Select the set in which the numbers are related in the same way as are the numbers of the following sets.

(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into its constituent digits. E.g., 13 – Operations on 13 such as adding /deleting /multiplying etc. to 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)

(4, 16, 32)

(7, 49, 98)

The correct option is (12, 144, 288).

Let us analyze the relationship between the numbers in the given sets:

Consider the set $(a,b,c)$:

First set: (4, 16, 32)

The second number is obtained by squaring the first number:

$b=a^2=4^2=16$

The third number is obtained by doubling the second number:

$c=2\times b=2\times 16=32$

Second set: (7, 49, 98)

Following the same pattern:

$b=a^2=7^2=49$

$c=2\times b=2\times 49=98$

Thus, the pattern governing the sets is:

$(a,a^2,2\times a^2)$

Now, applying this pattern to the given correct option (12, 144, 288):

First number, $a=12$

Second number: ${12}^2=144$

Third number: $2\times 144=288$

Therefore, the set (12, 144, 288) follows the exact same relationship.