Which of the following is the incorrect option for equation $Y(t) = \,[Y(0) - \frac{{{M_s}}}{\alpha }]{e^{ - (\frac{\alpha }{\beta })}} + \frac{{{M_s}}}{\alpha }$ ?

• A) The value of $\frac{{{M_s}}}{\alpha }$ will is the equilibrium value
• B) The equation have complementary and particular solutions
• C) The value of ${\frac{\alpha }{\beta }}$>0 will ensure convergence towards equilibrium value
• D) The value of ${\frac{\alpha }{\beta }}$ >0 will lead to divergence from equilibrium value

Which of the following is the correct option for dynamic stability in the pollution function given by P(t) = 10e-0.2t ?

• A) The time path should converge towards the zero
• B) The time path should be equal to 10
• C) The time path should diverge from 10
• D) The time path should converge towards the complementary solution

Which of the following the the correct option for the case of complex roots?

• A) There will be real and imaginary value in roots
• B) The value of the discriminant $a_1^2 = 4{a_2}$ will lead to complex roots
• C) The value of the roots will be equal to each other
• D) The value of root will be positive for dynamic stability

Which of the following is the correct option for (Qd - Qs) in static sense of equilibrium in market price?

• A) The negative value will show a surplus of goods
• B) The positive value will show a shortage of goods
• C) The zero value will show an equilibrium state
• D) All of the given options

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

• A) The particular solution will be equal to 4
• B) It is a non homogeneous second order differential equation
• C) It is a homogeneous second order differential equation
• D) The particular solution will be equal to 3

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

Which of the following is the incorrect option for dynamic stability of P(t) = [P(0)-P*]e-kt + P* ?

• A) The complimentary function (Pc) will not be equal to P* only
• B) All of the options
• C) The particular solution can have non constant (kt) value
• D) The complimentary function (Pc) will not converge to P*

Which of the following is the incorrect option for the ${y^n}(t) + {\alpha _1}{y^{n - 1}} + .... + {\alpha _{n - 1}}{y^1}(t) + {\alpha _n}y = b$ ?

• A) It is nth degree differential equation with nth order
• B) All of the given options
• C) It is a non linear differential equation which have been converted from linear equation
• D) It is second degree differential equation with nth order

Which of the following is the correct option for reservation price in equation Q(PR) = -PR2 - 10PR + 75?

• A) Reservation price will be 12
• B) Reservation price will be 5
• C) Reservation price will be 11
• D) Reservation price will be 4

Depending on the value of discriminant in the $P'' + \frac{m}{n}p' + [ - \frac{{\beta + \delta }}{n}]P = - \frac{{\alpha + \gamma }}{n}$ , the nature of roots of characteristic equation gets defined. This gives rise to?

• A) Two cases of complementary functions
• B) None of the given options
• C) Three cases of particular solution
• D) Four cases of complementary functions

Which of the following is the correct option for the Phillips equation p= α- βU - T ?

• A) All of the given options
• B) Unemployment and inflation are inversely related
• C) Inflation will decrease when productivity (T) increases
• D) Inflation will increase when unemployment increase

Expectations-augmented Phillips relation is based mostly on supply side and deals with?

• A) Wages and money supply
• B) Unemployment and money supply
• C) GDP and inflation
• D) Unemployment and actual/expected inflation

Which of the following is the incorrect option for the dynamic stability of price equation; $P'' + \frac{m}{n}p' + [ - \frac{{\beta + \delta }}{n}]P = - \frac{{\alpha + \gamma }}{n}$ When n=0 ?

• A) The system will dynamically stable with A1 >0 and A2 >0
• B) All of the given options
• C) The system will dynamically stable with A1 = 0 and A2 >0
• D) The system will dynamically stable with A1 >0 and A2 = 0

Which of the following is the incorrect option for the Phillips equation p= α- βU - T + g.π ?

• A) All of the given options
• B) It is original Phillips relation
• C) It is adapted Phillips relation
• D) It is adapted money supply and GDP relation

Which of the following is the incorrect option for the gold mine equation dG/dt + 0.02G(t)= 17 ?

• A) The value of 17 will ensure convergence towards equilibrium value
• B) All of the given options
• C) Time path is not involved in the equation
• D) The value of 0.02 will lead to divergence from equilibrium value

Which of the following is the correct option for unemployment equation U(t) = 80e-3t +90 when time t=0?

• A) The Unemployed individual U(t) will be 170
• B) The Unemployed individual U(t) will be 90
• C) The Unemployed individual U(t) will be 80
• D) The Unemployed individual U(t) will be 10

Which of the following is the correct option for the equation; y’’ + 2y’ +3y = 2t2+t+12 ?

• A) Particular solution for this equation will be equal to complementary solution
• B) Method of undetermined coefficients will be used to calculate particular solution
• C) Method of undetermined coefficients will be used to calculate both complementary and particular solution
• D) Method of undetermined coefficients will be used to calculate complementary solution

Which of the following is the correct option for the definite solution of equation; Yt=1 - Yt = 9 ?

• A) The definite solution will be equal to 9t only
• B) The definite solution will be equal to 9 only
• C) The definite solution will be equal to Y0 +9 only
• D) The definite solution will be undefined

Which of the following is the correct option for the equation $\frac{{dy}}{{dt}} + \,(3)y = \,5$ using phase diagram?

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

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

• A) It is first order second degree differential equation
• B) It is first order first degree differential equation
• C) It is a modified form of elasticity of money demand and money supply
• D) The equation cannot be resolved using differential equation method