Which of the following is the incorrect option for the equation, I= δY + $\gamma \frac{{dY}}{{dt}}$ ?

• A) The value of δ >1will lead towards convergence
• B) The value of δ >1will lead towards divergence
• C) The value of γ will determine income over time
• D) All of the given options

Which of the following is the correct option for the dynamic stability of the time-path of $i(t) = [i(0) - (\frac{{\alpha + \gamma }}{{\beta + \delta }})]{e^{\frac{{\beta + \delta }}{{\rho - \sigma }}t}}{\mkern 1mu} + \frac{{\alpha + \gamma }}{{\beta + \delta }}$ ?

• A) There is a particular solution to the equation
• 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 correct option for the dynamic stability in case of repeated Real Roots?

• A) The equation will have two and no exponential terms
• B) The equation will have two and similar exponential term with negative sign
• C) The equation will have two and different exponential terms with positive sign
• D) The equation will have two and different exponential terms with negative sign

Which of the following is the correct option for the Government Expenditure equation, dG/dt = -0.07G ?

• A) The value of G(t) does not depend on time
• B) It is first order non homogeneous differential equation
• C) It is first order homogeneous differential equation
• D) It is first order second degree differential equation

Which of the following is the correct option for equation π(t) = π(0)ert ?

• A) There will be convergence towards zero
• B) There will be convergence towards particular solution
• C) There will be divergence from the equilibrium value
• D) There will be convergence towards complementary solution

Which of the following is the correct option for the equation, 3LK + 2KL=0 ?

• A) It is first order differential equation with complex solution
• B) It is first order first degree non homogeneous differential equation
• C) The equation will have no general solution
• D) The equation represents non linear homogeneous differential equation

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

Which of the following is the correct option for \frac{{dP}}{{dt}}\, \propto (Qd - Qs)?

• A) Price adjustments are inversely proportional to excess demand
• B) Price adjustments are directly proportional to excess/shortage of demand
• C) Price adjustments are inversely proportional to excess supply
• D) Price adjustments are directly proportional to equilibrium quantity

Given the equation for rate of consumption \frac{{dC}}{{dt}} = -4C+10 , Which of the following is the incorrect option?

• A) It is a case of homogeneous first order differential equation
• B) All of the given options
• C) There is a particular solution to the equation
• D) It is a case of non homogeneous first order differential equation

Which of the following is the incorrect option for the equation, \frac{{dy}}{{dt}} + \,u(t).y = w(t) ?

• A) None of the given options
• B) It is first order differential equation with variable term and variable coefficient
• C) It is first order second degree differential equation
• D) The value of the equation will depend on time

Which of the following is the incorrect option for \frac{{dP}}{{dt}}= j(Qd - Qs) ?

• A) The value of j is known as adjustment coefficient
• B) The value of j will be zero at equilibrium point
• C) The value of j will be negative
• D) All of the given options

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

• A) None of the given options
• B) There will be no convergence towards particular solution
• C) There will be convergence towards complementary solution
• D) There will be no impact of the convergence mechanism

Which of the following is the incorrect option for the equation, I= δY + \gamma \frac{{dY}}{{dt}} ?

• A) The value of δ >1will lead towards divergence
• B) All of the given options
• C) The value of γ will determine income over time
• D) The value of δ >1will lead towards convergence

Which of the following is the incorrect option for static sense of equilibrium in market price, {P^*} = \,\frac{{\alpha + \gamma }}{{\beta + \delta }} ?

• A) The value of price cannot be predicted
• B) The value of price will be inversely related to \alpha + \gamma
• C) The value of the price will be positively related to \alpha + \gamma
• D) The value of price will be constant

Which of the following is the incorrect option for the equation,\frac{{dY}}{{dt}} + \frac{{1 - \beta + \tau \beta - \delta }}{\gamma }Y = \frac{\alpha }{\gamma }?

• A) It is first order third degree differential equation
• B) It is first order second degree differential equation
• C) The equation represent a modified form of elasticity of investment
• D) All of the given options

Which of the following is the incorrect option for the equation, \frac{{dQ}}{{dP}} +2P = -8?

• A) The value of price will be constant
• B) The definite solution can be calculated using integration
• C) The standard first order differential equation cannot be used
• D) None of the given options

Which of the following is the incorrect option for the money market equation, \alpha Y\, + \,\beta \frac{{dy}}{{dt}} = \,{M_s} ?

• A) The value of money supply (Ms) will be constant
• B) The standard first order differential equation can be used
• C) All of the given options
• D) The value of income (Y) will be inversely related money supply (Ms)

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

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

Which of the following is the correct option for the time-path of fish stock function F(t) = -70e-0.12t +90 when time t=0?

• A) The quantity of fish stock function F(t) will be 70
• B) The quantity of fish stock function F(t) will be 20
• C) The quantity of fish stock function F(t) will be 90
• D) The quantity of fish stock function F(t) will be 160

Which of the following is the correct option for the dynamic stability of the time-path of fish stock function F(t) = -70e-0.12t +90 ?

• A) The complementary function will converge to zero
• B) The complimentary function will converge to 90
• C) The particular function will converge to complementary solution
• D) The complementary function will converge to zero