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

• A) The tools of analysis will include lags and leads
• B) The nature of values of will be integers only
• C) The analysis is also known as period analysis
• D) All of the given options

Which of the following is the incorrect option for static sense of equilibrium in market price, ${P^*} = \,\frac{{\alpha + \gamma }}{{\beta + \delta }}$ ?

• A) The value of price will be inversely related to $\alpha + \gamma$
• B) The value of price will be constant
• C) The value of the price will be positively related to $\alpha + \gamma$
• D) The value of price cannot be predicted

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

• A) The value of income (Y) will be inversely related money supply (Ms)
• B) The standard first order differential equation can be used
• C) All of the given options
• D) The value of money supply (Ms) will be constant

Which of the following is the correct option for the equation of price Qd = α-βP+mP’ + nP’’ when m>0 ?

• A) It will increase the demand Qd at increasing rate
• B) It will increase the demand of Qd
• C) It will increase the demand Qd at decreasing rate
• D) It will decrease the demand of Qd

Which of the following is the incorrect option for the higher order differential equation in general ? I

• A) It can be a maximum of 5th order differential equation
• B) It can be a maximum of 10th order differential equation
• C) All of the given options
• D) t can be a maximum of 100th order differential equation

Which of the following is the correct option for consumption function, C=α+βY ?

• A) β is the marginal propensity of consumption
• B) It has autonomous consumption α
• C) All of the given options
• D) Consumption is positively related with income (Y)

Which of the following is the incorrect option for initial price P(0) in dynamic sense of equilibrium in market price?

• A) Time path can start from above the equilibrium price
• B) Time path can be equal to the equilibrium price
• C) Time path can start from below the equilibrium price
• D) None of the given options

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