Explanation:
A Pythagorean triplet is a set of three positive integers (a, b, c) that satisfy the Pythagorean theorem, which states that in a right-angled triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.

The Pythagorean theorem can be written as:
a^2 + b^2 = c^2

Let's analyze each option to determine which one is not a Pythagorean triplet:

a) (3, 4, 5)
Substituting the values into the Pythagorean theorem:
3^2 + 4^2 = 5^2
9 + 16 = 25
25 = 25

Since the equation is true, (3, 4, 5) is a Pythagorean triplet.

b) (6, 8, 10)
Substituting the values into the Pythagorean theorem:
6^2 + 8^2 = 10^2
36 + 64 = 100
100 = 100

Since the equation is true, (6, 8, 10) is a Pythagorean triplet.

c) (2, 3, 4)
Substituting the values into the Pythagorean theorem:
2^2 + 3^2 = 4^2
4 + 9 = 16
13 ≠ 16

Since the equation is not true, (2, 3, 4) is not a Pythagorean triplet.

d) (12, 35, 37)
Substituting the values into the Pythagorean theorem:
12^2 + 35^2 = 37^2
144 + 1225 = 1369
1369 = 1369

Since the equation is true, (12, 35, 37) is a Pythagorean triplet.

Therefore, the correct answer is option 'C' (2, 3, 4) as it does not satisfy the Pythagorean theorem.