For the truss shown below, the member $$PQ$$ is short by $$3$$ $$mm.$$ The magnitude of vertical displacement of joint $$R$$ (in $$mm$$) is ______________________

Match the information given in Group $$-$$ $${\rm I}$$ with those in Group $$-$$ $${\rm II}.$$

Mathematical idealization of a crane has three bars with their vertices arranged as shown in the figure with a load of $$80$$ $$kN$$ hanging vertically. The coordinates of the vertices are given in parentheses. The force in the member $$QR,\,\,{F_{QR}}$$ will be

In a beam of length $$L,$$ four possible influence line diagrams for shear force at a section located at a distance of $${L \over 4}$$ from the left end support (marked as $$P,Q,R$$ and $$S$$ ) are shown below. The correct influence line diagram is