The eigen values of the matrix $$\left[ {\matrix{ 5 & 3 \cr 2 & 9 \cr } } \right]$$ are

The determinant of the following matrix $$\left[ {\matrix{ 5 & 3 & 2 \cr 1 & 2 & 6 \cr 3 & 5 & {10} \cr } } \right]$$

A 15 cm length of steel rod with relative density of 7.4 is submerged in a two layer fluid. The bottom layer is mercury and the top layer is water. The height of top surface of the rod above the liquid interface in 'cm' is

The effective spans for a simple one-way slab system, with an overhang are indicated in the figure below. The specified ultimate design loads on the slab are $$6.0\,kN/{m^2}$$ and $$4.5\,kN/{m^2}$$ for dead loads and live loads respectively. Considering the possibility of live loads not occurring simultaneously on both spans, determine the maximum spacing (in $$mm$$ units) of $$8$$ $$mm$$ diameter bars required as bottom reinforcement in the span $$AB,$$ assuming an effective depth of $$125$$ $$mm.$$ Assume $$M20$$ concrete and $$Fe$$ $$415$$ steel.