This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 39 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 39 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Solve the differential equation(x-y)dy-(x+y)dx=0 A) Tan$^{-1}$(y/x)+(1/2)log|x$^{2}$+y$^{2}$|+c. B) -tan$^{-1}$(y/x)-(1/2)log|x$^{2}$+y$^{2}$|+c. C) Tan$^{-1}$(y/x)-(1/2)log|x$^{2}$+y$^{2}$|+c. D) Tan$^{-1}$(y/x)-(1/3)log|x$^{2}$+y$^{2}$|+c. Show Answer Correct Answer: C) Tan$^{-1}$(y/x)-(1/2)log|x$^{2}$+y$^{2}$|+c. 2. The divergence of a vector valued function is a scalar valued function. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 3. L\{(1/8b$^{4}$)((3-(bt)$^{2}$sin bt-3bt cos bt)\} A) B/(s$^{2}$+b$^{2}$). B) B/(s$^{2}$+b$^{2}$)$^{2}$. C) B/(s$^{2}$+b$^{2}$)$^{3}$. D) B/(s$^{2}$+b$^{2}$)$^{4}$. Show Answer Correct Answer: C) B/(s$^{2}$+b$^{2}$)$^{3}$. 4. A non-exact equation can become exact by: A) Transformation of axes. B) Adding constants. C) Multiplying by integrating factor. D) Changing variables arbitrarily. Show Answer Correct Answer: C) Multiplying by integrating factor. 5. Dy/dx=0.04y(3-y/120). What is the carrying capacity of the population? A) 0.04. B) 3. C) 120. D) 360. Show Answer Correct Answer: D) 360. 6. If the auxiliary equation has complex roots, the complementary function involves: A) Exponential and trigonometric terms together. B) Polynomials only. C) Arbitrary constants. D) None. Show Answer Correct Answer: A) Exponential and trigonometric terms together. 7. Find the particular solution to the equation dy/dx = 4x/y, with the initial condition y(2) =-2? A) $y=2x-6$. B) $y=\sqrt[]{4x^2-12}$. C) $y=-\sqrt[]{4x^2-6}$. D) $y=-\sqrt[]{4x^2-12}$. Show Answer Correct Answer: D) $y=-\sqrt[]{4x^2-12}$. 8. Dy/dy=.04y(1-y/100). At what value of y is population increasing the fastest? A) 100. B) 50. C) .04. D) Cannot be determined. Show Answer Correct Answer: B) 50. 9. The equation \( u ..... \{xy\} + u ..... \{x\} = 0 \) is classified as: A) First-order linear equation. B) First-order partial differential equation. C) Second-order partial differential equation. D) Second-order ordinary differential equation. Show Answer Correct Answer: B) First-order partial differential equation. 10. Which of the following are vector spaces under usual addition and scalar multiplication? A) M$_{2}$(R) over R. B) Q over R. C) Z over R. D) R over C. Show Answer Correct Answer: A) M$_{2}$(R) over R. 11. If the number of constants to be eliminated is equal to number of independent variables, then the result is ..... A) First order PDE. B) Second order PDE. C) Third order PDE. D) Second order linear PDE. Show Answer Correct Answer: A) First order PDE. 12. Provide an example of a physical phenomenon modeled by a PDE. A) Heat conduction in a solid, modeled by the heat equation. B) Population dynamics in ecology, modeled by the Laplace equation. C) Fluid flow in a pipe, modeled by the wave equation. D) Electromagnetic waves in a vacuum, modeled by the diffusion equation. Show Answer Correct Answer: A) Heat conduction in a solid, modeled by the heat equation. 13. $\frac{dy}{dx}-\frac{1}{\left(\pi-1\right)x}y=\frac{3}{1-\pi}xy^{\pi}$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: C) Bernoulli. 14. Form a PDE by eliminating arbitrary constants from z= a(x+y) + b A) P+q=0. B) Px = qy. C) Qx = py. D) P-q=0. Show Answer Correct Answer: D) P-q=0. 15. Page 392 #14 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: C) C. 16. A solution containing as many arbitrary constants as there are independent variables is called ..... A) Complete integral. B) Particular integral. C) Singular integral. D) General integral. Show Answer Correct Answer: A) Complete integral. 17. Verify that $y(x) = e^{-2x}$ $y" + 4y' + 4y = 0$ A) Yes, it is a solution. B) No, it is not a solution. C) Only for $x = 0$. D) Only for $x = 1$. Show Answer Correct Answer: A) Yes, it is a solution. 18. How is a constant treated when it is raised to the power of e in the context of solving differential equations? A) As an exponent. B) As an unknown variable. C) As a coefficient. D) As a new variable. Show Answer Correct Answer: C) As a coefficient. 19. Solve the partial differential equation $\frac{\partial z}{\partial x}=3.$ A) Z=3y+f(x). B) Z=3+f(y). C) Z=3x+f(y). D) Z=3+f(x). Show Answer Correct Answer: C) Z=3x+f(y). 20. Which method is most commonly used to solve PDEs with boundary conditions? A) Taylor's series. B) Separation of variables. C) Runge-Kutta. D) Newton-Raphson. Show Answer Correct Answer: B) Separation of variables. 21. A curve has a slope of 2x + 3 at each point (x, y) on the curve. Which of the following is an equation for this curve if it passes through the point (1, 2)? A) $y=x^2+3x$. B) $y=x^2+1$. C) $y=x^2+3x-2$. D) $y=x^2+3x-3$. Show Answer Correct Answer: C) $y=x^2+3x-2$. 22. The general solution of the differential equation $\frac{\text{d}y}{\text{d}x}+y=2e^{-x}$ A) $y=e^{-x}\left(A+2x\right)$. B) $y=Ae^{-x}+2e^{-x}$. C) $y=Ae^x+2xe^{-x}$. D) $y=Ae^{-x}+Bxe^{-x}$. Show Answer Correct Answer: A) $y=e^{-x}\left(A+2x\right)$. 23. $x^2\frac{\text{d}^2x}{\text{d}y^2}-5y=x+1$ A) TRUE. B) FALSE. C) All the above. D) None of the above. Show Answer Correct Answer: B) FALSE. 24. Jelaskan signifikansi Wronskian dalam konteks persamaan homogen. A) Wronskian membantu menentukan ketergantungan linier solusi untuk persamaan homogen. B) Wronskian menunjukkan jumlah solusi untuk persamaan diferensial. C) Wronskian mengukur konvergensi solusi deret. D) Wronskian digunakan untuk menyelesaikan persamaan non-homogen. Show Answer Correct Answer: A) Wronskian membantu menentukan ketergantungan linier solusi untuk persamaan homogen. 25. Variation of parameters requires solving for: A) One variable. B) Two functions of the independent variable. C) Constant coefficients. D) No additional unknowns. Show Answer Correct Answer: B) Two functions of the independent variable. ← 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