One brand of milling machine has the following two index plates supplied along with the indexing head:
Plate 1: $$15, 16, 17, 18, 19, 20$$ hole circles.
Plate 2: $$21, 23, 27, 29, 31, 33$$ hole circles.

It is proposed to mill a spur gear of $$28$$ teeth using simple indexing method. Which one of the following combinations of index plate and number of revolutions is correct?

Match List - $${\rm I}$$ (Milling problem) with List - $${\rm I}$$$${\rm I}$$ (Probable causes) and select the correct answer using the codes given below the lists:

Match List - $${\rm I}$$ (Cutting tools) with List - $${\rm I}$$$${\rm I}$$ (Features) and select the correct answer using the codes given below the lists:

A non standard thread of pitch $$3.175$$ $$mm$$ is to be cut on a lathe having lead screw of pitch $$6$$ $$mm.$$ A change gear set provided with the lathe has one gear each with the following number of teeth: $$20, 30, 40, 50, 60, 70, 80,$$ $$90, 100, 110, 120, 127.$$ The correct pairs of change gears $$\left( {a/b\,\,x\,\,c/d} \right)$$ for machining the given thread are (assuming that the transmission ratio of the rest of the kinematic train between the lathe spindle and lead screw is equal to