What is the Arithmetic mean of the first n natural numbers? from

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 Multiple Choice QuestionsMultiple Choice Questions

101.

The average of nine numbers is 50. The average of the first five numbers is 54 and that of the last three number is 52. Then, the sixth number is

  • 34

  • 24

  • 44

  • 39

32 Views

102.

The average of the first nine integral multiples of 3 is

  • 12

  • 15

  • 18

  • 21

56 Views

103.

The average age of 14 girls and their teacher's age is 15 yr. If the teacher's age is excluded, then the average reduces by 1. What is the teacher's age?

  • 29 yr

  • 35 yr

  • 32 yr

  • 30 yr

23 Views

104.

The arithmeic mean of the scores of a group of students ia a test was 52. The brightest 20% of them secured a mean score of 80 and the dullest 25%, a mean score of 31. The mean score of remaining 55% is

  • 54.6%

  • 45%

  • 50%

  • 51.4%

31 Views

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105.

A cricket player after playing 10 tests scored 100 runs in the 11th test. As a result, the average of his runs is increased by 5. The present age of runs is

  • 45

  • 40

  • 50

  • 55

26 Views

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106.

What is the Arithmetic mean of the first n natural numbers?

  • fraction numerator straight n squared left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction

  • fraction numerator straight n plus 1 over denominator 2 end fraction

  • 2(n+1)

  • fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction


B.

fraction numerator straight n plus 1 over denominator 2 end fraction

Sum of first n natural numbers:
                       equals space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 end fraction

∴  Average mean (average):
               equals space fraction numerator straight n left parenthesis straight n plus 1 right parenthesis over denominator 2 space cross times space straight n end fraction space equals space fraction numerator straight n plus 1 over denominator 2 end fraction


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107.

The average weight of 15 oarsmen in a boat is increased by 1.6 kg when one of the crew who weighs 42 kg is replaced by a new man. Find the weight of the new man (in kg).

  • 67

  • 43

  • 66

  • 65


108.

The average of 17 results is 60. If the average of first 9 results is 57 and that of the last 9 results is 65, then what will be the value of 9th result?

  • 39

  • 78

  • 117

  • 156


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109.

A batsman makes a score of 111 runs in the 10th match and thus increases his average runs per match by 5. What will be his average after the 10th match?

  • 66

  • 61

  • 62

  • 64


110.

What is the sum of 11 terms of an arithmetic progression if the 4th term is 11 and the 7th term is -4?

  • -75

  • 55

  • 11

  • 100


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