What is correct approach to solve such questions ?

Question

Answer 1

Generally brute force, or understanding what the language is.

In the question, as far as I can understand, the language $a^{2m + 1}b^{2n + 1}$ is Odd number of $a’s$ followed by some odd number of $b’s$ and those odd numbers will be greater than $1$ as $m$ and $n$ cannot be 0.

Since, the length 10 is asked, what odd numbers we can take?

$\{3, 5, 7, 9\}$

And how can we make $10$ from selecting $2$ numbers independently ? (because $m$ and $n$ have no relation with each other)

$a^7b^3, a^5b^5, a^3b^7$

These $3$ strings can be made.