A box contains $$4$$ red balls and $$6$$ black balls. Three balls are selected randomly from the box one after another, without replacement. The probability that the selected set contains one red ball and two black balls is

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