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

Which of the following is the incorrect option for the terms of price equation (dp/dt+d2p/dt2) ?

• A) It is slope of rate of change in price over time
• B) It is market price of goods over time
• C) All of the given options
• D) It is rate of change in price over time

Which of the following is the correct option for the particular solution of first difference equation; Yp = 5 ?

• A) There will be no equilibrium
• B) There will be a static equilibrium
• C) There will be continuous equilibrium
• D) There will be a stepped equilibrium

Which of the following is the correct option for y’’(t) +3y’(t) - 4y = 0?

• A) It is a homogeneous second order differential equation
• B) The particular solution will be equal to three
• C) The particular solution will be equal to four
• D) It is a non homogeneous second order differential equation

Which of the following is the correct option for the marginal product of labor and capital, MPk= 5L and MPL= 1.2 LK ; assuming it is on an Iso-quant (dQ=0) ?

• A) It is the general solution of the second order homogeneous differential equation
• B) If it is exact differential equation, it will be solved in four steps
• C) If it is inexact differential equation, it will be solved in four steps
• D) It is the definite solution of the first order homogeneous differential equation

Which of the following is the correct option for the complementary function in case of Complex Roots ?

• A) It shall have one but Complex exponential terms
• B) It shall have two but Similar exponential terms
• C) It shall have three but Repeated exponential terms
• D) It shall have two but Complex exponential terms

Which of the following is the correct option for the equation $\frac{{dy}}{{dt}} + \,( - 1)y = \,6$file:///C:\Users\MUHAMM~1.SHA\AppData\Local\Temp\ksohtml5460\wps12.jpgusing phase diagram?

• A) The inter temporal equilibrium will be unaffected
• B) The inter temporal equilibrium will be convergent
• C) It can be solved with the Bernoulli equation method
• D) The inter temporal equilibrium will be divergent

Which of the following is the incorrect option for transaction demand for money, L [ P(t). Y] ?

• A) It is inversely related with price (P) and positively with income (Y)
• B) None of the given options
• C) It is positively related with income (Y)
• D) It is positively related with price (P)

Which of the following is the correct option for reservation price?

• A) The price at which there is maximum profit
• B) The price at which consumer surplus is maximum
• C) The price at which there is maximum demand of product
• D) The price at which there is no demand

Which of the following is the correct option for the marginal product of labor and capital, MPk= 3LK and MPL= 5LK ; assuming it is on an Iso-quant (dQ=0) ?

• A) The values cannot be used to apply the exactness test
• B) There will be three steps involved if it is exact differential equation
• C) It is a non linear first order homogeneous differential equation
• D) It is first order non homogeneous differential equation

Which of the following is the correct option for the complementary function in case of Repeated Real Roots ?

• A) It shall have two but different exponential terms
• B) It shall have three but Repeated exponential terms
• C) It shall have one but Repeated exponential terms
• D) None of the given options

Which of the following is the correct option for the, $2yt.dy + {y^3}.dt = \,0$ ?

• A) None of the options
• B) It is a case of homogeneous first order differential equation
• C) It is a case of non homogeneous first order differential equation
• D) It is a case of inexact differential equation

Which of the following is the correct option for the complementary function in case of Distinct Real Roots?

• A) The equation can be solved with exact differential equation method
• B) The equation will have two and similar exponential terms
• C) The equation will have two and different exponential terms
• D) The equation will have two and no exponential terms

Which of the following is the correct option for the equation; α0yn(t) + α1yn-1(t) +………..+αn-1y’ +αny = b if αn > 0 and αn-1 = 0 ?

• A) The particular solution will be equal to kt2 as trial solution
• B) The particular solution will be equal to b/αn
• C) The particular solution will be equal to b/αn-1
• D) The complementary solution will be equal to b/α2