This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 6 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 6 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The solution of simultaneous linear differential equations is of the form ..... A) $\Phi\left(u, v\right)=0$. B) $\Phi\left(u\right)=0$. C) $\Phi\left(v\right)=0$. D) $\Phi\left(x, y\right)=0$. Show Answer Correct Answer: A) $\Phi\left(u, v\right)=0$. 2. Which of the following is a method of solution for separable differential equations? A) Method of separation of variables. B) Runge-Kutta method. C) Method of undetermined coefficients. D) Euler's method. Show Answer Correct Answer: A) Method of separation of variables. 3. Find the integrating factor to solve the equation $\frac{dy}{dx}+6y=x^2$ A) $6y$. B) $6x$. C) $e^{7x}$. D) $e^{6x}$. Show Answer Correct Answer: D) $e^{6x}$. 4. Which method is used to solve first-order linear PDEs? A) Method of characteristics. B) Green's function approach. C) Fourier series method. D) Separation of variables. Show Answer Correct Answer: A) Method of characteristics. 5. Find the general solution of the following DE $\frac{dy}{dx}=\frac{2x}{e^{2y}}$ A) $y=\frac{1}{2}\ln\left(2x^2+C\right)$. B) $y=\ln\left(2x^2+C\right)$. C) $y=e^{2x}+C$. D) $y=\frac{1}{2}\ln\left(x^2+C\right)$. Show Answer Correct Answer: A) $y=\frac{1}{2}\ln\left(2x^2+C\right)$. 6. Wave equation is classified as: A) Parabolic PDE. B) Hyperbolic PDE. C) Elliptic PDE. D) Ordinary differential equation. Show Answer Correct Answer: B) Hyperbolic PDE. 7. What is the significance of the Laplace equation? A) The Laplace equation is significant for modeling steady-state phenomena in physics and engineering. B) The Laplace equation is used to calculate the speed of sound in fluids. C) The Laplace equation describes the motion of celestial bodies in space. D) The Laplace equation is essential for analyzing time-dependent processes in thermodynamics. Show Answer Correct Answer: A) The Laplace equation is significant for modeling steady-state phenomena in physics and engineering. 8. Which method is used to solve homogeneous linear differential equations with constant coefficients? A) Method of undetermined coefficients. B) Method of variation of parameters. C) Method of separation of variables. D) Method of Laplace transforms. Show Answer Correct Answer: C) Method of separation of variables. 9. The highest order derivative present in a differential equation determines its: A) Degree. B) Order. C) Homogeneity. D) Type. Show Answer Correct Answer: B) Order. 10. $L\left(xe^{3x}\right)= ..... $ A) $\frac{1}{\left(s-3\right)^2}$. B) $-\\\\frac{1}{\left(s-3\right)^2}$. C) $\frac{1}{\left(s+3\right)^2}$. D) $-\\\frac{1}{\left(s+3\right)^2}$. Show Answer Correct Answer: A) $\frac{1}{\left(s-3\right)^2}$. 11. If a function $f$ $x, $ $a>0, \\b>0, $ $\int_0^af\left(x\right)dx$ $\int_b^{a+b}f\left(x-b\right)dx$ $\int_b^{a+b}f\left(x+b\right)dx$ A) I and II only. B) I and III only. C) II and III only. D) None. Show Answer Correct Answer: A) I and II only. 12. Identify the order and degree of the equation dy/dx + y = sin(x). A) 2, 1. B) 0, 1. C) 1, 1. D) 3, 1. Show Answer Correct Answer: C) 1, 1. 13. If $\frac{dy}{dx}=\frac{x^2}{y}$ $x=0$ $y=4, $ A) $y=\frac{x^3}{3}$. B) $\frac{y^2}{2}=\frac{x^3}{3}$. C) $\frac{y^2}{2}=\frac{x^3}{3}+4$. D) $\frac{y^2}{2}=\frac{x^3}{3}+8$. Show Answer Correct Answer: D) $\frac{y^2}{2}=\frac{x^3}{3}+8$. 14. Clairaut's equation is important because it demonstrates the existence of: A) Singular solutions. B) Particular integrals. C) Complementary functions. D) None. Show Answer Correct Answer: A) Singular solutions. 15. To solve simultaneous equations, we can eliminate variables using: A) Determinants. B) Laplace transforms. C) Substitution or matrix methods. D) Euler's method. Show Answer Correct Answer: C) Substitution or matrix methods. 16. The general solution of a non-homogeneous DE = A) Complementary function. B) Particular solution. C) CF + Particular solution. D) None. Show Answer Correct Answer: C) CF + Particular solution. 17. The following Differential Equation is $x\frac{\text{d}y}{\text{d}x}=yx^2$ A) Separable. B) Non Separable. C) All the above. D) None of the above. Show Answer Correct Answer: A) Separable. 18. Define Zeno behavior in the context of CPS. A) Zeno behavior in CPS is the non-terminating or oscillatory behavior caused by discrete events interacting with continuous dynamics. B) Zeno behavior is a method for optimizing continuous processes. C) Zeno behavior is the phenomenon of continuous systems achieving instant results. D) Zeno behavior refers to the rapid convergence of discrete events. Show Answer Correct Answer: A) Zeno behavior in CPS is the non-terminating or oscillatory behavior caused by discrete events interacting with continuous dynamics. 19. What are the basic types of partial differential equations? A) Elliptic, Parabolic, and Hyperbolic. B) Scalar, Vector, Matrix. C) Linear, Nonlinear, Quadratic. D) Algebraic, Geometric, Trigonometric. Show Answer Correct Answer: A) Elliptic, Parabolic, and Hyperbolic. 20. The velocity of a particle is given by the equation of 8t$^{3}$+9t$^{2}$. If the position at t=0 is 0, find the position of the particle at t=5. Do not use a calculator. A) 1625. B) 1225. C) 715. D) 750. Show Answer Correct Answer: A) 1625. 21. Which of the following is an example for first order linear partial differential equation? A) Lagrange's Partial Differential Equation. B) Clairaut's Partial Differential Equation. C) One-dimensional Wave Equation. D) One-dimensional Heat Equation. Show Answer Correct Answer: A) Lagrange's Partial Differential Equation. 22. Solve the homogeneous equation y" + 2y' + y = 0. A) $y_c=Ae^{-x}+Bxe^{-x}$. B) $y_c=Ae^{-x}+Bxe^x$. C) $y_c=Ae^{-x}+Be^{-x}$. D) $y_c=Ae^x+Bxe^x$. Show Answer Correct Answer: A) $y_c=Ae^{-x}+Bxe^{-x}$. 23. Which of the following function is neither even nor odd? A) $\sin x$. B) $x^2+x$. C) $\cos x$. D) $x^2$. Show Answer Correct Answer: B) $x^2+x$. 24. The sum of a power series is not analytic at the end points inside the interval of convergence. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 25. Solve the initial value problem:$y' = 0.02y + 6$ $y(0) = 100$ $y(t) =$ A) $300e^{0.02t}-200$. B) $200e^{0.02t}$. C) $100e^{0.02t}$. D) $200e^{0.02t}-300$. Show Answer Correct Answer: C) $100e^{0.02t}$. ← 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 7Class 12 Mathematics Chapter 9 Differential Equations Quiz 8Class 12 Mathematics Chapter 9 Differential Equations Quiz 9Class 12 Mathematics Chapter 9 Differential Equations Quiz 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books