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)

(14, 28 , 84)

(17, 34, 102)

To find the correct set, let us analyze the mathematical relationship between the numbers in the given sets.

Consider the first set: $(14,28,84)$

Let the three numbers in the set be represented as $A$, $B$, and $C$ respectively.
Here, $A=14$, $B=28$, and $C=84$.

If we look at the relationship between the first and second numbers:
$B=A\times 2$
Let's check this: $14\times 2=28$ (This is correct).

If we look at the relationship between the second and third numbers:
$C=B\times 3$
Let's check this: $28\times 3=84$ (This is correct).

Alternatively, the relationship can be written as:
$B=2A$ and $C=6A$ (since $14\times 6=84$).

Let us verify this logic with the second set: $(17,34,102)$

Here, $A=17$, $B=34$, and $C=102$.
First operation: $B=17\times 2=34$ (This is correct).
Second operation: $C=34\times 3=102$ (This is correct).

Thus, the pattern followed by the sets is: $(x,2x,6x)$.

Now, let's test the option $(21,42,126)$ using the same logic:

Here, $A=21$.
$B=21\times 2=42$
$C=42\times 3=126$

Since the numbers in $(21,42,126)$ follow the exact same logic, it is the correct set.