Question 1
10.22
16.46
15.16
19.61
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Solution: Average of squares of first 'n' natural numbers = ((n+1)(2n+1))/6 Here, n= 6 Therefore, Average of the squares of natural numbers from 1 to 6 =((6+1)(2x6+1))/6 =7x13/6 = 15.16
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Question 2
10
26
35
25
Solution: Average of cubes of first 'n' natural numbers = (n(n+1)^{2})/4 Here, n= 4 Therefore, Average of the cubes of natural numbers from 1 to 4 =(4(4+1)^{2})/4 = 25
Question 3
11
Solution: Let number of innings be N. Since increase in average is by 2 runs (from 68 to 70), runs in each innings would increase by 2 runs Total increase in runs = 2 x N = 2N Also, Sachin needs to score 22 runs more to increase average. ∴ 2N = 22 ∴ N = 11 = Number of innings
Question 4
50
40
30
Solution: Sum of Averages all 6 Numbers = 6 x 18 = 108 Sum of Averages First 3 Numbers = 3 x 6 = 18 Sum of Averages of Last 3 Numbers = 10818 = 90 ∴ Average of the Last 3 numbers = 90/3 = 30
Question 5
75
90
85
73
Solution: Total of 8 tests = 8x83 = 664 Total of first 5 tests = 5x89 = 445 Total of last 3 tests = 664445 =219 Average of last 3 tests = 219/3 = 73
Question 6
44
24
48
34
Solution: 33+46+27+M = 35+35+35+35 M = 34
Question 7
84
89
88
83
Solution: Average after 13 innings should be 23 So, required score = (13x23) – (12x18) = 83
Question 8
42
49
58
53
Solution: Sum of all the ages of father and his sons = 12x7 = 84 Sum of all the ages of sons = (125) x 6 = 42 Age of father = 84 – 42 = 42 years
Question 9
12.76
19.00
18.67
23.24
Solution: Prime numbers between 10 and 30 are 11, 13,17,19,23, and 29 Average of prime numbers between 10 and 30 will be = (11+13+17+19+23+29)/6=18.67
Question 10
32
39
38
Solution: Average = (55+5)/2 = 60/2= 30
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March 25, 2021