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