**Problem:**

In an examination, there are 6 papers out of which 2 are mathematical. We need to find out the number of ways the papers can be arranged so that 2 mathematical papers are not consecutive.

**Solution:**

To solve the problem, we need to first calculate the total number of ways in which the papers can be arranged. After that, we need to subtract the number of arrangements in which the two mathematical papers are consecutive.

**Total number of ways:**

The total number of ways in which the papers can be arranged is given by:

6! = 720

Here, we are considering all the papers to be distinct.

**Number of arrangements in which two mathematical papers are consecutive:**

Let's assume that the two mathematical papers are M1 and M2. We can arrange them in 2! ways (M1M2 or M2M1).

Now, we need to place the remaining papers in the remaining 4 slots. We can do this in 4! ways.

Therefore, the total number of arrangements in which two mathematical papers are consecutive is:

2! × 4! = 48

**Number of arrangements in which two mathematical papers are not consecutive:**

To find the number of arrangements in which two mathematical papers are not consecutive, we need to subtract the number of arrangements in which two mathematical papers are consecutive from the total number of arrangements.

Therefore, the number of arrangements in which two mathematical papers are not consecutive is:

720 - 48 = 672

Therefore, there are 672 ways in which the papers can be arranged so that 2 mathematical papers are not consecutive.

**Conclusion:**

In this way, we can solve the given problem by calculating the total number of ways in which the papers can be arranged, finding the number of arrangements in which two mathematical papers are consecutive, and subtracting it from the total number of arrangements.

5!×2!=240.~number of maths paper consecutive
720720-240=480.~.not consecutive