Chapter 6: Applications of DifferentiationMarch 14, 2024 Maven Leave a Comment Welcome to the Chapter 6: Applications of Differentiation Quiz! Name Email 1. If the demand function is said to be elastic, then $\begin{vmatrix} \eta_{d } \end{vmatrix}> 1$ $\begin{vmatrix} \eta_{d } \end{vmatrix}= 1$ $\begin{vmatrix} \eta_{d } \end{vmatrix}< 1$ $\begin{vmatrix} \eta_{d } \end{vmatrix}= 0$ None 2. If demand and the cost function of a firm are p= 2–x and C=$2x^{2}+2x+7$, then its profit function is $x^{2}+7$ $x^{2}-7$ $-x^{2}+7$ $-x^{2}-7$ None 3. The elasticity of demand for the demand function x $=\frac{1}{p}$ 0 1 $\frac{-1}{p}$ $\infty$ None 4. Instantaneous rate of change of y=$2x^{2}+5x$ with respect to x at x=2 is 4 5 13 9 None 5. Marginal revenue of the demand function p= 20–3x is 20–6x 20–3x 20+6x 20+3x None 6. For the cost function C $=\frac{1}{25}e^{5x}$, the marginal cost is $\frac{1}{25}$ $\frac{1}{5}e^{5x}$ $\frac{1}{125}e^{5x}$ $25e^{5x}$ None 7. If the average revenue of a certain firm is Rs. 50 and its elasticity of demand is 2, then their marginal revenue is Rs. 50 Rs. 25 Rs. 100 Rs. 75 None 8. Relationship among MR, AR and $ \eta_{d}$ is $\eta_{d}=\frac{AR}{AR-MR}$ $\eta_{d}=AR-MR$ MR=AR$=\eta_{d}$ $AR=\frac{MR}{\eta_{d}}$ None 9. Average fixed cost of the cost function C(x)$=2x^{3}+5x^{2}-14x+21$ is $\frac{2}{3}$ $\frac{5}{x}$ $\frac{-14}{x}$ $\frac{21}{x}$ None 10. Profit P(x) is maximum when MR = MC MR = 0 MC = AC TR = AC None 11. Average cost is minimum when Marginal cost = Marginal revenue Average cost = Marginal cost Average cost = Marginal revenue Average Revenue = Marginal cost None 12. The maximum value of f(x)= sinx is 1 $\frac{\sqrt{3}}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{-1}{\sqrt{2}}$ None 13. If q=$1000+8p_{1}-p_{2}$, then $\frac{\partial q}{\partial p_{1}}$ is -1 8 1000 $1000- p_{2}$ None 14. If R = 5000 units / year, $C_{1}$= 20 paise, $C_{3}$= Rs 20, then EOQ is 5000 100 1000 200 None 15. If u$=e^{x^{2}}$, then $\frac{\partial u}{\partial x}$ is equal to $2xe^{x^{2}}$ $e^{x^{2}}$ $2e^{x^{2}}$ 0 None 16. The demand function is always Increasing function Decreasing function Non-decreasing function Undefined function None 17. If u$=x^{3}+3xy^{2}+y^{3}$, then $\frac{\partial ^{2}u}{\partial x\partial y}$ is equal to 3 6y 6x 2 None 18. A company begins to earn profit at Maximum point Breakeven point Stationary point Even point None 19. If u$=4x^{2}+4xy+y^{2}+4x+32y+16$, then $\frac{\partial ^{2}u}{\partial x\partial y}$ is equal to 8x + 4y + 4 4 2y + 32 0 None 20. If f(x,y) is a homogeneous function of degree n, then $x\frac{\partial f}{\partial x} + y \frac{\partial f}{\partial y}$ is equal to (n–1)f n(n–1)f nf f None Time's upRelated Posts:Chapter 1: Applications of Matrices and DeterminantsChapter 1: Introduction to Micro EconomicsChapter 2. Consumption AnalysisChapter 3: Production Analysis
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