Question : Find the average of the cubes of the first five natural numbers.
Option 1: 35
Option 2: 40
Option 3: 45
Option 4: 50
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Correct Answer: 45
Solution : Average of the cubes of the first $n$ natural numbers = $\frac{n(n+1)^2}{4}$ Here, $n$ = 5 So, the average of the cubes of the first five natural numbers = $\frac{5(5+1)^2}{4}$ = $\frac{5×36}{4}$ = $45$ Hence, the correct answer is 45.
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Question : The average of five positive numbers is 56. If the first number is three-fourths of the sum of the last four numbers, then the average of the last four numbers is:
Question : The average of two numbers is 8, and the average of the other three numbers is 3. The average of the five numbers is:
Question : Of the three numbers whose average is 40, the first is $\frac{1}{3}$rd of the sum of the other two. What is the first number?
Question : The cube of the difference between two given natural numbers is 1728, while the product of these two given numbers is 108. Find the sum of the cubes of these two given numbers.
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