If N ÷ 5 leaves remainder 3 and N ÷ 2 leaves remainder 0,

False

Explanation:

Given that, when N is divided by 5, it leaves the remainder 5. (i.e) N = 5n+3 where n= 0, 1, 2, 3, …

Similarly, when N is divided by 2, it leaves the remainder 0. So N is an even Number. (Using divisibility test rule of 2).

But in N = 5n+3, the second term is odd.

So, 5n is an odd number.

When you substitute n = 1, 3, 5 … in 5n+3, we will get 8, 18, 28 …

Now, if we divide N by 10, it should be written as

N = 10 n+8

So, when N is divided by 10, it always leaves the remainder 8.