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

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

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

• A) All of the given options
• B) It is nth order differential equation of higher order
• C) It is a non linear differential equation where b causes non linearity
• D) It is second order differential equation in Lagrange notation

Which of the following is the incorrect option for the oil equation, dV/dt + 0.03V(t)= 18 ?

• A) It is first order homogeneous differential equation
• B) It is first order non homogeneous differential equation
• C) The value of V(t) depends on time
• D) It has both complementary and particular solutions

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

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

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

• A) It shall have two but Similar exponential terms
• B) It shall have one but Complex exponential terms
• C) All of the given options
• D) It shall have three but Repeated exponential terms

Which of the following is the incorrect option for the dynamic stability of equation; Yt = Abt ?

• A) All of the given options
• B) The term t will determine the dynamic stability of the equation
• C) The term A will determine the dynamic stability of the equation
• D) The equation cannot be determined for the dynamic stability

Which of the following is the incorrect option for second order differential equations?

• A) It measures the aggregate value of the variable over time
• B) All of the given options
• C) It measures rate of change of the variable over time
• D) It measure average relationship over time

Which of the following is the correct option for gold mining equation, G(t) = 2000e-0.03 +0 ?

• A) It is first order differential homogeneous equation
• B) It will not converge towards equilibrium value
• C) It has both complementary and particular solutions
• D) It is first order differential non homogeneous equation

Which of the following is the correct option for the fuel (in litre) equation F’((x) = -0.03F(x) -18 ?

• A) Time path is not involved in the equation
• B) The value of 0.03 will lead to divergence from equilibrium value
• C) The value of 18 is not involved in convergence mechanism of the equation
• D) The value of 18 will ensure convergence towards equilibrium value

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

• A) The system will dynamically unstable when repeated real roots are negative
• B) The system will dynamically stable when repeated real roots are negative
• C) The system will be dynamically stable when one root is positive and second is negative
• D) The system will dynamically stable when repeated real roots are positive

Which of the following is the correct option for the case of repeated real Roots ?

• A) α12 - 4α2 = 0
• B) None of the options
• C) α12 - 4α2 < 0
• D) α12 - 4α2 > 0

Which of the following is the correct option for the term Adapted Phillips relation?

• A) None of the given options
• B) Rate of growth of money wage and rate of unemployment
• C) Average growth rate of money supply
• D) Rate of growth of money supply and GDP growth

Which of the following is the correct option for the price equation with solution ${Y_p} = \,\frac{{\alpha + \gamma }}{{\beta + \delta }}$ ?

• A) All of the given options
• B) α2 ≠ 0
• C) (α1)2 > 4α2
• D) There is a stationary equilibrium for the system

Which of the following is the correct option for the equation, G(t) = 300e-0.05t ?

• A) It is homogeneous first order differential equation with definite solution
• B) It is first order differential equation with general solution
• C) The equation represent a modified form of investment multiplier
• D) It is first order first degree non homogeneous differential equation with definite solution

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

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

Which of the following is the correct option for the equation of price Qd = α-βP+mP’ + nP’’ when there are no price expectations ?

• A) It will slightly increase the demand of Qd
• B) It will have no effect on the demand Qd
• C) It will increase the demand Qd at decreasing rate
• D) It will increase the demand Qd at increasing rate

Which of the following is the correct option in the equation, $\frac{{dy}}{{dt}} + \,ty = \,t{y^2}$ ?

• A) None of the given options
• B) The function can be solved with using exact differential equation method
• C) The value of the m=1 and R=2 in the given equation
• D) Using Bernoulli equation method, it can be substituted file:///C:\Users\MUHAMM~1.SHA\AppData\Local\Temp\ksohtml5460\wps9.jpgz in place of y to linearize the equation

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 b/αn
• B) The complementary solution will be equal to b/α2
• C) The particular solution will be equal to b/α2
• D) The particular solution will be equal to (b/αn-1)t

Which of the following is the incorrect option for national income equation $\frac{{dy}}{{dt}} + (\frac{{1 - \beta + \tau \beta - \delta }}{{ - \gamma }})Y = - \frac{\alpha }{\gamma }$ ?

• A) None of the given options
• B) It has only the particular solution
• C) It is first order differential non homogeneous equation
• D) It has both complementary and particular solutions

Which of the following is the incorrect option for the first order difference equation ?

• A) A period is a length of time that elapses before the variable file:///C:\Users\MUHAMM~1.SHA\AppData\Local\Temp\ksohtml3832\wps1.jpg undergoes a change
• B) The Period doesn’t necessarily relate to calendar rather than analytical sense.
• C) The dynamic stability will be computed for the equation
• D) None of the given options