The digits indicated by * in 3422213** so that this number is divisible by 99 are :

Solution(By Examveda Team)

Let the unit's digit be x and ten's digit be y
Then, the number is 3422213yx
Also, 99 = (11 × 9), where 11 and 9 are co-primes
Since the given number is divisible by 9, it follows that (3 + 4 + 2 + 2 + 2 + 1 + 3 + y + x) = (17 + y + x) must be divisible by 9
So, y + x = 1 or y + x = 10
Again, the given number is divisible by 11
So, (x + 3 + 2 + 2 + 3) - (y + 1 + 2 + 4) = x - y + 3 is either 0 or 11
∴ (x - y + 3 = 0 or x - y + 3 = 11)
⇒ (y - x = 3 or x - y = 8)
Now, (y + x = 1 and y - x = 3)
⇒ y = 2 and x = - 1
(y + x = 1 and x - y = 8)
⇒ x = $$\frac{9}{2}$$
(y + x = 10 and y - x = 3)
⇒ y = $$\frac{13}{2}$$
(y + x = 10 and x - y = 8)
⇒ x = 9 and y = 1
Thus, x = 9, y = 1
So, required number is 342221319