Question

The general form of an even number is:
(a). $2n-1$
(b). $2n$
(c). $2n+1$
(d). $2$

Answer 1

Hint: The even number is defined by a number which is divisible by 2 so the general form of an even number should be divisible by 2. . From this we can say that the general form of an even number contains 2 as one of the factors and any integer say “n” .Hence, we will get the general form of an even number.

Complete step-by-step answer:

We know that the even number is a number which is divisible by 2 and we are asked to find the general form of the even number so we need a general form which should be divisible by 2. For a number to be divisible by 2 it must contain 2 as one of its factors so the general form contains 2 and as it’s a general form so let’s multiply 2 with “n” where “n” is any integer.
From the above discussion that we just had, we can say that the general form of an even number is 2n.
Hence, the correct option is (b).

Note: There is an alternative way of solving the above problem is:
We know that an even number is a number which is divisible by 2 so divide the options by 2 and see which is divisible by 2.
Now, if you divide the option (a) of the problem i.e. $2n-1$ you will get -1 as remainder. It could not be the answer because we are getting the non – zero remainder.
Similarly, you can check for the option (b) on dividing $2n$ by 2 you will get the remainder 0 so this is the correct answer.
Now, check for the option (c) i.e. $2n+1$, on dividing this by 2 you will get the remainder as 1 so this option is not correct.
Now, check the option (d) which is 2 so on dividing 2 by 2 you will get the remainder 0 so this is the correct option.
From the above, we have found the two options as correct i.e. (b) and (d). As the question asked us to find the general form means the form should be applicable for a range of numbers so the correct answer would be option (b) because it is 2n where n can be any integer.