Machine Design
When a hole of diameter ‘d’ is punched in a metal of thickness 't', then the force required to punch a hole is equal to (where τu = Ultimate shear strength of the material of the plate)

π/4 × d².τu
π/4 × d² × tτu
πd.t.τu
t.τu

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Machine Design
A bolt of uniform strength can be developed by

Keeping the core diameter smaller than the diameter of the unthreaded portion
None of these
Keeping the core diameter of threads equal to the diameter of unthreaded portion of the bolt
Keeping the nominal diameter of threads equal to the diameter of unthreaded portion of the bolt

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Machine Design
Cap screws are

Provided with detachable caps
Used to prevent relative motion between parts
Similar to small size tap bolts except that a greater variety of shapes of heads are available
Slotted for a screw driver and generally used with a nut

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