Correct Answer: 12

Solution : Given:
6 @ 4 @ 7 = 101, 2 @  5 @ 11 = 150

Use the following operations in place of the given symbols @.
Like, 6 @ 4 @ 7 = 101 i
= 6 ² + 4 ² + 7 ² = 36 + 16 + 49 = 101
And, 2 @ 5 @ 11 = 150
= 2 ² + 5 ² + 11 ² = 4 + 25 + 121 = 150
Similarly, A @ 8 @ 9 = 289
⇒ A ² + 8 ² + 9 ² = 289
⇒ A ² + 64 + 81 = 289
⇒ A ² + 145 = 289
⇒ A ² = 289 – 145
⇒ A ² = 144
⇒ A = √ 144
⇒ A = 12

So, the value of A is equal to 12. Hence, the third option is correct.