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Four squares of sides $x\: cm$ each are cut off from the four corners of a square metal sheet  having side $10\: cm.$ The residual sheet is then folded into an open box which is then filled with a liquid costing Rs. $x^{2}$ per $cm^{3}.$ The value of $x$ for which the cost of filling the box completely with the liquid is maximized, is

  1. $100$
  2. $50$
  3. $30$
  4. $10$
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