Correct Option: D

Given, 2^a + 3^b = 17
and 2^{a + 2} - 3^{b + 1} = 5
⇒ 2² x 2² - 3^b x 3¹ = 5
⇒ 4.2^a - 3.3^b = 5
Let 2^a = x amd 3^b = y
Then, x + y = 17 ...(i)
4x - 3y = 5 ...(ii)
On multiplying Eq. (i) by 3 and adding to Eq (ii), we get
3x + 3y = 51
4x - 3y = 5
------------------
7x = 56
⇒ x = 8

On putting the value of x in Eq. (i), we get
8 + y = 17
∴ y = 9

Now, 2^a = x
⇒ 2^a = 8 (2)³
∴ 3^b = y = 9
⇒ 3^b = 3²
∴ b = 2
Hence, a = 3 and b = 2