore, weight of six such pieces is \[6\times ~20=120\text{ }gm\] Hence the total weight of original cake \[=2\times ~120=240\text{ }gm\]   Algebraic expressions and identities  
  • The expression that contains only one term is called a monomial.
          For example,  \[3{{x}^{2}},8xy,\,-6z,\,9x{{y}^{2}},\,2x,\,-3,\,22qrs,\,\,\] etc. are the monomials.
  • The expression that contains two terms is called a binomial.
          For example, \[4a+5b,\,3l-8m,\,2m+7,3-7{{x}^{2}}y,\,4{{x}^{2}}-{{z}^{2}},\] etc. are the binomials.
  • The expression that contains two terms is called a trinomial.
          For example, \[a+b+c,\text{ }2x+3y-5z,{{x}^{2}}{{y}^{2}}z-{{x}^{3}}{{y}^{2}}z+1,\] etc. are the trinomials.
  • An expression containing, one or more terms with non-zero coefficient (with variables having non-negative exponents) is called a polynomial. A polynomial may contain any number of terms, one or more than one.
          For example, \[6xy,\,\,8{{x}^{2}}yz-7,\,\,5x+9y+8z,\] etc. are the polynomials.
  • The terms which contain similar variables having same powers are called like terms. Coefficients of like terms need not be the same.
  • The terms which contain different variables are called unlike terms.
  • Only like terms can be added or subtracted.
  • Some standard algebraic identities are as follows:
         \[{{\left( a+b \right)}^{2}}={{a}^{2}}+2ab+{{b}^{2}}\]          \[{{\left( a-b \right)}^{2}}={{a}^{2}}-2ab+{{b}^{2}}\]          \[{{a}^{2}}-{{b}^{2}}=\left( a+b \right)\left( a-b \right)\]          \[\left( x+a \right)\left( x+b \right)={{x}^{2}}+\left( a+b \right)x+ab\]   Example 1. The product of \[\left( \mathbf{-3}{{\mathbf{x}}^{\mathbf{2}}}\mathbf{-x+7} \right)\] and \[\left( \mathbf{3-2x+}{{\mathbf{x}}^{\mathbf{2}}} \right)\] is____. (a) \[-3{{x}^{4}}+5{{x}^{3}}-17x+21\]                     (b) \[{{x}^{5}}+24{{x}^{4}}+5{{x}^{2}}+x+21\] (c) \[8{{x}^{5}}+{{x}^{4}}-12+7x+1\]         (d) \[3{{x}^{5}}-4{{x}^{4}}+1{{x}^{3}}-5{{x}^{2}}-7x+2\] (e) None of these Answer: (a) Explanation: \[\left( more...

  Statistics   Learning Objectives  
  • Data Handing
  • Introduction to Graphs
  Data Handling  
  • Pictograph: A pictograph is a way of showing data using images.
  • The number of times that a particular entry occurs in a data is called its frequency.
  • In the class interval, 10-20, 10 is called the lower class limit and 20 is called the upper class limit.
  • The difference between the upper class limit and lower class limit is called the width or size of the class interval.
  Introduction to Graphs  
  • Bar Graph: It is a display of information using bars of uniform width, their heights being proportional to the respective values.
  • Double Bar Graph: It is a type of bar graph showing two sets of data simultaneously. It is useful for the comparison of the data.
  • Histogram: A histogram is a bar graph that shows data in intervals. It has adjacent bars over the continuous intervals.
  • Pie graph: The representation of data on a pie chart is called a pie graph. It is used to compare parts of a whole.
  • A line graph displays data that changes continuously over periods of time. It is a whole unbroken line.
  • For fixing a point on the graph sheet we need, x-coordinate and y-coordinate.
  • The relation between dependent variable and independent variable is shown through a graph.
  Commonly Asked Questions   1. Observe the following histogram and answer the questions.   2. What information is being given by the graph? (a) Height of the students of class 8           (b) Number of students in class 8 (c) Weight of the students of class 8           (d) All of these (e) None of these   3. The following pie-chart represents the expenditures of a family on different items. What percent of total expenditure is spent by the family on housing? (a) 61%                         (b) 16.7% (c) 13.9%                       (d) 12.7% (e) None of these Answer: (b) Explanation: Percentage expenditure on housing  \[=\frac{60{}^\circ \times 100}{360{}^\circ }=16.7%\]  

  Analogy   Learning Objectives
  • What is Analogy
  • Worker and Product
  • Worker and Tool Relationship
  • Tool and Action
  • Worker and Working Place
  • Product and Raw Material
  • Quantity and Unit
  • Study and Topic
  • Animal and Young Ones
  Analogy   In general, 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. In the questions based on analogy, a particular relationship is given and another similar relationship has to be identified from the alternatives provided. Analogy tools are therefore meant to test one's ability to reason - how far you are able to compare and comprehend the relationship that exists between two objects, things or figures. There are many possibilities in establishing a relationship. Here are some useful points on the basic knowledge required for the test.   Worker and Product  
  • Example
Carpenter: Furniture:: Mason : Wall Explanation: Carpenter makes Furniture and Mason builds a Wall.
  • Author: Book
  • Architect: Design
  • Butcher: Meat
  • Chef: Food
  • Choreographer: Ballet
  • Cobbler: Shoes
  • Editor: Newspaper
  • Farmer: Crop
  • Judge: Justice
  • Poet: Poem
  • Painter: Painting
  • Tailor: Clothes
  •            Worker and Tool Relationship  
    • Example
    Woodcutter: Axe :: Soldier: Gun Explanation: Axe is the tool used by a Woodcutter, likewise a Soldier uses Gun to shoot.
  • Author: Pen
  • Astronomer: Telescope
  • Barber: Scissors
  • Butcher: Chopper
  • Blacksmith: Anvil
  • Bricklayer: Trowel
  • Carpenter: Saw
  • Cobbler: Awl
  • Doctor: Stethoscope
  • Farmer: Plough
  • Gardener: Harrow
  • Painter: Brush
  • Sculptor: Chisel
  • Surgeon: Scalpel
  • Surgeon: Scalpel
  •   Tool and Action
    • Example
    Pen: Write :: Knife: Cut Explanation: Pen is used for Writing and Knife is used for Cutting.
  • Sword : Slaughter
  • Auger: Bore
  • Chisel: Carve
  • Gun : Shoot
  • Loudspeaker: Amplify
  • Microscope : Magnify
  • Oar: Row
  • Spade : Dig
  • Shovel : Scoop
  • Spoon : Feed
  • Spanner: Grip
  • Steering : Drive
  •   Worker and Working Place
    • Example
    Farmer: Field :: Doctor: Hospital Explanation: A Farmer works on a Field while a Doctor works in a Hospital.
  • Artist: Theatre
  • Actor: Stage
  • Clerk: Office
  • Driver: Cabin
  • Engineer: Site
  • Lawyer: Court
  • Mechanic : Garage
  • Pilot: Cockpit
  • Sailor: Ship
  • Scientist: Laboratory
  • Teacher: School
  • Warrior: Battlefield
  • Worker: Factory
  •   Product and Raw Material
    • Example
    Cloth: Fibre :: Petrol : Crude Oil Explanation: Cloth is made of Fibre and Petrol is extracted from Crude oil.
  • Book : Paper
  • Butter: Milk
  • Furniture : Wood
  • Fabric : Yarn
  • Jaggery : Sugarcane
  • Sack: Jute
  • Oil: Seed
  • Omlette : Egg
  • Paper: Pulp
  • Road: Asphalt
  • Rubber: Latex
  • Shoes : Leather
  •   Quantity and Unit
    • Example
    Length: Metre :: Mass: Kilogram Explanation: Metre is the unit of Length and Kilogram is the unit of Mass.
  • Angle : Radians
  • Current: Ampere
  • Energy : Joule
  • Force : Newton
  • Temperature : Kelvin
  • Potential : Volt
  • Power: Watt
  • Pressure : Pascal
  • Resistance : Ohm
  • Time : Seconds
  • Volume : Litre
  • Work : Joule
  •   Instrument and Measurement
    • Example
    Barometer: more...

      Blood Relation             Learning Objectives
    • Introduction
    • Understanding of some relations
    • Relations from one generation to next
    • Types of questions
      Introduction Blood relation means a 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.   Let's understand some relations:
    • Mother's or father's son = Brother
    • Mother's or father's daughter = Sister
    • Mother's or father's brother = Uncle
    • Mother's or father's sister = Aunt
    • Mother's or father's father = Grandfather
    • Mother's or father's mother = Grandmother
    • Son's wife = Daughter-in-Law
    • Daughter's husband = Son-in-Law
    • Husband's or wife's sister = Sister-in-Law
    • Husband's or wife's brother = Brother-in-Law
    • Brother's son = Nephew
    • Brother's daughter = Niece
    • Uncle or aunt's son or daughter = Cousin
    • Sister's husband = Brother-in-Law
    • Brother's wife = Sister-in-Law
    • Grandson's or Granddaughter's daughter = Great grand daughter
      There are mainly two types of blood relations: (i) Blood relation from paternal side (ii) Blood relation from maternal side   Relations of Paternal side
    • Father's father \[\to \]               Grandfather
    • Father's mother     \[\to \]               Grandmother
    • Father's brother    \[\to \]               Uncle
    • Father's sister     \[\to \]               Aunt
    • Children of uncle \[\to \]                 Cousin
    • Wife of uncle     \[\to \]               Aunt
    • Children of aunt \[\to \]                 Cousin
    • Husband of aunt    \[\to \]               Uncle
      Relations of Maternal Side
    • Mother's father                        \[\to \]    Maternal grandfather
    • Mother's mother                       \[\to \]    Maternal grandmother
    • Mother's brother                       \[\to \]    Maternal uncle
    • Mother's sister                         \[\to \]    Aunt
    • Children of maternal uncle \[\to \]    Cousin
    • Wife of maternal uncle             \[\to \]    Maternal aunt
      Relations from one generation to next Generation I:       Grandfather, grandmother, maternal grandfather, maternal grandmother \[\downarrow \] Generation II: Mother, father, uncle, aunt, maternal uncle, maternal aunt \[\downarrow \] Generation III:       Self, sister, sister-in-law, brother, brother-in-law (Present Generation)                           \[\downarrow \] Generation IV: Son, daughter, nephew, niece   Types of questions Various types of questions can be asked on blood relations.  
    • Type 1
    In these types of questions, a family tree or a relationship chart is required to be drawn I from the information given in the questions.  
    • Example
    Pointing towards a person in a photograph, Raman said, "She is the only daughter of the mother of my brother's sister." How is the person related to Raman? (a) Uncle (b) Nephew's (c) Mother (d) Sister (e) None of these Answer: (d) Explanation: The mother of Raman's brother's sister is the mother of Raman and only daughter of Raman's mother means Raman's sister. Hence, the person is related as sister to Raman.   Commonly Asked Questions  

      Series   Learning Objectives
    • Number Series
    • Letter Series
    • Mixed Series
      Series Series is a sequence of elements put together according to a certain rule. Series is mainly of three types - Letter Series, Number Series and Mixed Series.     Number Series Such type of series consists of numbers that are arranged in a particular sequence, in the question related to number series, candidates are asked either to insert a missing number or find the one that does not follow the pattern of the series. On this basis we divided the questions of number series in two types. Let’s discuss them one by one.   Type - I (To insert a missing number)
    • Example 1
    4, 9, 19, 34, 54, ?, 109 (a) 89                            (b) 84 (c) 74                                        (d) 79 (e) None of these Answer: (d) Explanation: The difference between the numbers increases by 5 at each step as it means left to right in the series, after beginning from 5, i.e.,    
    • Example 2
    27, 28, 25, 25, 23, 22, 21? (a) 20                                        (b) 21 (c) 19                                        (d) 18 (e) None of these Answer: (c) Explanation: There are two alternate series: Series I: 27, 25, 23, 21 (following - 2 pattern) Series II: 28, 25, 22, 19 (following - 3 pattern)  
    • Example 3
    3, 15, 90, 630, 5040,? (a) 35280                       (b) 40320 (c) 45360                                   (d) 10080 (e) None of these Answer: (c) Explanation: The series follows the pattern given below.    
    • Example 4
    6, 7, 9, 11, 15, 15, 24, 19 ? (a) 32                                        (b) 34 (c) 36                                        (d) 37 (e) None of these Answer: (c) Explanation: There are two alternate series.   Type - II (To find the number that does not follow the pattern of the series)
    • Example 1
    10, 13, 26, 37, 51, 85, 154 (a) 10                              (b) 26 (c) 51                            (d) 154 (e) None of these Answer: (c) Explanation: The given series contains two alternate series.  
    • Example 2
    9, 13, 21, 37, 69, 132, 261? (a) 21                                        (b) 37 (c) 69                            (d) 132 (e) 261 Answer: (d) Explanation: Hence, the wrong number is 132 and should be replaced by 133.  
    • Example 3
    2, 5, 11, 23, 48, 95, 191, 383 (a) 5                                          (b) 11 (c) 23                                        (d) 48 (e) 95 Answer: (d) Explanation: Hence, number 48 is wrong and more...

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    Figure Shape Area
        Rectangle   \[a\times b\]
          Square     \[\begin{align}   & {{a}^{2}} \\  & \frac{1}{2}{{d}_{1}}{{d}_{2}} \\ \end{align}\] Where \[{{d}_{1}}={{d}_{2}}=\sqrt{2}a\]
          Triangle     \[\frac{1}{2}\times b\times h\]
        Parallelogram     \[b\times h\]