This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 38 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 38 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The order and degree of the differential equation $dy/dx + x^2 d^2y/dx^2 + xy = sin(x)$ A) 1, 1. B) 2, 1. C) 3, 2. D) 2, not defined. Show Answer Correct Answer: B) 2, 1. 2. How do you sketch a slope field for a given differential equation? A) Use a protractor to measure the angles of the lines on the coordinate plane. B) Use a compass to draw circles on the coordinate plane. C) Write out the equation in words instead of sketching it on the coordinate plane. D) Identify the equation and use small line segments to represent the slope at various points on the coordinate plane. Show Answer Correct Answer: D) Identify the equation and use small line segments to represent the slope at various points on the coordinate plane. 3. Differential equation of the curve y= Acos2x+B sin2x, where A & B are constant is A) Y$^{"}$+4y=0. B) Y$^{"}$-4y=0. C) Y$^{"}$-4y$^{'}$=0. D) Y$^{"}$+4y$^{'}$=0. Show Answer Correct Answer: A) Y$^{"}$+4y=0. 4. The solution z = ax + g(a)y +c is getting from A) F(x, p, q)=0. B) F(p, q)=0. C) F(x, p)=g(y, q). D) F(z, p, q)=0. Show Answer Correct Answer: B) F(p, q)=0. 5. What is the general form of a separable differential equation? A) Dy/dx = g(x) / h(y). B) Dy/dx = g(x)-h(y). C) Dy/dx = g(x) + h(y). D) Dy/dx = g(x) * h(y). Show Answer Correct Answer: D) Dy/dx = g(x) * h(y). 6. CHOOSE THE CORRECT FORM OF PARTIAL DIFFERENTIAL EQUATION BY ELIMINATING ARBITARY CONSTANTS z=ax+by+ab A) Z=ax+by+ab. B) Z=px+qy+pq. C) Z=py-rx+pq. D) Z=py+q+p. E) Z=px+qy-q. Show Answer Correct Answer: B) Z=px+qy+pq. 7. F(s) = L\{(1)\} (s) A) 1/s. B) N!/s$^{(n+1)}$. C) 1/(s-a). D) N!/(s-a)$^{(n+1)}$. E) S/(s$^{2}$+b$^{2}$). Show Answer Correct Answer: A) 1/s. 8. Equations solvable for x are often reduced by: A) Eliminating y. B) Differentiating w.r.t. y. C) Separation of variables. D) None. Show Answer Correct Answer: A) Eliminating y. 9. If $\overrightarrow{f}$ $\overrightarrow{g}$ $\overrightarrow{f}\times\overrightarrow{g}$ A) Irrotational. B) Harmonic. C) Solenoidal. D) Neither irrotational nor solenoidal. Show Answer Correct Answer: C) Solenoidal. 10. Let PDE c$^{2}$(u$_{xx }$+ u$_{yy }$)= u$_{t}$, By is known as A) 2-D heat equation. B) 2-D wave equation. C) Laplace equation. D) None of these. Show Answer Correct Answer: A) 2-D heat equation. 11. Find the linear first order ODE. A) $y' + y^{2} = 0$. B) $y' + \sin(x)y =\cos(x)$. C) $y' = y^{2} + x$. D) $y' = x y^{2}$. Show Answer Correct Answer: B) $y' + \sin(x)y =\cos(x)$. 12. Which mathematician is credited with being the first to solve a differential equation using the method of 'separation of variables' in 1691? A) Gottfried Wilhelm Leibniz. B) Isaac Newton. C) Leonhard Euler. D) Joseph-Louis Lagrange. Show Answer Correct Answer: A) Gottfried Wilhelm Leibniz. 13. What is the integrating factor for the differential equation:$\frac{1}{x}\frac{\text{d}y}{\text{d}x}-\frac{y}{1+x^2}=x^3$ A) $\ln\left(x^2\right)$. B) $-\frac{1}{x^2}$. C) $-\frac{1}{\sqrt{x}}$. D) $\frac{1}{\sqrt{\left(1+x^2\right)}^{ }}$. Show Answer Correct Answer: D) $\frac{1}{\sqrt{\left(1+x^2\right)}^{ }}$. 14. It is number of the highest degree in a differential equation A) Variable. B) Degree. C) Order. D) Derivative. Show Answer Correct Answer: C) Order. 15. Find the particular solution of the differential equation $\frac{dy}{dx}=3e^{\left(x-y\right)}$ $y\left(-1\right)=\ln\left(\frac{\left(e+3\right)}{e}\right)$ A) $y=\ln\left(3e^x+1\right)$. B) $y=\ln\left(2e^x+3\right)$. C) $y=\ln\left(2e^x+1\right)$. D) $y=\ln\left(3e^x+2\right)$. Show Answer Correct Answer: A) $y=\ln\left(3e^x+1\right)$. 16. What is the general solution to the differential equation $\frac{dy}{dx} = 2x$ A) $y = x^2 + C$. B) $y = 2x + C$. C) $y = x^2$. D) None of the above. Show Answer Correct Answer: A) $y = x^2 + C$. 17. What is the role of the particular solution (PS) in a second order ODE? A) It is irrelevant to the overall solution. B) It addresses the non-homogeneous portion of the differential equation. C) It solves the homogeneous equation. D) It determines the roots of the characteristic equation. Show Answer Correct Answer: B) It addresses the non-homogeneous portion of the differential equation. 18. General solution of $\left(D^2+9\right)y=0$ A) $y=c_1\cos x+c_2\sin x$. B) $y=c_1\cos x+c_2\sin x+x$. C) Y=x. D) Y+x. Show Answer Correct Answer: A) $y=c_1\cos x+c_2\sin x$. 19. Find the value of k for which the constant function x(t) = k is a solution of the differential equation $2t^2 \frac{dx}{dt} + 4x + 9 = 0$ A) K =-9/4. B) K = 9/4. C) K = 0. D) K = 4. Show Answer Correct Answer: A) K =-9/4. 20. Singular solution of Partial differential equation can be obtained by A) General solution. B) Complete solution. C) Both a & b. D) None of the above. Show Answer Correct Answer: B) Complete solution. 21. What is the significance of boundary conditions in solving PDEs? A) Boundary conditions are irrelevant to the solution process. B) Boundary conditions determine the uniqueness and behavior of solutions to PDEs. C) Boundary conditions only affect initial values in PDEs. D) Boundary conditions simplify the equations of PDEs. Show Answer Correct Answer: B) Boundary conditions determine the uniqueness and behavior of solutions to PDEs. 22. The solution of Lagrange's partial differential equation xp+yq=z is A) $f\left(\frac{x}{y}, \frac{y}{z}\right)=0$. B) $f\left(\frac{x}{y}, \frac{x}{z}\right)=0$. C) $f\left(\frac{y}{x}, \frac{y}{z}\right)=0$. D) $f\left(\frac{y}{x}, \frac{x}{z}\right)=0$. Show Answer Correct Answer: A) $f\left(\frac{x}{y}, \frac{y}{z}\right)=0$. 23. 6y" +11y'+3y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: B) OVERDAMPED. 24. The derivative of $\sin x$ A) $-\sin x$. B) $\cos x$. C) $-\cos x$. D) $\tan x$. Show Answer Correct Answer: B) $\cos x$. 25. Page 393 #16 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: E) E. ← 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