This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 10 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 10 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which of the following is a general form of a second order homogeneous differential equation with constant coefficients? A) $y" + p(x)y' + q(x)y = 0$. B) $y" + ay' + by = 0$. C) $y" + y' + y = f(x)$. D) $y" + ay' + by = f(x)$. Show Answer Correct Answer: B) $y" + ay' + by = 0$. 2. The ends A and B of a rod of length10cm are at 30$^{0}$C and 80$^{0}$C at end points until steady state prevails. Then Initial temperature distribution in the rod A) 10+(5x)/2. B) 30+(5x)/2. C) 30+5x. D) None of these. Show Answer Correct Answer: C) 30+5x. 3. An antiderivative of $\dfrac{1}{x}$ A) $x^{-1}$. B) $e^x$. C) $\ln|x|$. D) $x$. Show Answer Correct Answer: C) $\ln|x|$. 4. What is the characteristic equation / auxiliary equation for $4\frac{\text{d}^2y}{\text{d}x^2}+3\frac{dy}{dx}=0$ A) $4\lambda^2+3\lambda=0$. B) $4\lambda^2+3=0$. C) $\lambda^2+3\lambda=0$. D) None of the above. Show Answer Correct Answer: A) $4\lambda^2+3\lambda=0$. 5. In growth/decay, the sign of k determines: A) Solution type only. B) Whether solution increases or decreases. C) The initial value. D) The domain of solution. Show Answer Correct Answer: B) Whether solution increases or decreases. 6. How many independent variables of an ordinary differential equation? A) Two variables. B) One variable. C) Many variable. D) More than one variable. Show Answer Correct Answer: B) One variable. 7. Determine the order of the differential equation:$\frac{d^5y}{dx^5} + \left(\frac{d^2y}{dx^2}\right)^3 + y = 0$ A) 5. B) 4. C) 3. D) 2. Show Answer Correct Answer: A) 5. 8. $L\left(x^n\right)$ A) $\frac{n!}{s+1}$. B) $\frac{n}{s^n+1}$. C) $\frac{n!}{s^n-1}$. D) $\frac{n!}{s^n+1}$. Show Answer Correct Answer: D) $\frac{n!}{s^n+1}$. 9. Which of the following is an equilibrium solution for the differential equation $\frac{dy}{dt} = y^3-3y$ A) $y = 0$. B) $y = 1$. C) $y =-1$. D) $y = \sqrt{3}$. Show Answer Correct Answer: A) $y = 0$. 10. Find the complementary function of $\left(D^3-3D^2D'+2DD^{'2}\right)Z=0$ A) $Z=f_1\left(y\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. B) $Z=f_1\left(y-x\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. C) $Z=f_1\left(y\right)+xf_2\left(y+x\right)+f_3\left(y+2x\right)$. D) $Z=f_1\left(y\right)+f_2\left(y-x\right)+f_3\left(y-2x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. 11. Can you give an example of a partial differential equation? A) The Pythagorean theorem. B) The law of gravity. C) The quadratic equation. D) The heat equation. Show Answer Correct Answer: D) The heat equation. 12. A PDE consists of A) Only one independent variable. B) More than one independent variable. C) More than one dependent varible. D) None of the above. Show Answer Correct Answer: B) More than one independent variable. 13. For $y" +y=\sin x$ A) $Ax\cos x$. B) $12x\cos x$. C) $A\sin x$. D) $12x\sin x$. Show Answer Correct Answer: B) $12x\cos x$. 14. Evaluate the definite integral \( \int ..... 0^1 (3x^2 + 2) \, dx \). A) 3. B) 5. C) 2. D) 4. Show Answer Correct Answer: A) 3. 15. Which differential equation has the solution $y=\sin x$ A) $y+y" =0$. B) $y-y" =0$. C) $y+y'-y" =0$. D) $y-y'+y" =0$. Show Answer Correct Answer: A) $y+y" =0$. 16. A particular solution for $y" +y=1$ A) 1. B) -1. C) Constant = 0. D) None. Show Answer Correct Answer: A) 1. 17. If $\overrightarrow{f}=xyi+yzj+zxk$ $curl\\overrightarrow{f}$ A) Yi+zj+xk. B) Xi+yj+zk. C) Yi+zj-xk. D) -yi-zj-xk. Show Answer Correct Answer: D) -yi-zj-xk. 18. What is the Eigen value of Upper triangular matrix of A= [ 2 3 6 0 1 8 0 0 3] A) 1, 2, 3. B) 1, 2, 1. C) 1, 1, 1. D) None of the above. Show Answer Correct Answer: A) 1, 2, 3. 19. A partial differential equation requires A) Exactly one independent variable. B) Two or more independent variables. C) More than one dependent variable. D) Equal number of dependent and independent variables. Show Answer Correct Answer: B) Two or more independent variables. 20. If D2+1y=11+Sinx, then the value of the Wronskin W = A) 2. B) -1. C) 1. D) 0. Show Answer Correct Answer: C) 1. 21. Dy/dx = x-y and y(0) = 1. Use Euler's Method with a step size of 0.5 to approximate y(1.5). A) 0.5. B) 0.8. C) 0.75. D) 1.25. Show Answer Correct Answer: C) 0.75. 22. What is the main method used to solve partial differential equations? A) Finite element method. B) Boundary element method. C) Method of characteristics. D) Finite difference method. Show Answer Correct Answer: D) Finite difference method. 23. Find the Integrating factor of the differential equation $x\frac{\text{d}y}{\text{d}x}-y=\sin x$ A) $-\frac{1}{x}$. B) $\frac{1}{x}$. C) $\ln\left|x\right|$. D) $\frac{1}{x^2}$. Show Answer Correct Answer: B) $\frac{1}{x}$. 24. Part B. Find the particular solution under the given conditions:12. y" +2y'-8y=0, y(0)=1, y'(0)=0 A) Y = $\frac{2}{3}e^{2x}+\frac{1}{3}e^{-4x}$. B) $y=2e^{2x}-4e^{-4x}$. C) $y=e^{2x}+e^{-4x}$. D) $y=e^{2x}-e^{-4x}$. Show Answer Correct Answer: A) Y = $\frac{2}{3}e^{2x}+\frac{1}{3}e^{-4x}$. 25. Find the Particular Integral of (D$^{2}$ +4DD'-4D'$^{2}$ )z = cos(x+y) A) $-\cos\left(x+y\right)$. B) $\frac{\cos\left(x+y\right)}{2}$. C) $\cos\left(x-y\right)$. D) $\frac{\cos\left(x+y\right)}{-2}$. Show Answer Correct Answer: A) $-\cos\left(x+y\right)$. ← 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 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books