PRASHNIKAप्रश्निका

Application of Calculus - ISC Class 12 Mathematics Questions with Answers

69 past-paper questions on Application of Calculus from ISC Class 12 Mathematics papers (2026-2017), newest first. Open one to see its answer.

Practise these questions with filters

Which one of the following statements is true about Marginal Revenue? 2026 · 1 mark · MCQ
A company produces a commodity with ₹36,000 as a fixed cost. The variable cost is estimated to be 25% of the total revenue… 2026 · 2 marks · Case based
The total cost function and the total revenue function of a commodity are given by $C(x) = x + 40$ and $R(x) = ax$ respectively… 2026 · 1 mark · Numerical
The demand function of a monopoly is given by $x = 100 - 4p$. Find the quantity at which the Marginal Revenue will be zero… 2026 · 2 marks · Short answer
Statement 1: Profit is maximum when marginal revenue equals marginal cost. Statement 2: At maximum profit, the slope of the… 2026 · 1 mark · MCQ
The cost of manufacturing $x$ units of a commodity is $27 + 12x + 3x^2$. Find the output for which Average Cost is decreasing. 2026 · 1 mark · Short answer
The cost of manufacturing $x$ units of a commodity is $5x^2 + 30x + 5$. Find the range of output where Average Cost is increasing. 2026 · 2 marks · Short answer
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. Which… 2026 · 5 marks · Short answer
A school is organising an art and craft exhibition. The management has decided to donate the profit earned from the sale of… 2026 · 2 marks · Short answer
A company produces a product whose cost function is $C(x) = x^3 - 27x + 2000$. Find the number of products when the marginal cost… 2026 · 1 mark · Numerical
A real estate company is going to build a new residential complex. The land they have purchased can hold at the most 500… 2026 · 2 marks · Short answer
The Revenue function for $x$ units of a commodity is $R(x) = x^3 + 3x^2 - 7x + 16$. Calculate the Marginal Revenue at $x = 5$. 2026 · 2 marks · Numerical
The total cost function for production and marketing of a product is given by $C(x) = \frac{3x^2}{4} - 7x + 3$, where $x$ is the… 2026 · 1 mark · Short answer
Anuj and Ashish launched a new fountain pen in their pen-factory which is consisting of ₹ 6400/- as overheads, ₹ 35/- per pen as… 2025 · 2 marks · Short answer
A company uses a demand function $p = \frac{a}{x+b} - c$, where $a, b, c \in \mathbb{R}$ and $x = \text{number of units}$. The… 2025 · 1 mark · Assertion-reason
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. Which… 2025 · 5 marks · Short answer
The cost function of a product is given by $C(x) = \frac{x^3}{3} - 45x^2 - 900x$ where $x$ is the number of units produced. What… 2025 · 1 mark · Short answer
Rohit joins a career counselling institute as a counsellor. The manager says, “Within a year I want a breakeven point. For that… 2025 · 1 mark · MCQ
The Average Revenue (AR) and Marginal Revenue (MR) of a company on selling $x$ units (on x-axis) is shown in the following graph… 2025 · 1 mark · Short answer
A company paid ₹ 8475 towards the rent of the building and ₹ 7625 interest on the loan. The cost of producing one unit of a… 2025 · 1 mark · Short answer
The demand function of a monopoly is given by $x = 100 - 4p$. Find the quantity at which the MR will be zero. [Application] 2025 · 2 marks · Short answer
A utensil manufacturer produces '$x$' dinner sets per week and sells each set at ₹ $p$, where $x = \frac{600 - p}{8}$. The cost… 2025 · 4 marks · Short answer
The fuel cost per hour for running a ship is proportional to the square of the speed generated in knots. The fuel cost is ₹ 75/h… 2025 · 6 marks · Long answer
To launch a new product in his company, Mr. Rajesh spends ₹ 1 lakh on the infrastructure and the variable cost of the product is… 2025 · 2 marks · Short answer
The cost function $C(x)$ of producing '$x$' quantities of a product is given by $C(x) = 500x^2 + 2500x + 5000$. If each unit of… 2025 · 4 marks · Short answer
The total revenue received from the sale of '$x$' units of a product is $R(x) = 3x^2 + 36x + 5$. Then, the actual revenue for… 2025 · 1 mark · MCQ
The total cost of producing and marketing $x$ units of bulbs by a wholesaler is given by $C(x) = \frac{1}{3}x^2 + e^{2x} + 3e$… 2025 · 1 mark · Short answer
The cost function of a commodity is $C(x) = 200 + 20x - \frac{1}{2} x^2$ (in rupees). Find the range where AC falls. [Application] 2025 · 2 marks · Short answer
Observe the graph shown below of Cost, Revenue versus Quantity. Statement 1: A denotes Profit area, B denotes Break-even point… 2025 · 1 mark · MCQ
The fixed cost of a new product is ₹ 200 and the variable cost per unit is ₹ $x$. If the demand function $p(x) = 30$, then what… 2025 · 1 mark · MCQ
The Average Cost of producing '$x$' units of commodity is given by: $AC = \frac{x}{200} + 30 + \frac{5000}{x}$ Find the Cost… 2025 · 4 marks · Short answer
The demand function for a product is given by $p = 1500 - 9x - 2x^2$ Find the revenue function. Write the marginal revenue… 2025 · 4 marks · Short answer
In Z Square Mall in Kanpur, there is a space to keep 300 cars and the entry fees per car is ₹ 20. It is estimated that if the… 2025 · 2 marks · Short answer
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. A company… 2024 · 5 marks · Short answer
The Average Cost function associated with producing and marketing $x$ units of an item is given by $AC = x + 5 + \frac{36}{x}$… 2024 · 2 marks · Short answer
A monopolist’s demand function is $x = 60 - \frac{p}{5}$. At what level of output will marginal revenue be zero? 2024 · 2 marks · Numerical
The fixed cost of a product is ₹ 30,000 and its variable cost per unit is ₹ 800. If the demand function is $p(x) = 4500 - 100x$… 2023 · 1 mark · Numerical
In subparts (i) and (ii) choose the correct options and in subparts (iii) to (v), answer the questions as instructed. Which… 2023 · 5 marks · Short answer
For the revenue function $R(x) = \frac{bx}{a+x}$, show that the marginal revenue function is increasing for all $b < 0$ and… 2023 · 2 marks · Derivation
The average revenue function is given by $AR = 25 - \frac{x}{4}$. Find total revenue function and marginal revenue function. 2023 · 2 marks · Short answer
The cost function is $C(x) = 3x^2 - 6x + 5$. Find the average cost when $x = 2$. 2023 · 1 mark · Numerical
The total cost function for $x$ units is given by $C(x) = \sqrt{6x + 5} + 2500$. Show that the marginal cost decreases as the… 2023 · 2 marks · Derivation
The total revenue function $R(x) = x + 2x^3 - 3\cdot 5x^2$. Find the point where marginal revenue curve cuts the co-ordinate axis. 2023 · 2 marks · Short answer
If the demand function is given by $p = 1500 - 2x - x^2$ then find the marginal revenue when $x = 10$: 2023 · 1 mark · MCQ
A company sells its product for ₹ 20 per unit. Fixed costs for the company is ₹ 45,000 and variable costs is estimated to run 25%… 2022 · 2 marks · MCQ
The demand function for a certain commodity is given by $p = 4000 - 100x$. What will be the total revenue from the sale of 3… 2022 · 2 marks · MCQ
A company sells $x$ packets of biscuits each day at ₹ 10 a packet. The cost of manufacturing these packets is ₹ 5 per packet plus… 2022 · 2 marks · MCQ
The cost function of a firm is given by $C(x) = 3x^2 - 2x + 6$. The average cost of the firm at $x = 3$ is: 2022 · 2 marks · MCQ
The demand function for a certain product is represented by the equation: $p = ax^2 + bx + c$ where $x$ is the number of units… 2022 · 8 marks · Case based
The total cost function for a production is given by $C(x) = \frac{3}{4}x^2 - 7x + 27$. Find the number of units produced for… 2021 · 2 marks · Short answer
[5×1] In sub-parts (i) and (ii) choose the correct options and in sub-parts (iii) to (v), answer the questions as instructed. The… 2021 · 5 marks · Short answer
A company produces a commodity with ₹ 24,000 as fixed cost. The variable cost estimated to be 25% of the total revenue received… 2021 · 2 marks · Short answer
The total cost function of a firm is given by $C(x) = \frac{1}{3}x^3 - 5x^2 + 30x - 15$ where the selling price per unit is given… 2020 · 4 marks · Short answer
The marginal cost of the production of the commodity is $30 + 2x$, it is known that fixed costs are ₹ $200$, find: The total… 2020 · 4 marks · Short answer
[3×2] The selling price of a commodity is fixed at ₹ $60$ and its cost function is $C(x) = 35x + 250$. (i) Determine the profit… 2020 · 6 marks · Short answer
The cost function of a product is given by $C(x) = \frac{x^3}{3} - 45x^2 - 900x + 36$ where $x$ is the number of units produced… 2019 · 4 marks · Numerical
[3×2] A company produces a commodity with ₹ 24,000 as fixed cost. The variable cost estimated to be 25% of the total revenue… 2019 · 6 marks · Short answer
The marginal cost function of $x$ units of a product is given by $\text{MC} = 3x^2 - 10x + 3$. The cost of producing one unit is… 2019 · 4 marks · Short answer
The fixed cost of new product is ₹ $35000$ and the variable cost per unit is ₹ $500$. If the demand function: $p = 5000 - 100x$… 2018 · 4 marks · Short answer
A product can be manufactured at a total cost $C(x) = \frac{x^2}{100} + 100x + 40$, where $x$ is the number of units produced… 2018 · 4 marks · Short answer
[3×2] Find the cost of increasing from 100 to 200 units if the marginal cost in Rupees per unit is given by the function… 2018 · 6 marks · Short answer
A manufacturer’s marginal cost function is $\frac{500}{\sqrt{2x+25}}$. Find the cost involved to increase production from 100… 2018 · 4 marks · Short answer
If the demand function is given by $x = \frac{600-p}{8}$, where the price is ₹ $p$ per unit and the manufacturer produces $x$… 2018 · 4 marks · Short answer
[3×2] Given the total cost function for $x$ units of a commodity as: $C(x) = \frac{1}{3}x^3 + 3x^2 - 16x + 2$. Find: (i) Marginal… 2018 · 6 marks · Short answer
A bill of ₹ 60,000 payable 10 months after date was discounted for ₹ 57,300 on 30th June, 2007. If the rate of interest was… 2017 · 5 marks · Short answer
The demand for a certain product is represented by the equation $p = 500 + 25x - \frac{x^2}{3}$ in rupees where $x$ is the number… 2017 · 5 marks · Short answer
The price relatives and weights of a set of commodities are given below: Commodity A B C D Price relatives 125 120 127 119… 2017 · 5 marks · Short answer
Construct 3 yearly moving averages from the following data and show on a graph against the original data: Year 2000 2001 2002… 2017 · 5 marks · Short answer
A machine costs ₹ 60,000 and its effective life is estimated to be 25 years. A sinking fund is to be created for replacing the… 2017 · 5 marks · Short answer

Application of Calculus - ISC Class 12 Mathematics Questions with Answers

Other Mathematics chapters