Consider two axially loaded columns, namely. $$1$$ and $$2,$$ made of a linear elastic material with Young's modulus $$2 \times {10^5}\,\,MPa,$$ square cross-section with side $$10$$ $$mm$$, and length $$1$$ $$m.$$ For Column $$1,$$ one end is fixed and the other end is free. For column $$2,$$ one end is fixed and the other end is pinned. Based on the Euler's theory, the ratio (up to one decimal place) of the buckling load of Column $$2$$ to the buckling load of column $$1$$ is ___________

Consider the stepped bar made with a linear elastic material and subjected to an axial load of $$1$$ $$kN$$, as shown in the figure

Segment $$1$$ and $$2$$ have cross-sectional area of $$100\,\,m{m^2}$$ and $$60\,\,m{m^2}$$, Young's modulus of $$2 \times {10^5}\,\,MPa$$ and $$3 \times {10^5}\,\,MPa,$$ and length of $$400$$ $$mm$$ and $$900$$ $$mm,$$ respectively. The strain energy (in $$N$$-$$mm,$$ up to one decimal place) in the bar due to the axial load is _________

A planar truss tower structure is shown in the figure:
Consider the following statements about the external and internal determinacies of the truss.
(P) Externally Determinate
(Q) External Static Indeterminacy = 1
(R) External Static Indeterminacy = 2
(S) Internally Determinate
(T) Internal Static Indeterminacy = 1
(U) Internal Static Indeterminacy = 2
Which one of the following options is correct?

Consider the beam $$ABCD$$ shown in figure

For a moving concentrated load of $$50$$ $$kN$$ on the beam, the magnitude of the maximum bending moment (in $$kN$$-$$m$$) obtained at the support $$C$$ will be equal to _________