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.

Consider the following two statements related to reinforced concrete design, and identify whether they are TRUE/FALSE:

$${\rm I}.$$ Curtailment of bars in the flexural tension zone in beams reduces the shear strength at the cut-off locations
$${\rm II}.$$ When a rectangular column section is subject to biaxially eccentric compression, the neutral axis will be parallel to the resultant axis of bending.