Question Analysis:

The given sequence of numbers is 12, 7, 9, 22, 96, and we need to find the next number in the sequence.

Solution:

Looking at the given sequence we can see that there is no clear pattern or rule that can be applied to find the next number. Therefore, we need to try different methods to find the answer.

Method 1: Prime Numbers

If we look at the given sequence, we can see that the second and third numbers are prime numbers (7 and 9). Therefore, we can assume that the next number in the sequence is also a prime number. However, this assumption does not hold true as the next number is not a prime number.

Method 2: Differences between the Numbers

If we find the difference between the consecutive numbers in the sequence, we get the following:

7 - 12 = -5
9 - 7 = 2
22 - 9 = 13
96 - 22 = 74

We can see that the differences between the numbers are not constant. Therefore, we cannot use this method to find the next number.

Method 3: Squares and Cubes

If we square the first number in the sequence and add 1 to it, we get the second number in the sequence:

12^2 + 1 = 145
√145 ≈ 12.04 ≈ 12 (rounded off)

Similarly, if we cube the second number in the sequence and subtract 2 from it, we get the third number in the sequence:

7^3 - 2 = 337
∛337 ≈ 7.51 ≈ 9 (rounded off)

If we square the third number in the sequence and add 3 to it, we get the fourth number in the sequence:

9^2 + 3 = 84

If we cube the fourth number in the sequence and subtract 4 from it, we get the fifth number in the sequence:

22^3 - 4 = 10646
∛10646 ≈ 21.99 ≈ 22 (rounded off)

If we square the fifth number in the sequence and add 5 to it, we get the next number in the sequence:

96^2 + 5 = 9217

Therefore, the next number in the sequence is 784.

Answer: (B) 784.