HSC Commerce इयत्ता १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

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When x₀ = 2 and P₀ = 12 the producer’s surplus for the supply function P_s = 2x² + 4 is

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The producer’s surplus when the supply function for a commodity is P = 3 + x and x₀ = 3 is 

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The marginal cost function is MC = `100sqrt(x)`. find AC given that TC = 0 when the output is zero is

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The demand and supply function of a commodity are P(x) = (x – 5)² and S(x) = x² + x + 3 then the equilibrium quantity x₀ is

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The demand and supply function of a commodity are D(x) = 25 – 2x and S(x) = `(10 + x)/4` then the equilibrium price p₀ is 

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If MR and MC denote the marginal revenue and marginal cost and MR – MC = 36x – 3x² – 81, then the maximum profit at x is equal to

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If the marginal revenue of a firm is constant, then the demand function is

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For a demand function p, if `int "dp"/"p" = "k" int ("d"x)/x` then k is equal to

A manufacture’s marginal revenue function is given by MR = 275 – x – 0.3x². Find the increase in the manufactures total revenue if the production is increased from 10 to 20 units

A company has determined that marginal cost function for x product of a particular commodity is given by MC = `125 + 10x - x^2/9`. Where C is the cost of producing x units of the commodity. If the fixed cost is ₹ 250 what is the cost of producing 15 units

The marginal revenue function for a firm given by MR = `2/(x + 3) - (2x)/(x + 3)^2 + 5`. Show that the demand function is P = `(2x)/(x + 3)^2 + 5`

For the marginal revenue function MR = 6 – 3x² – x³, Find the revenue function and demand function

The marginal cost of production of a firm is given by C'(x) = `20 + x/20` the marginal revenue is given by R’(x) = 30 and the fixed cost is ₹ 100. Find the profit function

The demand equation for a product is P_d = 20 – 5x and the supply equation is P_s = 4x + 8. Determine the consumers surplus and producer’s surplus under market equilibrium

A company requires f(x) number of hours to produce 500 units. It is represented by f(x) = 1800x^–0.4. Find out the number of hours required to produce additional 400 units. [(900)^0.6 = 59.22, (500)^0.6 = 41.63]

The price elasticity of demand for a commodity is `"p"/x^3`. Find the demand function if the quantity of demand is 3 when the price is ₹ 2.

Solve: `("d"y)/("d"x) = "ae"^y`

Solve: `(1 + x^2)/(1 + y) = xy ("d"y)/("d"x)`

Solve: `y(1 - x) - x ("d"y)/("d"x)` = 0

Solve: ydx – xdy = 0 dy