\begin{gathered} y = f(g(x)) \hfill \ \frac{{dy}} {{dx}} = \frac{d} {{dx}}\{ f(g(x))\} = f'(g(x)).g'(x) \hfill \\\ \end{gathered} Given the above expression; g(x) represents:

• A) Outside function
• B) Inside function
• C) Derivative of inside function
• D) Derivative of outside function

Given the saving function \[ S = 0.35Y + i \] ; \[ S_Y = \frac{{\partial S}} {{\partial Y}} \] is?

• A) 0.35
• B) 1/0.35
• C) 1
• D) 1.35

\[ \begin{gathered} y = f(g(x)) \hfill \ \frac{{dy}} {{dx}} = \frac{d} {{dx}}\{ f(g(x))\} = f'(g(x)).g'(x) \hfill \\\ \end{gathered} \] Given the above expression; \[ g(x) \] represents:

• A) Outside function
• B) Derivative of outside function
• C) Inside function
• D) Derivative of inside function

Which of the following shows the differential of \[ y = f(x) = 4x^2 + 20 \] ?

• A) \[ dy = (8x).dx \]
• B) \[ dy(8x) = dx \]
• C) \[ dx = (8x).dy \]
• D) \[ dy + dx = (8x) \]

Which of the following shows the differential of \[ y = f(x) = 3x + 2 \] ?

• A) \[ dy = (3 + x).dx \]
• B) \[ dy = (2 + 3).dx \]
• C) \[ dy = (3).dx \]
• D) \[ dx = (\frac{1} {3}).dy \]

\[ 2x + 3y = 20 \] is an example of:

• A) Quadratic function
• B) Cubic function
• C) Implicit function
• D) Production function

Which of the following shows the differential of y = f(x) = Ax^2 ?

• A) dy = (\frac{{Ax}} {2}).dx
• B) dy = (2 + Ax).dx
• C) dx = (2Ax).dy
• D) dy = (2Ax).dx

\[ f'(x) \] shows the:

• A) First derivative of the function \[ y = f(x) \]
• B) Second derivative of the function \[ y = f(x) \]
• C) Third derivative of the function \[ y = f(x) \]
• D) Fourth derivative of the function \[ y = f(x) \]

Given the Cobb-Douglas production function;\[ Q = AK^\alpha L^\beta \] A represents:

• A) Output
• B) Constant
• C) Capital
• D) Labor

Total derivative of the function y = f(g(w),w) is:

• A) \frac{{dy}} {{dw}} = f_x .\frac{{dx}} {{dw}} + f_w .\frac{{dw}} {{dw}}
• B) \frac{{dy}} {{dw}} = \frac{{dx}} {{dw}} + \frac{{dw}} {{dw}}
• C) \frac{{dy}} {{dw}} = dx + f_w .\frac{{dw}} {{dw}}
• D) \frac{{dy}} {{dw}} = f_x .\frac{{dx}} {{dw}} + dx

\[ \pi = PQ - wK \] is the profit function of the labor market; what does K show in this function?

• A) Price of output
• B) Quantity of capital input
• C) Quantity of output
• D) Price of capital input

\begin{gathered} y = f(g(x)) \hfill \\ \frac{{dy}} {{dx}} = \frac{d} {{dx}}\{ f(g(x))\} = f'(g(x)).g'(x) \hfill \\\ \end{gathered} Given the above expression; g'(x) represents:

• A) Derivative of inside function
• B) Inside function
• C) Derivative of outside function
• D) Outside function

Given the Cobb-Douglas production function; Q = AK^\alpha L^\beta L represents:

• A) Labor
• B) Constant
• C) Output
• D) Capital

Which of the following is the correct option for equation $Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta - \delta }})]{e^{\frac{{1 - \beta - \delta }}{\gamma }t}}{\mkern 1mu} + \frac{\alpha }{{1 - \beta - \delta }}$ ?

• A) Time path is not involved in the equation
• B) The value of $\frac{\alpha }{{1 - \beta - \delta }}$ = 0 will ensure convergence towards equilibrium value
• C) The value of $\frac{\alpha }{{1 - \beta - \delta }}$ >0 will ensure convergence towards equilibrium value
• D) The value of $\frac{\alpha }{{1 - \beta - \delta }}$ is the particular solution of the equation

Which of the following is the incorrect option for consumption function, $Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta - \delta - g}})]{e^{\frac{{1 - \beta - \delta - g}}{\gamma }t}}{\mkern 1mu} + \frac{\alpha }{{1 - \beta - \delta - g}}$ ?

• A) It has both complementary and particular solutions
• B) It will not converge towards to the particular solution
• C) It will converge towards to the particular solution
• D) It is first order differential non homogeneous equation

Which of the following is the correct option for the equation $\frac{{dk}}{{dt}} + \lambda k = s{k^\alpha }$ if $\alpha = 1$ ?

• A) None of the given options
• B) The equation can be solved with Bernoulli equation method
• C) The equation can be solved with separable variable method
• D) The equation can be solved with exact differential equation method

Which of the following is the correct option for the equation; y’’ + 2y’ +3y = 2e-2t ?

• A) There is no value for the complementary solution
• B) The value of particular solution cannot be calculated
• C) The particular solution will not be a constant value
• D) The particular solution will be a constant value

Which of the following is the correct option for unemployment equation U(t) = 80e-3t +90 ?

• A) The particular solution of the equation is 80
• B) The complementary solution of the equation is 60
• C) The particular solution of the equation is 90
• D) The value of complementary solution has not been given in the equation

Which of the following is the correct option for the rate of change of monthly sales; S(t) = (C-M)e-kt +M ?

• A) The time path should converge towards the particular solution
• B) The time path should diverge from the particular solution
• C) The time path should converge towards the complementary solution
• D) The time path should be equal to the particular solution

Which of the following is the incorrect option for equation if value of file:///C:\Users\MUHAMM~1.SHA\AppData\Local\Temp\ksohtml1148\wps5.jpg is negative $Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta + \tau \beta - \delta }})]{e^{\frac{{1 - \beta + \tau \beta - \delta }}{\gamma }t}}\, + \frac{\alpha }{{1 - \beta + \tau \beta - \delta }}$ ?

• A) There will be divergence from the particular solution
• B) There will be no convergence towards particular solution
• C) All of the given options
• D) There will be convergence towards complementary solution