This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 45 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 45 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Classify the PDE:u ..... t + a u ..... x = 0. A) Parabolic. B) Hyperbolic. C) Linear. D) Elliptic. Show Answer Correct Answer: B) Hyperbolic. 2. It pertains to the highest order of the derivative that appears in the differential equation. A) Differential Equation. B) Order. C) Solution. D) Separable. Show Answer Correct Answer: B) Order. 3. What is the general solution to $y" + 9y = 0$ A) $y(x) = Ce^{3x} + De^{-3x}$. B) $y(x) = C\sin(3x) + D\cos(3x)$. C) $y(x) = Ce^{3ix} + De^{-3ix}$. D) $y(x) = Cx^3 + Dx^9$. Show Answer Correct Answer: B) $y(x) = C\sin(3x) + D\cos(3x)$. 4. Which of the following is NOT a solution to $y" + y = 0$ A) $y(x) = \sin(x)$. B) $y(x) =\cos(x)$. C) $y(x) = e^{ix}$. D) $y(x) = e^{x}$. Show Answer Correct Answer: D) $y(x) = e^{x}$. 5. What type of differential equations are discussed in the text? A) First-order linear differential equations. B) Second-order linear differential equations. C) Non-linear differential equations. D) Partial differential equations. Show Answer Correct Answer: B) Second-order linear differential equations. 6. Which of the following initial value problems can be solved using Euler's Method? A) $\frac{dy}{dx} = x^2$ $y(0) = 1$. B) $y = x^2 + 1$. C) $x^2 + y^2 = 1$. D) $y = 2x + 3$. Show Answer Correct Answer: A) $\frac{dy}{dx} = x^2$ $y(0) = 1$. 7. What is the role of simulation in CPS modeling? A) Simulation is only used for visual representation of CPS models. B) Simulation has no impact on the performance of CPS models. C) Simulation is primarily for aesthetic purposes in CPS modeling. D) Simulation enables testing, validation, and optimization of CPS models. Show Answer Correct Answer: D) Simulation enables testing, validation, and optimization of CPS models. 8. 5y" +7y'+3y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: A) UNDERDAMPED. 9. What are the Lagrange's multipliers while solving the PDE $p\left(y-z\right)-q\left(2x+y\right)=2x+z$ A) $x, y, z$. B) $2x, y, z$. C) $x, -2y, z$. D) $2x, -z, -y$. Show Answer Correct Answer: D) $2x, -z, -y$. 10. $\frac{dy}{dt}=\frac{4t}{y}$ $y\left(0\right)=1$ A) An initial value problem. B) A boundary value problem. C) All the above. D) None of the above. Show Answer Correct Answer: A) An initial value problem. 11. The general solution of a nonhomogeneous differential equation is A) CF-PI. B) CF alone. C) CF + PI. D) PI alone. Show Answer Correct Answer: C) CF + PI. 12. If R(x) is an increasing concave down function, then a Trapezoidal Riemann sum will be an ..... A) Underapproximation. B) Overapproximation. C) All the above. D) None of the above. Show Answer Correct Answer: A) Underapproximation. 13. Which method is commonly used to solve second order homogeneous differential equations with constant coefficients? A) Separation of variables. B) Integrating factor. C) Characteristic equation. D) Variation of parameters. Show Answer Correct Answer: C) Characteristic equation. 14. If R(x) is an increasing function, then a Left Hand Riemann sum will be an ..... A) Underapproximation. B) Overapproximation. C) All the above. D) None of the above. Show Answer Correct Answer: A) Underapproximation. 15. Degree of $\left[1+\left(\frac{\text{d}y}{\text{d}x}\right)^2\right]^3=\left(\frac{\text{d}^2y}{\text{d}x^2}\right)^2$ A) 6. B) 2. C) 3. D) 4. Show Answer Correct Answer: B) 2. 16. Which of the following is a limitation of the Variation of Parameters method? A) It cannot be applied to equations with constant coefficients. B) It cannot be applied when the Wronskian is zero. C) It cannot be applied to second-order differential equations. D) It requires the forcing function f(x) to be a polynomial. Show Answer Correct Answer: B) It cannot be applied when the Wronskian is zero. 17. The roots of the auxiliary equation help in determining the: A) Complementary function. B) Particular integral. C) Singular solution. D) None. Show Answer Correct Answer: A) Complementary function. 18. Determine the order of the following equation $5\left(\frac{\text{d}^4x}{\text{d}y^4}\right)^3+7\left(\frac{\text{d}x}{\text{d}y}\right)^{10}+y=x$ A) 10. B) 7. C) 12. D) 4. Show Answer Correct Answer: D) 4. 19. Solves this following DE by using Separable Variable Method $y^5\frac{\text{d}y}{\text{d}x}=e^x$ A) $y^6=e^x+c$. B) $\frac{y^6}{6}=e^x+c$. C) $y^5=\frac{e^x}{x}+c$. D) $\frac{y^6}{5}=xe^x+c$. Show Answer Correct Answer: B) $\frac{y^6}{6}=e^x+c$. 20. $\frac{dy}{dx}=\frac{x^3}{y}$ A) $y=\sqrt{x^4+50}$. B) $y=\frac{x^4+50}{2}$. C) $y=\sqrt{\frac{x^4+50}{2}}$. D) None of the above. Show Answer Correct Answer: C) $y=\sqrt{\frac{x^4+50}{2}}$. 21. Clairaut's form is a special case of equations solvable for: A) Y. B) X. C) Dy/dx. D) None. Show Answer Correct Answer: C) Dy/dx. 22. Which of the following situations do not require differential equations? A) Concentration of pollutant. B) Amount of cement in concrete. C) Multi-storey building subjected to earthquake. D) Velocity of a vehicle. Show Answer Correct Answer: B) Amount of cement in concrete. 23. $\frac{1}{y}dy=\left(2-x\right)dx$ A) $\ln\left(y\right)=x-x^2+C$. B) $\ln\left|y\right|=2x-\frac{1}{2}x^2+C$. C) $-\frac{1}{2}y^{-2}=x-\frac{1}{2}x^2+C$. D) $\ln\left|y\right|=\frac{1}{2}x^2-2x+C$. Show Answer Correct Answer: B) $\ln\left|y\right|=2x-\frac{1}{2}x^2+C$. 24. Find the general solution. $\frac{dy}{dx}=\frac{x+3}{y}$ A) $y=\sqrt[]{2x^2+6x+C}$. B) $y=\ln\left(x^2+3x+C\right)$. C) $y=\sqrt[]{x^2+6x+C}$. D) $y=Ce^{\left(x^2+3x\right)}$. Show Answer Correct Answer: C) $y=\sqrt[]{x^2+6x+C}$. 25. Average rate of change is ..... A) $\frac{1}{b-a}\int_a^bf\left(x\right)dx$. B) $\frac{f\left(b\right)-f\left(a\right)}{b-a}$. C) $\int_a^bf\left(x\right)dx$. D) $y-y_1=m\left(x-x_1\right)$. Show Answer Correct Answer: B) $\frac{f\left(b\right)-f\left(a\right)}{b-a}$. ← 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