In a residential society comprising of 100 houses, there were 60 children between the ages of 10-15 years. They were inspired by their teachers to start composing to ensure that biodegradable waste is recycled. For this purpose, instead of each child doing it for only his/her house,children convinced the Residents welfare association to do it as a society initiative. For this they identified a square area in the local park. Local authorities charged amount of ₹ 50 per square metre for space so that there is no misuse of the space and Resident welfare association takes it seriously. Association hired a labourer for digging out 250 m3 and he charged ₹ 400 x (depth)2. Association will like to have minimum cost.Based on this information, answer the any 4 of the following questions :(1) Let side of square plot is x m and its depth is h metres, then cost c for the pit is :(a) \(\frac{50}{h}\) + 400 h2(b) \(\frac{12500}{h}\) + 400 h2(c) \(\frac{250}{h}\) + h2(d) \(\frac{250}{h}\) + 400 h2(2) Value of h (in m) for which \(\frac{dc}{dh}\) = 0 is :(a) 1.5(b) 2(c) 2.5(d) 3(3) \(\frac{d^2c}{dh^2}\) is given by ;(a) \(\frac{25000}{h^3}\) + 800(b) \(\frac{500}{h^3}\) + 800(c) \(\frac{100}{h^3}\) + 800(d) \(\frac{500}{h^3}\) + 2(4) Value of x (in m) for minimum cost is :(a) 5(b) \(10\sqrt{\frac{5}{3}}\) (c) 5√5(d) 10(5) Total minimum cost of digging the pit (in ₹) is :(a) 4,100(b) 7,500(c) 7,850(d) 3,220