The word 'SCHOOL' has 6 letters with 'O' repeated twice. The arrangements are 6! / 2! = 720 / 2 = 360.

Each ball has 3 choices (boxes), so for 5 balls, the total arrangements = 3^5 = 243.

The number of ways to arrange 5 students in 5 chairs is 5! = 120.

The word 'LEVEL' has 5 letters with 'E' repeated twice. The arrangements are 5! / 2! = 60 / 2 = 30.

A number is divisible by 15 if it is divisible by both 3 and 5. 70 is not divisible by 3.

A number is divisible by 3 if the sum of its digits is divisible by 3. The sum of the digits of 100 (1 + 0 + 0 = 1) is not divisible by 3.

Geometric progression does not relate to harmonic progression, as harmonic progression is defined through the reciprocals of an arithmetic progression.

The terms 1/2, 1/3, 1/4, and 1/5 are in harmonic progression, but 1/6 does not fit as its reciprocal does not maintain the arithmetic progression.

'110' in base-2 = 1*2^2 + 1*2^1 + 0*2^0 = 4 + 2 + 0 = 6.

'1010' in binary is 1*8 + 0*4 + 1*2 + 0*1 = 10.

'1010' in binary is 10 in decimal, which is represented as 'A' in hexadecimal.

'A' represents 10, so 'B' represents 11 in decimal.

'A' = 10 in decimal, '5' = 5 in decimal. Their sum is 10 + 5 = 15.

In base-7, 'A' = 5*7^1 + 0*7^0 = 35 + 0 = 50 in decimal.

'A' (10) + 5 = 15, which is 'F' in hexadecimal.

In base-4, '22' equals 2*4^1 + 2*4^0 = 8 + 2 = 10.

'43' in base 5 is calculated as 4*5^1 + 3*5^0 = 20 + 3 = 23.

'1A' in hexadecimal is calculated as 1*16^1 + 10*16^0 = 16 + 10 = 26.

'D' in hexadecimal represents 13 in decimal.

'2C' in hexadecimal is calculated as 2*16^1 + 12*16^0 = 32 + 12 = 44.

50 in decimal is '110' in base-7 (1*7^2 + 1*7^1 + 0*7^0 = 50).

'320' in base 5 = 3*5^2 + 2*5^1 + 0*5^0 = 75.

215 in decimal is '543' in base-6, so 'X' is 4.

'XYZ' in base 5 means X*25 + Y*5 + Z = 100. The only valid solution is X=2.

In base-3, 'XYZ' means X*9 + Y*3 + Z = 26. The only valid digit for X is 2.

In base-4, 'XYZ' = 4^2*X + 4^1*Y + 4^0*Z = 27. The only valid combination is X=3, Y=3, Z=3.

30% of 10 liters = 0.3 * 10 = 3 liters of salt.

Since 1000 can be expressed as 10^3, we have 10^x = 10^3, thus x = 3.

1000 can be expressed as 10^3, so x + 1 = 3, leading to x = 2.

Since 1000 can be expressed as 10^3, we have 10^(x+2) = 10^3, thus x + 2 = 3, leading to x = 1.