Chapter 3: Integral Calculus IIJanuary 13, 2025 Maven Leave a Comment Welcome to the Chapter 3: Integral Calculus II Quiz! Name Email 1. The given demand and supply function are given by $D(x)= 20 − 5x$ and $S(x) = 4x + 8$ if they are under perfect competition then the equilibrium demand is $40$ $\dfrac{40}{3}$ $\dfrac{41}{2}$ $\dfrac{41}{5}$ None 2. If MR and MC denotes the marginal revenue and marginal cost functions, then the profit functions is $P = \displaystyle \int_{}^{}(MR − MC) dx + k$ $P = \displaystyle \int_{}^{}(MR + MC) dx + k$ $P = \displaystyle \int_{}^{}(MR)(MC) dx + k$ $P = \displaystyle \int_{}^{}(R-C)dx + k$ None 3. Area bounded by the curve $y = x (4 − x)$ between the limits 0 and 4 with x − axis is $\dfrac{30}{3} sq.units$ $\dfrac{31}{2} sq.units$ $\dfrac{32}{3} sq.units$ $\dfrac{15}{2} sq.units$ None 4. Area bounded by the curve $y =\dfrac{1}{x}$ between the limits 1 and 2 is $log 2 sq.units$ $log 5 sq.units$ $log 3 sq.units$ $log 4 sq.units$ None 5. The demand and supply functions are given by $D(x)= 16 − x^{2}$ and $S(x) = 2x^{2} + 4$ are under perfect competition, then the equilibrium price x is $2$ $3$ $4$ $5$ None 6. If the marginal revenue $MR = 35 + 7x − 3x^{2} , $ then the average revenue AR is $35x+\dfrac{7x^{2}}{2}-x^{3}$ $35+\dfrac{7x}{2}-x^{2}$ $35+\dfrac{7x}{2}+x^{2}$ $35+7x+x^{2}$ None 7. The profit of a function p(x) is maximum when $MC − MR = 0$ $MC = 0$ $MR = 0$ $MC + MR = 0$ None 8. Area bounded by the curve $y = e−2x$ between the limits $0 \le x \le \infty$ is $1 sq.units$ $\dfrac{1}{2} sq.units$ $5 sq.units$ $ 2 sq.units$ None 9. If the marginal revenue function of a firm is $MR=e^{\frac{-x}{10}}$ then revenue is $-10e^{\frac{-x}{10}}$ $1-e^{\frac{-x}{10}}$ $10 (1-e^{\frac{-x}{10}})$ $e^{\frac{-x}{10}}+10$ None 10. The marginal revenue and marginal cost functions of a company are MR = 30 − 6x and MC = −24 + 3x where x is the product, then the profit function is $9x^{2} + 54x$ $9x^{2} - 54x$ $54x-\dfrac{9x^{2}}{2}$ $54x-\dfrac{9x^{2}}{2}+k$ None 11. When$ x_{0}=2 \; and \; p_{0}=12 $ the producer's surplus for the demand function $p_{S} = 2x^{2}+4$ is $\dfrac{31}{5}units$ $\dfrac{31}{2}units$ $\dfrac{32}{3}units$ $\dfrac{30}{7}units$ None 12. The marginal cost function is $MC = 100\sqrt{x}$ find AC given that TC =0 when the out put is zero is $\dfrac{200}{3}x^{\frac{1}{2}}$ $\dfrac{200}{3}x^{\frac{3}{2}}$ $\dfrac{200}{3x^{\frac{3}{2}}}$ $\dfrac{200}{3x^{\frac{1}{2}}}$ None 13. The demand and supply function of a commodity are $D(x)= 25 − 2x$ and $S(x) = \dfrac{10+x}{4} $ then the equilibrium price $P_{0}$ is $5$ $2$ $3$ $10$ None 14. When $x_{0}=5 \; and \; p_{0}=3$ the consumer’s surplus for the demand function $p_{d} = 28 − x^{2} $ is $250 units$ $\dfrac{250}{3}units$ $\dfrac{251}{2}units$ $\dfrac{251}{3}units$ None 15. The producer’s surplus when the supply function for a commodity is $P = 3 + x \; and \; x_{0} = 3 $ is $\dfrac{5}{2}$ $\dfrac{9}{2}$ $\dfrac{3}{2}$ $\dfrac{7}{2}$ None 16. The demand and supply function of a commodity are $P(x)= (x − 5)^{2} $ and $ S(x)= x^{2} + x + 3 $ then the equilibrium quantity $x_{0}$ is $5$ $2$ $3$ $1$ None 17. The demand function for the marginal function $MR = 100 − 9x^{2}$ is $100-3x^{2}$ $100x-3x^{2}$ $100x-9x^{2}$ $100x+9x^{2}$ None 18. Area bounded by $y = x$ between the lines y = 1, $ y = 2\; with \; y = axis$ is $\dfrac{1}{2}units$ $\dfrac{5}{2}units$ $\dfrac{3}{2}units$ $1 sq.unit$ None 19. If MR and MC denote the marginal revenue and marginal cost and $MR − MC = 36x − 3x^{2} − 81, $ then the maximum profit at x is equal to $3$ $6$ $9$ $5$ None 20. For the demand function p(x), the elasticity of demand with respect to price is unity then revenue is constant cost function is constant profit is constant none of these None 21. The area bounded by the parabola $y^{2} = 4x$ bounded by its latus rectum is $\dfrac{16}{3}sq.units$ $\dfrac{8}{3}sq.units$ $\dfrac{72}{3}sq.units$ $\dfrac{1}{3}sq.units$ None 22. Area bounded by $ y = x$ between the limits 0 and 2 is $1 sq.units$ $3 sq.units$ $2 sq.units$ $4 sq.units$ None 23. For a demand function p, $if\; \displaystyle \int_{}^{}\frac{dp}{p}=k,\; \displaystyle \int_{}^{}\frac{dx}{x}, \;$ then k is equal to $\eta_{d}$ $-\eta_{d}$ $\dfrac{-1}{\eta_{d}}$ $\dfrac{1}{\eta_{d}}$ None 24. Area bounded by $y = e^{x}$ between the limits 0 to 1 is $( e −1) sq.units$ $( e +1) sq.units$ $( 1-\dfrac{1}{e}) sq.units$ $( 1+\dfrac{1}{e}) sq.units$ None 25. If the marginal revenue of a firm is constant, then the demand function is $MR$ $MC$ $C(x)$ $AC$ None Time's upRelated Posts:Chapter 2: Integral Calculus IChapter 5: Differential CalculusChapter 5: Numerical MethodsChapter 4: Differential Equations
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