This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 15 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 15 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Eliminate the arbitrary constants c and r from x$^{2}$+y$^{2}$+(z-c)$^{2}$=r$^{2}$ A) Px = qy. B) Px+qy=0. C) Py = qx. D) Py+qx=0. Show Answer Correct Answer: C) Py = qx. 2. Which of the following is a solution to the differential equation y" + y = 0? A) Y = ln(x). B) $y = e^x$. C) Y = x. D) Y = sin(x). Show Answer Correct Answer: D) Y = sin(x). 3. If $\frac{dP}{dt} = P-3$ A) $e^{t-4} + 1$. B) $e^{t-4}-1$. C) $-e^{t-4} + 3$. D) $-e^{t-4}-3$. Show Answer Correct Answer: C) $-e^{t-4} + 3$. 4. Which of the following represents a condition for the existence of a unique solution in simultaneous equations? A) Determinant of coefficients is zero. B) Determinant of coefficients is non-zero. C) Sum of ratios equals one. D) All variables are equal. Show Answer Correct Answer: B) Determinant of coefficients is non-zero. 5. Find the degree of the differential equation:$\left(\frac{d^4y}{dx^4}\right)^3 + 2\left(\frac{d^2y}{dx^2}\right)^2-y = 0$ A) 4. B) 3. C) 2. D) 1. Show Answer Correct Answer: B) 3. 6. The Wronskian of two solutions of a 2x2 linear systems is? A) Always zero. B) Always constant. C) Nonzero if solutions are linearly independent. D) Equal to determinant of A. Show Answer Correct Answer: C) Nonzero if solutions are linearly independent. 7. Find particular integral of (D$^{2}$+D'$^{2}$)z=x$^{2}$+y$^{2}$ A) PI=y$^{2}$/2. B) PI=x$^{2}$y$^{2}$/4. C) PI=x$^{2}$y$^{2}$/2. D) PI=x$^{2}$/4. Show Answer Correct Answer: C) PI=x$^{2}$y$^{2}$/2. 8. Identify the order of the differential equation:$\sin\left(\frac{d^2y}{dx^2}\right) +\cos\left(\frac{dy}{dx}\right) = 0$ A) 0. B) 1. C) 2. D) 3. Show Answer Correct Answer: C) 2. 9. If $\frac{dy}{dx} = 4y$ $y(0) = 2$ A) $y = 2e^{4x}$. B) $y = 4e^{2x}$. C) $y = 2e^{x}$. D) $y = 4e^{x}$. Show Answer Correct Answer: A) $y = 2e^{4x}$. 10. Find the particular solution W = W(t) to the differential equation $\frac{dW}{dt}=\frac{1}{25}\left(W-300\right)$ A) $W\left(t\right)=300+1100e^{\frac{1}{25}t}$. B) $W\left(t\right)=300+\frac{1}{25}e^{1100t}$. C) $W\left(t\right)=1100+300e^{\frac{1}{25}t}$. D) $W\left(t\right)=300t+1100e^{\frac{1}{25}}$. Show Answer Correct Answer: A) $W\left(t\right)=300+1100e^{\frac{1}{25}t}$. 11. A population of fish starts at 8, 000 and decreases by 6% per year. What is the population of fish after 10 years? A) 14327. B) 4309. C) 839. D) 7680. Show Answer Correct Answer: B) 4309. 12. In which quadrant(s) is the differential equation $\frac{dy}{dx} = \frac{xy^2}{e^y}$ A) Quadrants I and II only. B) Quadrants II and III only. C) Quadrants I and III only. D) Quadrants II, III, and IV only. Show Answer Correct Answer: B) Quadrants II and III only. 13. In the method of undetermined coefficients, what is the first step to find the particular solution? A) Guess a form for the particular solution based on f(t). B) Solve the characteristic equation. C) Substitute the complementary function into the original equation. D) Differentiate the non-homogeneous term. Show Answer Correct Answer: A) Guess a form for the particular solution based on f(t). 14. Name the method used to solve first order linear ODEs? A) Separation of variables only. B) Integrating factor method. C) Variation of parameters. D) Laplace transform. Show Answer Correct Answer: B) Integrating factor method. 15. The matrix exponential is defined as ..... A) $e^A = det(|A|)$. B) $e^A = I + A$. C) $e^A = \Sigma_{n=0}^{\infty} \left(\frac{A^n}{n!}\right)$. D) $e^A = A^t$. Show Answer Correct Answer: C) $e^A = \Sigma_{n=0}^{\infty} \left(\frac{A^n}{n!}\right)$. 16. If $\overrightarrow{f}=\left(x^2+y^2\right)\overrightarrow{i}+\left(x^2-y^2\right)\overrightarrow{j}$ $\int_Cf.d\overrightarrow{r}$ $y=x^2$ A) 0. B) 9/10. C) 7/10. D) 2. Show Answer Correct Answer: C) 7/10. 17. If $\nabla\phi$ $\nabla^2\phi=$ A) 0. B) 2. C) 1. D) -1. Show Answer Correct Answer: A) 0. 18. If the gradient of a curve is given as $\frac{1}{x^2y}$ $\left(2, 3\right)$ A) $y=\sqrt{\frac{10x-2}{x}}$. B) $y=\sqrt{9-\ln16-\frac{2}{x}}$. C) $y=\sqrt{-\frac{1}{x}+\frac{19}{2}}$. D) None of the above. Show Answer Correct Answer: A) $y=\sqrt{\frac{10x-2}{x}}$. 19. The solution of non-linear partial differential equation $q-p+x-y=0$ A) $z=\frac{\left(x-a\right)^2}{2}+\frac{\left(y-a\right)^2}{2}+c$. B) $z=\left(x+a\right)^2+\left(y+a\right)^2+c$. C) $z=\frac{\left(x+a\right)^2}{2}+\frac{\left(y-a\right)^2}{2}+c$. D) $z=\frac{\left(x-a\right)^2}{2}+\frac{\left(y+a\right)^2}{2}+c$. Show Answer Correct Answer: A) $z=\frac{\left(x-a\right)^2}{2}+\frac{\left(y-a\right)^2}{2}+c$. 20. In the context of differential equations, what does exponentiating both sides of an equation solve for? A) The constant of integration. B) The variable y. C) The integral of x. D) The derivative dy/dx. Show Answer Correct Answer: B) The variable y. 21. What are the multiples while solving $\left(3z-4y\right)p+\left(4x-2z\right)q=2y-3x$ A) $2, 3, 4$. B) $3, 4, 2$. C) $4, 2, 3$. D) $1, 1, 1$. Show Answer Correct Answer: A) $2, 3, 4$. 22. What is the role of initial conditions in solving partial differential equations? A) Initial conditions are only necessary for linear partial differential equations. B) Initial conditions have no role in solving partial differential equations. C) Initial conditions only apply to ordinary differential equations. D) Initial conditions specify the values of the unknown function and its derivatives at a given point in the domain. Show Answer Correct Answer: D) Initial conditions specify the values of the unknown function and its derivatives at a given point in the domain. 23. Modified Euler's method gives better accuracy than: A) Taylor method. B) Euler method. C) Runge-Kutta method. D) Milne's method. Show Answer Correct Answer: B) Euler method. 24. Lagrange's Auxiliary equation is A) $\frac{\text{d}x}{\text{P}}=\frac{\text{d}z}{\text{Q}}=\frac{\text{d}y}{\text{R}}$. B) $\frac{\text{d}x}{\text{P}}=\frac{\text{d}y}{\text{Q}}$. C) $\frac{\text{d}x}{\text{P}}=\frac{\text{d}y}{\text{Q}}=\frac{\text{d}z}{\text{R}}$. D) None. Show Answer Correct Answer: C) $\frac{\text{d}x}{\text{P}}=\frac{\text{d}y}{\text{Q}}=\frac{\text{d}z}{\text{R}}$. 25. The subsidiary equation for Lagrange's linear equation A) $\frac{dx}{x}=\frac{dy}{y}=\frac{dz}{z}$. B) $\frac{dx}{p}=\frac{dy}{q}=\frac{dz}{r}$ $\frac{dx}{p}=\frac{dy}{q}=\frac{dz}{r}$. C) $\frac{dx}{P}=\frac{dy}{Q}=\frac{dz}{R}$. D) None of the above. Show Answer Correct Answer: C) $\frac{dx}{P}=\frac{dy}{Q}=\frac{dz}{R}$. ← 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