ISC Class 12th Mathematics Chapter 8 - Application of Calculus Important Questions with Answers

A bill of ? 1,800 drawn on 10th September 2010 at 6 months was discounted for ? 1,782 at a bank. If the rate of interest was 5% per annum, on what date was the bill discounted?

If the demand function is given by p = 1500 – 2x – x² then find the marginal revenue when x = 10.

The cost function C(x) = 3x² – 6x + 5. Find the average cost when x = 2.

The fixed cost of a product is ? 30,000 and its variable cost per unit is ? 800. If the demand function is p(x) = 4500 – 100x. Find the break-even values.

The total cost function for x units is given by C(x) = `sqrt(6x + 5) + 2500`. Show that the marginal cost decreases as the output x increases.

The average revenue function is given by AR = `25 - x/4`. Find total revenue function and marginal revenue function.

A company sells hand towels at ? 100 per unit. The fixed cost for the company to manufacture hand towels is ? 35,000 and variable cost is estimated to be 30% of total revenue. What will be the total cost function for manufacturing hand towels?

If the total cost function is given by `C = x + 2x^3 - 7/2x^2`, find the Marginal Average Cost function (MAC).

The manufacturer of a pen fixes its selling price at ? 45 and the cost function is C(x) = 30x + 240. The manufacturer will begin to earn profit if he sells more than 16 pens. Why? Give one reason.

The Average Cost function associated with producing and marketing x units of an item is given by AC = `x + 5 + 36/x`.

1. Find the Total cost function.
2. Find the range of values of x for which Average Cost is increasing.