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

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

A $$\phi $$ $$20$$ $$mm$$ through hole is to be drilled in a $$30$$ $$mm$$ thick plate using a double fluted, $${120^ \circ }$$ lip angle drill. The drill tip is at a distance of $$3$$ $$mm$$ from the plate surface when cutting is started and an over travel of $$2$$ $$mm$$ is recommended as a margin to ensure drilling through the full thickness of the plate. If the drill rotates at $$500$$ $$rev/min$$ and the feed per tooth is $$0.01$$ $$mm,$$ the machining time of the operation (in sec) will be

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?