In the following number-pairs, the second number is obtained by applying certain mathematical operations to the first number. 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 their constituent digits. E.g. 13 – Operations on 13 such as adding / subtracting /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.)

21, 274

34, 443

The correct option is 26, 339.

To find the relationship, let us analyze the pattern between the two numbers in each of the given pairs:

First Pair: (21, 274)
If we multiply the first number by 13 and then add 1, we obtain the second number:

$$(21\times 13)+1=273+1=274$$

Second Pair: (34, 443)
Applying the exact same mathematical operations to the second pair:

$$(34\times 13)+1=442+1=443$$

Thus, the rule connecting the numbers in each set is:

$$\text{Second Number}=(\text{First Number}\times 13)+1$$

Now, let us verify the options using this rule:

For the option 26, 339, we apply the formula to the first number (26):

$$(26\times 13)+1=338+1=339$$

Since the result matches the second number, this pair follows the same relationship.