Consider the differential equation $$\,\,{x^2}{{{d^2}y} \over {d{x^2}}} + x{{dy} \over {dx}} - 4y = 0\,\,\,$$ with the boundary conditions of $$\,\,y\left( 0 \right) = 0\,\,\,$$ and $$\,\,y\left( 1 \right) = 1.\,\,\,$$ The complete solution of the differential equation is

Two steel truss members, AC and BC, each having cross sectional area of 100 mm², are subjected to a horizontal force F as shown in figure. All the joints are hinged.

The maximum force F in kN that can be applied at C such that the axial stress in any of the truss members DOES NOT exceed 100MPa is

Two steel truss members, AC and BC, each having cross sectional area of 100 mm², are subjected to a horizontal force F as shown in figure. All the joints are hinged.

If F = 1 kN, the magnitude of the vertical reaction force developed at the point B in kN is

A large tank with a nozzle attached contains three immiscible, inviscid fluids as shown. Assuming that the changes in $${h_1},\,\,{h_2}$$ and $${h_3}$$ are negligible, the instantaneous discharge velocity is