Which of the following is the correct option for the dynamic stability of higher order differential equation by Routh Theorem ?

• A) It is based on the characteristic roots of the equation
• B) It can be used only to calculate the stable dynamic path only
• C) It is not based on the calculation of characteristic roots
• D) It can be used only when order of differential equation is more than 5

Which of the following is the correct option for the equation,V(t) = 1000e-0.04t +V(0) ?

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

Which of the following is the correct option for the dynamic stability of the time-path of rate of change of population; dN/dt = 0.01 N and N(t) 40000e0.017t ?

• A) The complimentary function will converge to particular solution
• B) The particular function will converge to complementary solution
• C) The complementary function will converge to zero
• D) It is first order homogeneous differential equation

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

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

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

• A) All of the given options
• B) There is no value for the complementary solution
• C) The value of particular solution cannot be calculated
• D) The particular solution will be a constant value

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

• A) It is first order homogeneous differential equation
• B) None of the given options
• C) It is a non linear differential equation which have been converted from linear equation
• D) If it is inexact differential equation, it will be solved in four steps

Which of the following is the correct option for the ore mining function, M(t) = 400e-0.02t ?

• A) There is no complementary solution to the equation
• B) There is a particular solution to the equation equals to 400
• C) It is a case of homogeneous first order differential equation
• D) It is a case of non homogeneous first order differential equation

Which of the following is the correct option for reservation price in equation, Q(PR) = -P2R - 3 PR + 28 ?

• A) Reservation price will be 4
• B) Reservation price will be 2
• C) Reservation price will be 10
• D) Reservation price will be 5

Which of the following is the correct option for the capital function, K(t)= 100(2t+4)2 ?

• A) It is definite solution of linear first order differential equation
• B) It represents the time path of the capital stock over time
• C) It represents the time path of the GDP over time
• D) It is definite solution of non linear differential equation

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

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

Which of the following is the correct option for the definite solution of equation; yt+1 = yt +4 at period t = 2 ?

• A) Y3 = Y2 + 4
• B) Y3 = Y1 + 2
• C) Y4 = Y1 + 4
• D) Y4 = Y3 + 4

Which of the following is the correct option for the equation, $\frac{{dQ}}{{dP}}$ +2P = -11 ?

• A) First order differential equation is not applicable as Q is independent variable
• B) Integration can be used to find value of Q as dependant variable
• C) All of the given options
• D) The equation represent a modified form of elasticity of demand

Which of the following the the incorrect option for the case of repeated real roots?

• A) The zero value of the discriminant α12 - 4α2 will lead to repeated real roots
• B) The value of the roots will be equal to each other
• C) The value of root will be negative for dynamic stability
• D) The positive value of the discriminant α12 - 4α2 will lead to repeated real roots

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