Question : The arithmetic mean of the following numbers
1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7 is:

Option 1: 4

Option 2: 5

Option 3: 14

Option 4: 20

Question : The sum of the cubes of two numbers is 793. The sum of the numbers is 13. Then the difference between the two numbers is:

Option 1: 7

Option 2: 6

Option 3: 5

Option 4: 8

Question : If the square of the sum of three positive consecutive natural numbers exceeds the sum of their squares by 292, what is the largest of the three numbers?

Option 1: 5

Option 2: 6

Option 3: 3

Option 4: 8

Question : If $x^2-15 x+1=0$, what is the value of $x^4-223 x^2+6 ?$

Option 1: 9

Option 2: 5

Option 3: 6

Option 4: 0

Question : A 6-digit number has digits as consecutive natural numbers. The number is always divisible by

Option 1: 4

Option 2: 5

Option 3: 2

Option 4: 3