This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 22 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 22 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the degree of the differential equation:$\left(\frac{d^3y}{dx^3}\right)^2 + 5y = 0$ A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: B) 2. 2. The general solution of $y'(t)-6y(t) = 12$ A) $y = Ce^{-6t} + 12$. B) $y = e^{6t} + C$. C) $y = Ce^{6t}-2$. D) None of the above. Show Answer Correct Answer: C) $y = Ce^{6t}-2$. 3. In IVPs, uniqueness of solutions is guaranteed if: A) Equation is linear. B) Coefficients are continuous. C) Both A & B. D) None. Show Answer Correct Answer: C) Both A & B. 4. Analyze the stability of the equilibrium solution $y = 0$ $\frac{dy}{dt} = y^2-4$ A) Stable. B) Unstable. C) Semi-stable. D) Cannot be determined. Show Answer Correct Answer: B) Unstable. 5. Which subject is the best? A) Math. B) Math. C) Math. D) C'mon, u don't like it. Show Answer Correct Answer: D) C'mon, u don't like it. 6. A population is modeled by a function P that satisfies the logistic differential equation $\frac{dp}{dt}=2P\left(1-\frac{P}{90}\right), $ A) 30. B) 45. C) 55. D) 90. Show Answer Correct Answer: B) 45. 7. The set $S=\left\{1, x+x^2, 4x^2\right\}$ A) Linearly independent. B) Linearly dependent. C) All the above. D) None of the above. Show Answer Correct Answer: A) Linearly independent. 8. Part B. Find the particular solution under the given conditions:11. y" -3y' + 2y = 0, y(0) = 4, y'(0) = 2 A) $y = 2e^{x} + 2e^{2x}$. B) $y = 4e^{x} + 2e^{2x}$. C) Y = $2e^{x} + 4e^{2x}$. D) $y = 4e^{x} + 4e^{2x}$. Show Answer Correct Answer: A) $y = 2e^{x} + 2e^{2x}$. 9. The governing differential equation for charge qin a series LCR circuit is: A) Ld2qdt2+Rq+1Cq=E(t). B) Ldqdt+Rq+1Cq=E(t). C) Ld2qdt2+Rdqdt+1Cq=E(t). D) D2qdt2+Rq=E(t). Show Answer Correct Answer: A) Ld2qdt2+Rq+1Cq=E(t). 10. What is the order and degree of the equation $(\frac{\text{d}y}{\text{d}x})^2+y=0$ A) 3, 2. B) 2, 1. C) 1, 2. D) 4, 1. Show Answer Correct Answer: C) 1, 2. 11. Dim M$_{4x3}$(R) is A) 12. B) 43. C) 64. D) 81. Show Answer Correct Answer: A) 12. 12. What is the primary use of differential equations? A) To find roots of polynomials. B) To model real-world phenomena. C) To solve algebraic equations. D) To calculate limits. Show Answer Correct Answer: B) To model real-world phenomena. 13. Classify the following differential equation:$\frac{\text{d}^3y}{\text{d}x^3}+y\frac{\text{d}^2y}{\text{d}x^2}=0$ A) Third-order, nonlinear, ordinar. B) Third order, ordinary, linear. C) Second-order, ordinary, nonlinear. D) Third-order, partial, linear. Show Answer Correct Answer: A) Third-order, nonlinear, ordinar. 14. Find the solution for $\cos x\\frac{\text{d}y}{\text{d}x}+y\sin x=e^x\cos^2x$ $x=0$ $y=2$ A) $y=\left(e^x+A\right)\cos x$. B) $y=\cos x\left(1+e^x\right)$. C) $y=-e^x\left(2\tan x+1\right)$. D) None of the above. Show Answer Correct Answer: B) $y=\cos x\left(1+e^x\right)$. 15. What type of differential equations can be solved using the method of variation of parameters? A) First order linear. B) Nonlinear. C) Higher order linear with constant coefficients. D) Partial differential equations. Show Answer Correct Answer: B) Nonlinear. 16. Identify the type of differential equation:y' + 2xy = 0 A) Quadratic. B) Linear. C) Trigonometric. D) Exponential. Show Answer Correct Answer: B) Linear. 17. If Dim V=4, and if $S=\left\{v_1, v_2, v_3\right\}\subseteq V$ A) $L\left(S\right)=V$. B) $L\left(S\right)\subseteq V$. C) $\dim(L(S))=3$. D) None of the others. Show Answer Correct Answer: B) $L\left(S\right)\subseteq V$. 18. Page 397 #39 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: B) B. 19. If the initial conditions are y(0) = 1, the solution of y ''+y=0 is A) Y = cos x. B) Y = sin x. C) Y = 1 + x. D) Y = ex. Show Answer Correct Answer: A) Y = cos x. 20. Which of the following equations is partial differential equation? A) $\frac{dy}{dt}+y=e^t$. B) $\frac{d^2y}{ds^2}+\frac{dy}{ds}+y=2s$. C) $u_{xx}+u_t=0$. D) $P_{tt}+P_t=t^2$. Show Answer Correct Answer: C) $u_{xx}+u_t=0$. 21. The value of a car is $ 15, 000 and depreciates at a rate of 8% per year. What is the decay factor? A) $^{.08}$. B) $^{1.08}$. C) .92. D) 8. Show Answer Correct Answer: C) .92. 22. What are the characteristic roots of Cauchy's and Euler's equations? A) Real and distinct. B) Complex conjugate. C) Repeated real. D) Imaginary. Show Answer Correct Answer: C) Repeated real. 23. L$^{-1 }$\{b/(s$^{2}$+b$^{2}$)\} A) E$^{at }$sin bt. B) E$^{at }$cos bt. C) Sin bt. D) T$^{n }$e$^{at}$. E) Cos bt. Show Answer Correct Answer: C) Sin bt. 24. What notation is used to represent the derivative in the separation of variables? A) Euler's notation. B) Leibniz notation. C) Lagrange's notation. D) Newton's notation. Show Answer Correct Answer: B) Leibniz notation. 25. Why is the formation of partial differential equations important in the field of mathematics? A) To make simple systems more complicated. B) To confuse students studying mathematics. C) To have a better understanding of basic arithmetic. D) To describe the behavior of complex systems in physics, engineering, and other scientific fields. Show Answer Correct Answer: D) To describe the behavior of complex systems in physics, engineering, and other scientific fields. ← 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