This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 13 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 13 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What type of differential equations can be solved using the method of separation of variables? A) Second order linear. B) Nonlinear. C) First order linear with constant coefficients. D) Partial differential equations. Show Answer Correct Answer: C) First order linear with constant coefficients. 2. Solve the differential equation. $\frac{dy}{dx}=y^2$ A) $-\frac{1}{y}=x+C$. B) $y=x+C$. C) $y^3=x^2+C$. D) $\frac{1}{y^2}=x+C$. Show Answer Correct Answer: A) $-\frac{1}{y}=x+C$. 3. The functions that are analytic at all points ..... A) $e^x$. B) $\sin x$. C) $\cos x$. D) All the above. Show Answer Correct Answer: D) All the above. 4. What is the solution to the PDE \( u ..... \{t\} = k u ..... \{xx\} \) called? A) Heat equation. B) Laplace equation. C) Wave equation. D) Poisson equation. Show Answer Correct Answer: A) Heat equation. 5. Determine the value of "c" that satisfies the differential equation $\frac{dy}{dx}=\frac{x+1}{y+2}$ A) 5/2. B) -3/2. C) -1/2. D) 1. Show Answer Correct Answer: B) -3/2. 6. Describe the method of characteristics for solving PDEs. A) The method of characteristics is a technique for solving PDEs by reducing them to ODEs along characteristic curves. B) The method of characteristics is a way to solve PDEs using numerical simulations. C) The method of characteristics simplifies PDEs by integrating them over a fixed domain. D) The method of characteristics involves applying Fourier transforms to PDEs directly. Show Answer Correct Answer: A) The method of characteristics is a technique for solving PDEs by reducing them to ODEs along characteristic curves. 7. Which of the following differential equation is a homogeneous equation of degree 2? A) $\frac{\text{d}y}{\text{d}x}=2xy$. B) $y\frac{\text{d}y}{\text{d}x}=2x$. C) $\frac{\text{d}y}{\text{d}x}=\frac{3xy+y^2}{xy}$. D) $xy\frac{\text{d}y}{\text{d}x}=y^2-1$. Show Answer Correct Answer: C) $\frac{\text{d}y}{\text{d}x}=\frac{3xy+y^2}{xy}$. 8. I want to solve the differential equation $\frac{dy}{dx}=6-y$ A) $\frac{dy}{dx}+y=6$. B) $dy+y=6dx$. C) $\frac{dy}{6-y}=dx$. D) $dy=\left(6-y\right)dx$. Show Answer Correct Answer: C) $\frac{dy}{6-y}=dx$. 9. Consider the differential equation dy/dx = e$^{y}$(4x$^{2}$-5x). Let y=f(x) be the particular solution to the differential equation that passes through (1, 0).Write an equation of the line tangent to the graph of f at the point (1, 0). A) Y=x-1. B) Y=2(x-1). C) Y=-(x-1). D) Y=-2(x-1). Show Answer Correct Answer: C) Y=-(x-1). 10. The particular integral of the equation (D$^{2}$+DD$^{'}$-6D$^{'2}$)z = e$^{3x+y}$ A) $\frac{e^{3x-y}}{6}$. B) $\frac{e^{3x+y}}{5}$. C) $\frac{e^{3x}}{6}$. D) $\frac{e^{3x+y}}{6}$. Show Answer Correct Answer: D) $\frac{e^{3x+y}}{6}$. 11. What is the degree of the differential equation:$\left(\frac{d^2y}{dx^2}\right)^2 + 3\left(\frac{dy}{dx}\right)^3-y = 0$ A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: B) 2. 12. What is the significance of the Wronskian in differential equations? A) It is used to find particular solutions. B) It provides the roots of the equation. C) It indicates the linear independence of solutions. D) It determines the order of the equation. Show Answer Correct Answer: C) It indicates the linear independence of solutions. 13. Let $y=f\left(x\right)$ $\frac{dy}{dx}=y-10x^2$ $f\left(0\right)=3$ $f\left(0.4\right)$ $x=0$ A) 4.120. B) 4.200. C) 4.240. D) 4.768. Show Answer Correct Answer: C) 4.240. 14. The condition of compatibility of partial differential equations $f\left(x, y, z, p, q\right)=0\, \\g\left(x, y, z, p, q\right)=0$ A) $\frac{\partial\left(f, g\right)}{\partial\left(p, q\right)}=0$. B) $\frac{\partial\left(f, g\right)}{\partial\left(p, q\right)}\ne0$. C) $\frac{\partial\left(f, p\right)}{\partial\left(g, q\right)}=0$. D) $\frac{\partial\left(f, q\right)}{\partial\left(g, p\right)}\ne0$. Show Answer Correct Answer: B) $\frac{\partial\left(f, g\right)}{\partial\left(p, q\right)}\ne0$. 15. What are the orthogonal trajectories of the family of curves $ y = x + c$ ? A) $ y =-x + c*$. B) $ y = x-c$. C) $ y =-x + c$. D) $ y = x + c*$. Show Answer Correct Answer: A) $ y =-x + c*$. 16. What is the full form of C.F. in solution of a linear differential equation? A) Complex Function. B) Continuous Function. C) Complimentary Function. D) None of these. Show Answer Correct Answer: C) Complimentary Function. 17. Solve $m^2-4m+4=0$ A) 2, 2. B) -2, -2. C) 2, -2. D) 0, 2. Show Answer Correct Answer: A) 2, 2. 18. The differential equation for a damped harmonic oscillator is given by:$\frac{d^2y}{dt^2}+4\\frac{dy}{dt}+5y=0$ A) Overdamped. B) Underdamped. C) Critically damped. D) Oscillatory without damping. Show Answer Correct Answer: B) Underdamped. 19. If the equation is in the form f(x, p, q)=0, then we assume A) P=a. B) Z=pq. C) Q=a. D) P=aq. Show Answer Correct Answer: C) Q=a. 20. Solve the differential equation. $\frac{dy}{dx}=5y$ A) $y=Ce^{5x}$. B) $\log y=5x+C$. C) $y=5x+C$. D) $y=x^2+C$. Show Answer Correct Answer: A) $y=Ce^{5x}$. 21. Solve the following differential equations:$\frac{\text{d}y}{\text{d}x}=3y$ A) $y=Ce^{3x}$. B) $y=3x+C$. C) $\frac{y^2}{2}=3x+C$. D) $\ln y=x+C$. Show Answer Correct Answer: A) $y=Ce^{3x}$. 22. Solution of a linear differential equation of first order can be obtain by A) Multiplying on both the sides by its integrating factor. B) Adding on both the sides by integrating factor. C) Subtracting integrating factor from both sides. D) None of the above. Show Answer Correct Answer: A) Multiplying on both the sides by its integrating factor. 23. If the velocity function is $v(t) = 2t^3-3t^2 + 4t$ $s(t)$ $s(0) = 7$ A) $s(t) = \frac{1}{2}t^4-t^3 + 2t^2 + 7$. B) $s(t) = \frac{1}{2}t^4-t^3 + 2t^2$. C) $s(t) = \frac{1}{2}t^4 + t^3 + 2t^2 + 7$. D) $s(t) = \frac{1}{2}t^4-t^3 + 4t^2 + 7$. Show Answer Correct Answer: A) $s(t) = \frac{1}{2}t^4-t^3 + 2t^2 + 7$. 24. If R(x) is a decreasing function, then a Right 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. 25. $\int_{\frac{\pi}{2}}^x\cos\left(t\right)dt=$ A) $-\sin x$. B) $\sin x+1$. C) $\sin x-1$. D) $-\sin x-1$. Show Answer Correct Answer: C) $\sin x-1$. ← 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