A $${20^ \circ }$$ full depth involute spur pinion of $$4mm$$ module and $$21$$ teeth is to transmit $$15kW$$ at $$960rpm.$$ Its face width is $$25mm.$$

The tangential force transmitted (in N) is

A spur gate has a module of $$3mm,$$ number of teeth $$16,$$ a face width of $$36mm$$ and a pressure angle of $${20^ \circ }$$. It is transmitting a power of $$3KW$$ at $$20rev/s.$$ Taking a velocity factor of $$1.5$$ and a form factor of $$0.3,$$ the stress in the gear tooth is about

Match the type of gears with their most appropriate description

Type of gear
(P)$$\,\,\,\,\,$$ Helical
(Q)$$\,\,\,\,\,$$ Spiral Bevel
(R)$$\,\,\,\,\,$$ Hypoid
(S)$$\,\,\,\,\,$$ Rack and pinion

Description
1.$$\,\,\,\,\,$$ Axes non parallel a and non intersecting
2$$\,\,\,\,\,$$. Axes parallel and teeth are inclined to the axis
3.$$\,\,\,\,\,$$ Axes parallel and teeth are parallel to the axis
4.$$\,\,\,\,\,$$ Axes are perpendicular and intersecting and teeth are inclined to the axis
5.$$\,\,\,\,\,$$ Axes are perpendicular and used for large speed reduction
6.$$\,\,\,\,\,$$ Axes parallel and one of the gears has infinite radius

One tooth of gear having $$4$$ module and $$32$$ teeth is shown in the figure. Assume that the gear tooth and the corresponding tooth space make equal intercepts on the pitch circumference.

The dimensions $$' a '$$ and $$' b '$$ respectively, are closest to