Chapter 6: Applications of DifferentiationMarch 14, 2024 Maven Leave a Comment Welcome to the Chapter 6: Applications of Differentiation Quiz! Name Email 1. Instantaneous rate of change of y=$2x^{2}+5x$ with respect to x at x=2 is 4 5 13 9 None 2. Profit P(x) is maximum when MR = MC MR = 0 MC = AC TR = AC None 3. 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 4. 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 5. 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 6. The elasticity of demand for the demand function x $=\frac{1}{p}$ 0 1 $\frac{-1}{p}$ $\infty$ None 7. 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 8. 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 9. 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 10. Marginal revenue of the demand function p= 20–3x is 20–6x 20–3x 20+6x 20+3x None 11. The maximum value of f(x)= sinx is 1 $\frac{\sqrt{3}}{2}$ $\frac{1}{\sqrt{2}}$ $\frac{-1}{\sqrt{2}}$ None 12. If q=$1000+8p_{1}-p_{2}$, then $\frac{\partial q}{\partial p_{1}}$ is -1 8 1000 $1000- p_{2}$ None 13. The demand function is always Increasing function Decreasing function Non-decreasing function Undefined function None 14. 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 15. 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 16. 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 17. If R = 5000 units / year, $C_{1}$= 20 paise, $C_{3}$= Rs 20, then EOQ is 5000 100 1000 200 None 18. Average cost is minimum when Marginal cost = Marginal revenue Average cost = Marginal cost Average cost = Marginal revenue Average Revenue = Marginal cost None 19. 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 20. A company begins to earn profit at Maximum point Breakeven point Stationary point Even point 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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