MCQ Bank
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) There is a particular solution to the equation
- D) It is a case of homogeneous first order differential equation
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 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 \({y^{ - m}}\frac{{dy}}{{dt}} + \,R{y^{1 - m}} = \,T\) assuming m>1?
- A) None of the given options
- B) It is first order homogeneous differential equation
- C) If it is inexact differential equation, it will be solved in four steps
- D) It is a non linear differential equation which have been converted from linear equation
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 unaffected
- B) The inter temporal equilibrium will be convergent
- C) It can be solved with the Bernoulli equation method
- D) The inter temporal equilibrium will be divergent
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 particular function will converge to complementary solution
- B) It is first order homogeneous differential equation
- C) The complementary function will converge to zero
- D) The complimentary function will converge to particular solution
Which of the following is the correct option for the dynamic stability of the time-path of i(t) = [i(0) - (\frac{{\alpha + \gamma }}{{\beta + \delta }})]{e^{\frac{{\beta + \delta }}{{\rho - \sigma }}t}}{\mkern 1mu} + \frac{{\alpha + \gamma }}{{\beta + \delta }} ?
- A) The time path should be equal to the particular solution
- B) The time path should diverge from the particular solution
- C) The time path should converge towards the complementary solution
- D) There is a particular solution to the equation
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) If it is inexact differential equation, it will be solved in four steps
- D) It is a non linear differential equation which have been converted from linear equation
Which of the following is the correct option for the equation, \frac{{dQ}}{{dP}} +2P = -11 ?
- A) Integration can be used to find value of Q as dependant variable
- B) First order differential equation is not applicable as Q is independent variable
- C) All of the given options
- D) The equation represent a modified form of elasticity of demand
Which of the following is the incorrect option for consumption function, Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta - \delta - g}})]{e^{\frac{{1 - \beta - \delta - g}}{\gamma }t}}{\mkern 1mu} + \frac{\alpha }{{1 - \beta - \delta - g}} ?
- A) It has both complementary and particular solutions
- B) It is first order differential non homogeneous equation
- C) It will not converge towards to the particular solution
- D) It will converge towards to the particular solution
Which of the following is the correct option for the \frac{{dy}}{{dt}} + \,Ry = \,T{y^m} assuming m=0?
- A) The value of the equation will not depend on time
- B) It will be a first order linear differential equation
- C) It is a non linear first order homogeneous differential equation
- D) There will be not general solution for the equation
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 equation have complementary and particular solutions
- B) The value of {\frac{\alpha }{\beta }} >0 will lead to divergence from equilibrium value
- C) The value of \frac{{{M_s}}}{\alpha } will is the equilibrium value
- D) The value of {\frac{\alpha }{\beta }}>0 will ensure convergence towards equilibrium value
Which of the following is the correct option for the equation \frac{{dk}}{{dt}} + \lambda k = s{k^\alpha } if \alpha = 1 ?
- A) The equation can be solved with separable variable method
- B) The equation can be solved with Bernoulli equation method
- C) The equation can be solved with exact differential equation method
- D) None of the given options
Which of the following is the correct option for the equation, \(\frac{{dQ}}{{dP}}\) +2P = -11 ?
- A) All of the given options
- B) First order differential equation is not applicable as Q is independent variable
- C) The equation represent a modified form of elasticity of demand
- D) Integration can be used to find value of Q as dependant variable
Which of the following is the correct option for the quantity supply of a sale function, Q(t) = 300e-0.04t +400 when time t=0?
- A) The quantity supplied of sale function Q(t) will be 700
- B) The quantity supplied of sale function Q(t) will be 300
- C) The quantity supplied of sale function Q(t) will be 400
- D) The quantity supplied of sale function Q(t) will be 100
Which of the following is the incorrect option for equation if value of file:///C:/Users/MUHAMM~1.SHA/AppData/Local/Temp/ksohtml1148/wps5.jpg is negative \(Y(t) = [Y(0) - (\frac{\alpha }{{1 - \beta + \tau \beta - \delta }})]{e^{\frac{{1 - \beta + \tau \beta - \delta }}{\gamma }t}}\, + \frac{\alpha }{{1 - \beta + \tau \beta - \delta }}\) ?
- A) There will be divergence from the particular solution
- B) All of the given options
- C) There will be convergence towards complementary solution
- D) There will be no convergence towards particular solution
Which of the following is the correct option for the dynamic stability of the time-path of \(i(t) = [i(0) - (\frac{{\alpha + \gamma }}{{\beta + \delta }})]{e^{\frac{{\beta + \delta }}{{\rho - \sigma }}t}}{\mkern 1mu} + \frac{{\alpha + \gamma }}{{\beta + \delta }}\)
- A) None of the given options
- B) The complementary function will converge to particular solution
- C) The particular function will converge to complementary solution
- D) The complimentary function will not converge to particular solution
Which of the following is the incorrect option for the equation, \frac{{dy}}{{dt}} + \,u(t).y = 0 ?
- A) The equation will have no definite solution
- B) It is first order differential equation with general solution
- C) All of the given options
- D) It is first order first degree non homogeneous differential equation
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 value of \({\frac{\alpha }{\beta }}\) >0 will lead to divergence from equilibrium value
- C) The equation have complementary and particular solutions
- D) The value of \({\frac{\alpha }{\beta }}\)>0 will ensure convergence towards equilibrium value
Which of the following is the correct option for the equation \(\frac{{dy}}{{dt}} + \,( - 1)y = \,6\)file:///C:/Users/MUHAMM~1.SHA/AppData/Local/Temp/ksohtml5460/wps12.jpgusing phase diagram?
- A) It can be solved with the Bernoulli equation method
- B) The inter temporal equilibrium will be unaffected
- C) The inter temporal equilibrium will be divergent
- D) The inter temporal equilibrium will be convergent
Which of the following is the correct option in the equation, \frac{{dy}}{{dt}} + \,ty = \,t{y^2} ?
- A) The value of the m=1 and R=2 in the given equation
- B) None of the given options
- C) 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
- D) The function can be solved with using exact differential equation method