Differentiate financial and economic costs with suitable example. The total revenue (TR) and Average Cost (AC) functions of a firm are given by $$\begin{gathered} TR=4350Q-13Q^2 \\ AC=Q^2-5.5Q +150+675Q^2 \end{gathered}$$ Where Q refers to quantity of output. Find the profit maximizing level of output and maximum profit.

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A place of stone fell from a balloon when it was flying in the upward direction with a velocity 20 m/sec. What will be the height of the balloon when the stone hit the ground in 10 seconds?

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Find the maximum value of z=6x+2y, subject to the conditions $x\ge 0, y\ge 0, x+y=5, x\le 2, y\le 4.$

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The sum of the digits of a two-digit number is subtracted from the number. How two-digit numbers can be formed so that the digit in the unit place of the resulting number many such 6?

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How many ways are there to divide 50 people into 3 groups so that each group contains members equal to a prime number?

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A semi circular sheet of metal of diameter 28 cm is bent into an open conical cup. Find the depth and capacity of cup.