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