The hardness of a ground water sample was found to be 420 mg/L as $$CaCO_3$$. A softener containing ion exchange resins was installed to reduce the total hardness to 75 mg/L as $$CaCO_3$$ before supplying to 4 households. Each household gets treated water at a rate of 540 L/day. If the efficiency of the softener is 100%, the bypass flow rate (expressed in L/day) is .

A sample of water has been analyzed for common ions and results are presented in the form of a bar diagram as shown. The non-carbonate hardness (expressed in mg/L as $${\mathrm{CaCO}}_3$$) of the sample is

As per $$IS$$ $$456$$ - $$2000$$ for the design of reinforced concrete beam, the maximum allowable shear stress $$\left( {{\tau _{c\,\,\max }}} \right)$$ depends on the

A launched (varying depth) reinforced concrete beam is simply supported at both ends, as shown in the figure. The beam is subjected to a uniformly distributed factored load of intensity $$10$$ $$kN/m.$$ The design shear force (expressed in $$kN$$) at the section $$X$$-$$X$$ of the beam is ____________