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CA Foundation Basic Differential and Integral Calculus — practice questions — page 2

Explore 65 free Basic Differential and Integral Calculus questions in CA Foundation Quantitative Aptitude. Open each question or exercise to read its content, reference answers and available explanation.

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Basic Differential and Integral Calculus questions and exercises with answers

Showing questions 31–60 of 65.

In a perfectly competitive market, marginal revenue equalsRead the answer and worked solution →To sell more output, a monopolist mustRead the answer and worked solution →Making 10 units costs 400 and making 11 units costs 430. The marginal cost of the 11th unit isRead the answer and worked solution →Why does fixed cost not affect marginal cost?Read the answer and worked solution →Marginal cost is the ratio of the change in total cost to the change inRead the answer and worked solution →In the long run, a firm hasRead the answer and worked solution →A firm sells 30 units at 20 each, then 31 units at 19 each. Marginal revenue of the 31st unit isRead the answer and worked solution →For a monopolist facing inelastic demand, selling more makes MRRead the answer and worked solution →A lower elasticity of demand implies aRead the answer and worked solution →If MR exceeds MC at the current output, a profit-maximising firm shouldRead the answer and worked solution →With C = 100 + 5x, the average cost of 10 units isRead the answer and worked solution →Marginal cost is MC = 6x + 4 and fixed cost is 100. Total cost at x = 10 isRead the answer and worked solution →Marginal revenue is MR = 50 - 2x with no revenue at x = 0. Revenue at x = 10 isRead the answer and worked solution →Marginal cost is MC = 2x + 5. The extra cost of raising output from 2 to 4 units isRead the answer and worked solution →Demand is q = 100 - 5p. The greatest revenue obtainable isRead the answer and worked solution →The integral of (3x^2 + 2x) dx isRead the answer and worked solution →What is the indefinite integral of e^x?Read the answer and worked solution →Evaluate the integral of x^2 dx from 0 to 3.Read the answer and worked solution →The integral of the square root of x dx from 0 to 4 equalsRead the answer and worked solution →The rule: integral of x^n dx = x^(n+1)/(n+1) + C fails only forRead the answer and worked solution →An integral is the continuous analog ofRead the answer and worked solution →The fundamental theorem of calculus says differentiation and integration areRead the answer and worked solution →In the integral of f(x) dx, the function f(x) is called theRead the answer and worked solution →In a definite integral, the numbers a and b are called theRead the answer and worked solution →An indefinite integral carries + C because the derivative of a constant isRead the answer and worked solution →A definite integral of a positive function between two limits givesRead the answer and worked solution →The minimum value of f(x) = x^2 - 6x + 5 isRead the answer and worked solution →The function f(x) = x^3 - 3x has a local maximum at x =Read the answer and worked solution →At a critical point where f'' is positive, the function has aRead the answer and worked solution →Maxima and minima are known together asRead the answer and worked solution →

Worked practice questions

In a perfectly competitive market, marginal revenue equals

  1. the average cost
  2. the fixed cost
  3. the market price
  4. the total revenue
Show answer and solution

Correct answer: C. the market price

A competitive firm sells every extra unit at the same market price.

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To sell more output, a monopolist must

  1. keep price fixed
  2. reduce its fixed costs
  3. lower price on all units
  4. raise price on all units
Show answer and solution

Correct answer: C. lower price on all units

Because the monopolist faces the market demand curve, more sales need a lower price on all units.

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Making 10 units costs 400 and making 11 units costs 430. The marginal cost of the 11th unit is

  1. 30
  2. 400
  3. 40
  4. 43
Show answer and solution

Correct answer: A. 30

The extra cost is 430 - 400 = 30.

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