Which of the following is the correct option for the dynamic stability in case of Distinct Real Roots?

• A) None of the given options
• B) The equation will have two and no exponential terms
• C) The equation will have two and similar exponential terms
• D) The equation will have two and different exponential terms with positive sign

Which of the following is the correct option for equation Q(P) = -P2 - 2P + 1?

• A) This is a definite solution of equation
• B) Time path is not involved in the equation
• C) All of the given options
• D) This is a general solution of equation

Which of the following is the correct option for y’’(t) + 2y’ + 3y = 10 ?

• A) The particular solution will be equal to 10
• 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 zero

Which of the following is the incorrect option for the Phillips equation; $\frac{{{d^2}\pi }}{{d{t^2}}} + \beta k(\frac{{d\pi }}{{dt}}) - j(g - 1)(\frac{{d\pi }}{{dt}}) + j\beta km = \,j\beta km$ ?

• A) The particular solution b/a2 will be file:///C:\Users\MUHAMM~1.SHA\AppData\Local\Temp\ksohtml6824\wps2.jpgm
• B) All of the options
• C) The complementary solution b/a2 will be $jm$
• D) The complementary solution b/a2 will befile:///C:\Users\MUHAMM~1.SHA\AppData\Local\Temp\ksohtml6824\wps3.jpg$j\beta km$

Which of the following is the correct option for the $\frac{{dy}}{{dt}} + \,Ry = \,T{y^m}$ assuming m<1?

• A) All of the given options
• B) It is a non linear differential equation where Ry causes non linearity
• C) It is a non linear differential equation where Ym causes non linearity
• D) It is a linear differential equation of first order

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

• A) It can be solve with exact differential equation method
• B) All of the given options
• C) It can be solve with exact differential equation method
• D) It can be solved with the Bernoulli equation method

Which of the following is the correct option for y’’(t) + y’ + 3y = 18 ?

• A) It is a homogeneous second order differential equation
• B) It is a non homogeneous first order differential equation
• C) The particular solution will be equal to 6
• D) The particular solution will be equal to 18

Which of the following is the incorrect option the equation $y(t) = \,A{e^{\int {u(t)\,dt} }}$ ?

• A) All of the given options
• B) It is the general solution of the second order homogeneous differential equation
• C) It is the definite solution of the first order homogeneous differential equation
• D) It is the definite solution of the first order non homogeneous differential equation

Which of the following is the correct option for second order differential equation with constant coefficient and variable terms i.e L.H.S is the f(t)?

• A) It will change both complementary and particular solution
• B) The value of particular solution cannot be calculated
• C) It will change the complementary solution
• D) It will change the particular solution

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

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

Which of the following is the correct option for the dynamic time path of the market price, P(t) = [P(0)-P*]e-kt + P* ?

• A) P(t) will converge towards P* regardless of value of P(0)
• B) There is a particular solution to the equation
• C) There is a complementary solution to the equation
• D) All of the given options

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

• A) The system will be dynamically undefined
• B) The system will dynamically unstable with A1 = 0 and A2 >0
• C) The system will dynamically stable with A1 = 0
• D) The system will dynamically stable with A1 >0 and A2 = 0

The time path should converge towards the complementary solution for dynamic stability in the pollution function given by P(t) = 30e-0.2t ?

• A) True
• B) False
• C)
• D)

Which of the following is the incorrect option for the deposit function, D(t) = 4000e-0.05t +20 ?

• A) It is first order differential non homogeneous equation
• B) It has both complementary and particular solutions
• C) It will converge towards to the particular solution
• D) It will diverge from the equilibrium value

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

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

Which of the following is the correct option for Fuel usage equation, F(t) = 12000e-0.001t - 6000 at time t=0?

• A) Fuel usage F(t) will be 12000 litre
• B) Fuel usage F(t) will be 18000 litre
• C) Fuel usage F(t) will be 6000 litre
• D) Fuel usage F(t) will be 4000 litre

Which of the following is the incorrect option for the equation, $\frac{{dy}}{{dt}} + \,u(t).y = 0$ ?

• A) All of the given options
• B) The equation will have no definite solution
• C) It is first order differential equation with general solution
• D) It is first order first degree non homogeneous differential equation

Which of the following is the correct option in the utility equation, 3xy.dx+x.dy=0 ?

• A) It is the definite solution of the first order non homogeneous differential equation
• B) It is first order non homogeneous differential equation
• C) None of the given options
• D) The equation cannot be used for the exactness test

Which of the following is the incorrect option for the possible cases of Phillips equation dπ/dt = j (p - π) ?

• A) j > 1
• B) j ><0
• C) j = 0
• D) j > 0

Which of the following is the incorrect option for second order differential equations with α12 - 4α2 <0 ?

• A) It will have distinct real roots
• B) It will have both repeated and real roots
• C) It will have repeated real roots
• D) All of the options