Correct Answer - Option 2 : 27

**Calculation:**

Here, m2- 4mn + 3n2 − 24 = 0

\(\rm ⇒m^2-4mn+(2n)^2-n^2-24=0\)

\(\rm ⇒(m-2n)^2=24+n^2\)

We have, m - 3n = 2 ⇒ m = 3n + 2

\(⇒\rm (3n +2-2n)^2=24+n^2 \)

\(\\⇒ (n+2)^2=24+n^2\)

\(⇒ n^2+4n+4=24+n^2\)

\(\rm ⇒4n=20\)

⇒ n = 5

Putting, value of n in m - 3n = 2, we get

m = 2 + 3(5) = 2 + 15 = 17

∴ (m + 2n) = 17 + 2(5)

= 17 + 10

= 27

Hence, option (3) is correct.