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 ____________

A rectangular beam of width $$(b)$$ $$230$$ $$mm$$ and effective depth $$(d)$$ $$450$$ $$mm$$ is reinforced with four bars of $$12$$ $$mm$$ diameter. The grade of concrete is $$M20$$ and grade of steel is $$Fe500.$$ Given that for $$M20$$ grade of concrete the ultimate shear strength, $${\tau _{uc}} = 0.36\,\,N/m{m^2}$$ for steel percentage, $$p = 0.25,$$ and $${\tau _{uc}} = 0.48\,\,N/m{m^2}$$ for $$p = 0.50.$$ For a factored shear force of $$45$$ $$kN,$$ the diameter (in $$mm$$) of $$Fe500$$ steel two legged stirrups to be used at spacing of $$375$$ $$mm,$$ should be

Consider two $$RCC$$ beams, $$P$$ and $$Q$$, each having the section $$400$$ $$mm$$ $$ \times \,\,750\,\,mm$$ (effective depth, $$d=750$$ $$mm$$) made with concrete having a $${\tau _{c\max }} = 2.1\,\,N/m{m^2}.$$ For the reinforcement provided and the grade of concrete used, it may be assumed that the $$\,{\tau _c} = 0.75\,\,N/m{m^2}.$$ The design shear in beam $$P$$ is $$400$$ $$kN$$ and in beam $$Q$$ is $$750$$ $$kN.$$ Considering the provisions of $$IS$$ $$456$$-$$2000.$$

Which of the following statements is TRUE?

A reinforced concrete beam of rectangular cross section of breadth $$230$$ $$mm$$ and effective depth $$400$$ $$mm$$ is subjected to maximum factored shear force of $$120$$ $$kN.$$ The grades of concrete, main steel and stirrup steel are $$M20,$$ $$Fe415$$ and $$Fe250$$ respectively. For the area of main steel provided, the design shear strength τc is per $$IS: 456$$-$$2000$$ is $$0.48$$ $$N/m{m^2}.$$ The beam is designed for collapse limit state.

The spacing $$(mm)$$ of $$2$$-legged $$8$$ $$mm$$ stirrups to be provided is