“Given below are four number-pairs out of which three are alike in some respect and one of them is incongruent. Select the incongruent number-pair.”

Check the pattern in each pair:

1. (547, 258)
   $5+4+7 = 16$, and $16^2 = 256 \approx 258$ (not exact, but check others first)
2. (723, 144)
   $7+2+3 = 12$, and $12^2 = 144$ ✔
3. (812, 121)
   $8+1+2 = 11$, and $11^2 = 121$ ✔
4. (546, 225)
   $5+4+6 = 15$, and $15^2 = 225$ ✔

Now check the first properly:
$5+4+7 = 16$, and $16^2 = 256 \ne 258$

So only the first pair does not follow the rule.

Answer: (547, 258)