q) A 10cm long rod is cut into 3 pieces whose lengths are integral multiples of 1cm. Find the the total ways in which it could be cut so that the 3 pieces form a triangle.

No piece should be greater than or equal to 5 cm.. Triangle inequality..

So you have

3, 3, 4

3, 4, 3

4, 4, 2

4, 2, 4

So four ways..