-  n < 0               2n < 0, -n > 0 and n2 > 0
Least of 2n, 0, -n and n2 is 2n

The given options are A = 0, B = -n, C = 2n, D = 4n, and E = None of these. We need to determine the least value among these options when n is a negative number.

To solve this problem, we first need to understand the properties of negative numbers. A negative number is any number less than zero and is denoted by a minus sign (-) before the number. For example, -5, -7, -10, etc., are negative numbers.

Now, let's consider each option and see which one is the least when n is a negative number:

Option A: 0 is a non-negative number and is not less than zero. Therefore, this option cannot be the answer.

Option B: -n is a negative number, but it is not necessarily the least. For example, if n = -2, then -n = 2, which is greater than 0 and 2n.

Option C: 2n is a negative number and is always less than 0. Therefore, this option is the least when n is a negative number.

Option D: 4n is also a negative number, but it is greater than 2n. For example, if n = -3, then 2n = -6 and 4n = -12.

Option E: This option cannot be the answer as we have already determined that option C is the correct answer.

Therefore, the correct answer is Option C, which is 2n.

In conclusion, when n is a negative number, the least value among the given options is 2n. Negative numbers have a number of important properties in mathematics, including:

• Negative numbers are less than zero and are denoted by a minus sign (-) before the number.
• The sum of two negative numbers is always a negative number.
• The product of two negative numbers is always a positive number.
• The opposite of a negative number is a positive number, and vice versa.

Some formulas related to negative numbers include:

• Absolute value: The absolute value of a negative number is its distance from zero, which is always a positive number. For example, the absolute value of -5 is 5.
• Addition and subtraction: To add or subtract two negative numbers, we can simply add or subtract their absolute values and then place a negative sign before the result. For example, -3 + (-5) = -8, because |(-3)| + |(-5)| = 3 + 5 = 8, and we place a negative sign before the result.
• Multiplication and division: To multiply or divide two negative numbers, we follow the usual rules of multiplication and division and then determine the sign of the result based on the number of negative factors. For example, (-2) x (-3) = 6, because we multiply 2 and 3 to get 6, and there are two negative factors, which cancel out each other to give a positive result.

If you think the solution is wrong then please provide your own solution below in the comments section .