Correct option is B. $$( 3 , 4 , 5 )$$
(A) In the triplet ( 1, 5, 10 )
$$1^{2}=1,5^{2}=25,10^{2}=100 \ and \ 1+25 =26\neq 100$$
The square of largest number is not equal to the sum of the square of the other two numbers.
$$\therefore (1, 5, 10)$$ is not pythagorean triplet.
In the triplet (3 , 4 , 5)
$$3^{2}= 9 , 4^{2} = 16 , 5^{2} =25 \ and \ 9 + 16 = 25$$
The square of the largest number is not equal to the sum of the square of the other two numbers.
$$\therefore (2,2,2)$$ is not a pythgorean triplet.
In the triplet (5,5,2)
$$2^{2}=4,5^{2}=25,5^{2}=25 \ and \ 4 +25 = 29\neq 25$$
The square of the largest number is not equal to the sum of the square of the other two numbers.
$$\therefore (5,5,12)$$ is not a pythagprean triplet
Hence, the correct option is $$(3,4,5)$$