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?

A job of the shape shown in the figure below is to be machined on a lathe. The tool best suited for machining of this job must have

Consider the following statements:

The helical flute in a twist drill provides the necessary
$$1.$$ Clearance angle for the cutting edge.
$$2.$$ Rake angle for the cutting edge.
$$3.$$ Space for the chip to come out during drilling.
$$4.$$ Guidance for the drill to enter into the work piece.

Which of the statements given above are correct?

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