This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 41 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 41 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Of the following, which is a solution to the differential equation? Select all that apply:$y" -y=0$ A) $y=\sin\left(x\right)$. B) $y=e^x$. C) All the above. D) None of the above. Show Answer Correct Answer: B) $y=e^x$. 2. A linear differential equation with constant coefficients is one where the coefficients are: A) Constants. B) Variable functions. C) Arbitrary functions. D) None. Show Answer Correct Answer: A) Constants. 3. Which type of differential equations are not suitable for the method of separation of variables? A) First order linear. B) Nonlinear. C) Second order linear with constant coefficients. D) Partial differential equations. Show Answer Correct Answer: B) Nonlinear. 4. Classify the following differential equation:$\frac{\partial u}{\partial t}+u\frac{\partial u}{\partial x}=v\frac{\partial^2u}{\partial x^2}$ A) Second order, ordinary, nonlinear. B) Second order, ordinary, linear. C) Second order, partial, nonlinear. D) Second order, partial, linear. Show Answer Correct Answer: C) Second order, partial, nonlinear. 5. Find the complete integral of pq=1 . A) I) z=z=ax-(1/a)y+c. B) Ii) z=ax+(1/a)y+c. C) Iii) z=ax+by+c. D) Z=ax+(1/b)y+c. Show Answer Correct Answer: B) Ii) z=ax+(1/a)y+c. 6. If $\overrightarrow{f}=\left(x+3y\right)i+\left(y-2z\right)j+\left(x+az\right)k$ A) -2. B) 2. C) 1. D) -1. Show Answer Correct Answer: A) -2. 7. Solve the following differential equations:$\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$ A) $y=Ax$. B) $y^2=\ln x+C$. C) $\ln y=\frac{x^2}{2}+C$. D) $A=yx$. Show Answer Correct Answer: A) $y=Ax$. 8. If $\frac{dy}{dx} = 4xy$ $y = 1$ $x = 2$ $y =$ A) $e^{2x^2-8}$. B) $2e^{2x^2-8}-1$. C) $4e^{2x^2-8}-3$. D) $8e^{2x^2-8}-7$. Show Answer Correct Answer: A) $e^{2x^2-8}$. 9. What is the result of eliminating arbitrary functions in solving PDEs? A) A general solution with no arbitrary functions. B) A solution with a specific boundary condition. C) A solution with a specific initial condition. D) A particular solution with no arbitrary functions. Show Answer Correct Answer: D) A particular solution with no arbitrary functions. 10. If R(x) is an increasing function, then a Right Hand Riemann sum will be an ..... A) Underapproximation. B) Overapproximation. C) All the above. D) None of the above. Show Answer Correct Answer: B) Overapproximation. 11. Consider the differential equation $\frac{dy}{dx}=y\sec^2x$ $y=f\left(x\right)$ $y\left(0\right)=5$ A) $\tan x+5e^x$. B) $5e^{\tan x}$. C) $\tan x+5$. D) $e^{\tan x}+4$. Show Answer Correct Answer: B) $5e^{\tan x}$. 12. Z-transform is linear A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 13. The C.F. of the equation $\left(D^2-9\right)y=e^{-3x}+1+e^{3x}$ A) $c_1e^{-3x}+c_2e^{-x}$. B) $c_1e^{3x}+c_2e^{3x}$. C) $c_1e^{3x}+c_2e^{-x}$. D) $c_1e^{3x}+c_2e^{-3x}$. Show Answer Correct Answer: D) $c_1e^{3x}+c_2e^{-3x}$. 14. $.$ $\left(D^3+D^2D'+DD'^2+D'^3\right)Z=0$ A) $1$. B) $0$. C) $e^x$. D) $none$. Show Answer Correct Answer: B) $0$. 15. Find the general solution of the differential equation dy/dx=3y/7x. A) $y^{\frac{1}{3}}=Cx^{\frac{1}{7}}$. B) $y^3=Cx^7$. C) $y=Cx^{\frac{1}{7}}$. D) $y^{\frac{1}{7}}=Cx^3$. E) $y^7=Cx^{\frac{1}{3}}$. Show Answer Correct Answer: A) $y^{\frac{1}{3}}=Cx^{\frac{1}{7}}$. 16. Determine the general solution of $y"-2y'+y=0$ A) $y=C_1e^x+C_2xe^x$. B) $y=C_1e^x+C_2e^x$. C) $y=e^x\left(C_1\cos x+C_2\sin x\right)$. D) $y=C_1e^x+C_2xe^{-x}$. Show Answer Correct Answer: A) $y=C_1e^x+C_2xe^x$. 17. The partial derivative of y(1+xy)dx +(2y-x)dy with respect to y is A) 2xy + 1. B) 2xy-1. C) 1. D) -1. Show Answer Correct Answer: A) 2xy + 1. 18. A vector $\overrightarrow{f}$ $curl\\overrightarrow{f}=0$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 19. Which of the following statements is true regarding Lagrange's equation? A) It can only be applied to nonlinear first-order PDEs. B) It can only be applied to linear first-order PDEs. C) It is only applicable for specific boundary conditions. D) It can be applied to any first-order PDE. Show Answer Correct Answer: B) It can only be applied to linear first-order PDEs. 20. (D$^{2}$+1)y=cosx has ..... A) Particular integral alone as general solution. B) Complementary function alone as general solution. C) No solution. D) Complementary function + particular integral as general solution. Show Answer Correct Answer: D) Complementary function + particular integral as general solution. 21. An equation is non-linear if the coefficients depend at most on the "independent" variables A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 22. Determine whether the functions $y_{1} = e^{4x}$ $y_{2} = e^{3x}$ A) Yes, they are linearly independent. B) No, they are linearly dependent. C) They are orthogonal. D) Not defined. Show Answer Correct Answer: A) Yes, they are linearly independent. 23. A differential equation mainly describes ..... A) A formula for a function. B) A numerical value. C) A relationship between a function and its rate(s) of change. D) A table of data. Show Answer Correct Answer: C) A relationship between a function and its rate(s) of change. 24. In order to solve the partial dierential equation p-x=q-y, the correctoption is ..... A) Dz=(k+x)dx+(k+y)dy. B) Dz=(k+x)dx-(k+y)dy. C) Dz=(k-x)dx+(k-y)dy. D) Dz=(k-x)dx-(k-y)dy. Show Answer Correct Answer: A) Dz=(k+x)dx+(k+y)dy. 25. Page 393 #23 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: B) B. ← PreviousNext →Related QuizzesClass 12 Mathematics Chapter 9 Differential Equations Quiz 1Class 12 Mathematics Chapter 9 Differential Equations Quiz 2Class 12 Mathematics Chapter 9 Differential Equations Quiz 3Class 12 Mathematics Chapter 9 Differential Equations Quiz 4Class 12 Mathematics Chapter 9 Differential Equations Quiz 5Class 12 Mathematics Chapter 9 Differential Equations Quiz 6Class 12 Mathematics Chapter 9 Differential Equations Quiz 7Class 12 Mathematics Chapter 9 Differential Equations Quiz 8Class 12 Mathematics Chapter 9 Differential Equations Quiz 9Class 12 Mathematics Chapter 9 Differential Equations Quiz 10 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books