What will come in place of the question mark (?) in the following equation if '$+$ ' and '$\times$ ' are interchanged and '$-$ ' and '$÷$ ' are interchanged?
$$14-7\times 10÷1+7=?$$

According to the given instructions, interchange the mathematical signs:
* $-$ becomes $÷$
* $\times$ becomes $+$
* $÷$ becomes $-$
* $+$ becomes $\times$

Rewriting the original equation with the interchanged signs:

$$14÷7+10-1\times 7=?$$

Now, solve using the BODMAS rule:

1. Division: $14÷7=2$

$$2+10-1\times 7=?$$

2. Multiplication: $1\times 7=7$

$$2+10-7=?$$

3. Addition: $2+10=12$

$$12-7=?$$

4. Subtraction: $12-7=5$

Thus, $?=5$.