Which of the following cannot be the sides of a triangle?

Concept use:

According to the triangle inequality theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side. If this condition is not met, the sides cannot form a triangle.

Calculations:

Let's check each option:

3 cm, 4 cm, 5 cm - This is a valid triangle as 3 + 4 > 5, 4 + 5 > 3, and 3 + 5 > 4.

4 cm, 5 cm, 6 cm - This is a valid triangle as 4 + 5 > 6, 5 + 6 > 4, and 4 + 6 > 5.

2 cm, 3 cm, 4 cm - This is a valid triangle as 2 + 3 > 4, 3 + 4 > 2, and 2 + 4 > 3.

1 cm, 2 cm, 3 cm - Here, 1 + 2 = 3, which is not greater than the third side. This violates the triangle inequality theorem.

So, the set of lengths that cannot form a triangle is:

1 cm, 2 cm, 3 cm.

Hence, The Correct Answer is option 4.