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Series Order tricks, shortcuts and examples.

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Series Order tricks : A category of three, four or some numbers is given in the competitive examination. There is a mutual relationship among these numbers. The same relationship has to be understand and the same basis is to be increased further. Examples : 1) What will be the next number in the following series. 3, 10, 31, 94, ----- Ans. : Each terms is increasing by : ( n × 3 ) + 1. Therefore, ( 3 × 3 ) + 1 = 10 ( 10 × 3 ) + 1 = 31 ( 31 × 3 ) + 1 = 94 ( 94 × 3 ) + 1 = 283 Therefore, next number : 283. 2) Find the next order in the category. 1, 4, 9, 16, ---- Ans. : Each term is a squares of consecutive numbers. therefore, 5 × 5 = 25. therefore, next number = 25. Examples : Q. What will be the next number in the following series .  1) 3, 6, 10, 15, 21, ---- Ans. : The difference in each term is increasing in the form of consecutive numbers. that is 3 + 3 = 6. 06 + 4 = 10. 10 + 5 = 15. 15 + 6 = 21. 21 + 7 = 28. There
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Mode in statistics | How to calculate the mode | Mode formula.

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Mode in statistics : Mode definition : For example, some data such as follows : 2, 1, 2, 5, 4, 2, 2, 7, 8, 2. Here, 2 value repeated 5 times that is repeated many times as compared another data. Therefore, 2 is Mode." It is straight forward to calculate mode in case of individual and discrete data.               Mean          Median         Quartile How do you find the mode of  Individual Data ? Que. 1) The following are the marks of 10 students. Calculate the mode. 60, 67, 76, 56, 77, 67, 48, 67, 89, 90. Ans. : Marks            : 48  56  60  67  76  77  89  90 Frequency   :  01  01  01  03  01  01  01  01 Here 67 mark repeated many times that is 3 times. therefore, Mode = 67. Que. 2)  The following are the height in cm of 12 students. Calculate the mode. 40, 41, 43, 41, 46, 47, 41, 41, 40, 42, 41,  46. Ans. : Heights         : 40  41  42  46  47 Frequency   :  02  05  01  03  01 Here 41 cm  height repeated many times that is 5 times. there
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Variation : Introduction, Types of variation : Direct variation | Inverse variation.

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Variation Introduction: Types of Variation : There are two types of variation such as follows : 1) Direct Variation 2) Inverse Variation. Examples of Direct Variation : 1) If 10 books cost Rs. 100, then what is the cost of 15 such books ? Ans. : Here, as the cost of book will increases with an increases in their number, we have a case of direct variation. x = Number of books = 10 y = Cost of 10 books = 100 therefore, x / y = 10 / 100 also, Number of books = 15 Suppose cost of 15 books = Rs. y In direct variation, the ratio of the number of books of the cost of books must be constant. therefore, 10 / 100 = 15 / y y = ( 100 × 15 ) / 10 y = 150 therefore, the cost of 15 books is Rs. 150 2) If the shadow of a 12 meter high building falls 9 meters then how many meters will the shadow of a 9 meter high building fall? Ans. : Suppose x = building height y = building of shadow x / y = 12 / 9 = 9 / y therefore, y = ( 9 × 9 ) / 12 y = 81 / 12 y = 6.75 meters Th
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