Eigen values of a matrix $$S = \left[ {\matrix{ 3 & 2 \cr 2 & 3 \cr } } \right]$$ are $$5$$ and $$1.$$ What are the eigen values of the matrix $${S^2} = SS?$$

The solution of the differential equation $${{dy} \over {dx}} + 2xy = {e^{ - {x^2}}}\,\,$$ with $$y(0)=1$$ is

If point A is in equilibrium under the action of the applied forces, the values of tensions and T _AB and T_AC are respectively.

A smooth flat plate with a sharp leading edge is placed along a gas stream flowing at $$U = 10\,m/s.$$ The thickness of the boundary layer at section $$r$$- $$s$$ is $$10$$ $$mm,$$ the breadth of the plate is $$1$$ $$m$$ (into the paper) and the density of the gas, $$\rho = 1.0\,kg/{m^3}.$$ Assume that the boundary layer is thin, two-dimensional, and follows a linear velocity distribution, $$u = U\left( {y/\delta } \right),$$ at the section $$r$$-$$s$$, where $$y$$ is the height from plate.

The integrated drag force (in $$N$$) on the plate, between $$p$$-$$s$$, is