Which of the following is the correct option for the Phillips equation dπ/dt = j (p - π) When j > 0 ?

• A) Actual Unemployment is than expected inflation
• B) Actual inflation and expected inflation are independent from each other
• C) Actual Inflation is more than expected inflation
• D) Actual Inflation is less than expected inflation

Which of the following is the incorrect option for second order differential equations with $a_1^2 = 4{a_2}$ ?

• A) It will have no real roots
• B) All of the option
• C) It will have complex roots
• D) It will have distinct real roots

Which of the following is the correct option for Mdy+ Ndt =0 ?

• A) None of the given options
• B) The equation cannot be used to find out the definite solution of the variables
• C) The equation is used to solve out the non linear differential equation
• D) The equation can be applied to confirm the exactness test

Which of the following is the correct option for equation, xy.dx+2x.dy=0 and U(x,y)= 0.5xy-c ?

• A) It is the general solution of the non linear homogeneous differential equation
• B) It is the definite solution of the non linear homogeneous differential equation
• C) All of the given options
• D) The function can be solved without using exactness test

Which of the following is the correct option for the quantity supply of a sale function, Q(t) = 300e-0.04t +400 when time t=0?

• A) The quantity supplied of sale function Q(t) will be 400
• B) The quantity supplied of sale function Q(t) will be 300
• C) The quantity supplied of sale function Q(t) will be 700
• D) The quantity supplied of sale function Q(t) will be 100

Which of the following is the incorrect option for the non linear differential equation?

• A) The equation will not depend on the time
• B) The equation cannot have power of dependent variable other than one
• C) The equation can have power of the independent variable other than one
• D) All of the given options

Which of the following is the correct option in the equation, y''(t)+a1y' +a2y = b if a1 = 0, a2 = 0 ?

• A) The particular solution of Yp will be equal to zero
• B) None of the given options
• C) The particular solution Yp will be equal to t
• D) The particular solution Yp will be equal to bt

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