This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 33 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 33 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The value of $\nabla\left(\overrightarrow{a}\cdot\overrightarrow{r}\right)$ A) $\left|\overrightarrow{a}\right|$. B) A. C) 0. D) $\overrightarrow{a}$. Show Answer Correct Answer: D) $\overrightarrow{a}$. 2. Page 393 #21 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: E) E. 3. Given the logistic differential equation $\frac{\text{d}P}{\text{d}t}=P\left(2-\frac{P}{900}\right)$ $\lim_{t\rightarrow\infty}P\left(t\right)$ A) 2. B) 450. C) 900. D) 1800. Show Answer Correct Answer: D) 1800. 4. How do you solve a separable differential equation? A) Multiply the variables and then integrate each side separately. B) Take the derivative of each side separately. C) Separate the variables and then integrate each side separately. D) Combine the variables and then integrate each side separately. Show Answer Correct Answer: C) Separate the variables and then integrate each side separately. 5. Solvability for y or x is usually done by differentiating with respect to: A) Independent variable only. B) The variable being eliminated. C) Constant. D) None. Show Answer Correct Answer: A) Independent variable only. 6. Which of the following differential equations is not linear? A) $\frac{\text{d}y}{\text{d}x}+xy^2=e^x$. B) $\frac{1}{x}\frac{\text{d}y}{\text{d}x}-y=x+1$. C) $x\frac{\text{d}y}{\text{d}x}+y=x-x^2y$. D) $\frac{\text{d}y}{\text{d}x}=1-xy$. Show Answer Correct Answer: A) $\frac{\text{d}y}{\text{d}x}+xy^2=e^x$. 7. The inverse differential operator D1 acting on a function f(x) is equivalent to which mathematical operation? A) Squaring the function. B) Differentiation with respect to x. C) Integration with respect to x. D) Taking the reciprocal of the function. Show Answer Correct Answer: C) Integration with respect to x. 8. What is the significance of the order of a differential equation? A) It shows the highest derivative present. B) It indicates the complexity of the equation. C) It defines the type of function involved. D) It determines the number of solutions. Show Answer Correct Answer: A) It shows the highest derivative present. 9. Bacteria in a certain culture increase at a rate proportional to the number present. If the number of bacteria doubles in three hours, in how many hours will the number of bacteria triple? A) $\ln\left(\frac{27}{2}\right)$. B) $\ln\left(\frac{9}{2}\right)$. C) $\frac{2\ln\left(3\right)}{\ln\left(2\right)}$. D) $\frac{3\ln\left(3\right)}{\ln\left(2\right)}$. E) $\frac{\ln\left(3\right)}{\ln\left(2\right)}$. Show Answer Correct Answer: D) $\frac{3\ln\left(3\right)}{\ln\left(2\right)}$. 10. L\{(1/2b$^{2}$)(sin bt-bt cos bt)\} A) B/(s$^{2}$+b$^{2}$). B) B/(s$^{2}$+b$^{2}$)$^{2}$. C) B/(s$^{2}$+b$^{2}$)$^{3}$. D) B/(s$^{2}$+b$^{2}$)$^{4}$. Show Answer Correct Answer: B) B/(s$^{2}$+b$^{2}$)$^{2}$. 11. What is the order of the differential equation:$\frac{d^3y}{dx^3} + \left(\frac{dy}{dx}\right)^2 + y = 0$ A) 3. B) 2. C) 1. D) 4. Show Answer Correct Answer: A) 3. 12. Determine the degree of the equation 2y" + 5y' + 3y = 0. A) 2. B) 3. C) 1. D) 4. Show Answer Correct Answer: C) 1. 13. Find the particular integral of (D$^{2}$-2DD$^{' }$+D$^{'2 }$)z = e$^{(x+2y)}$ A) 2e$^{x}$. B) E$^{x+2y}$. C) E$^{x-y}$. D) 3e$^{x+2y}$. Show Answer Correct Answer: B) E$^{x+2y}$. 14. Method of undetermined coefficients is used when: A) DE has polynomial, exponential, sine, cosine RHS. B) DE is nonlinear. C) Initial value problems only. D) None. Show Answer Correct Answer: A) DE has polynomial, exponential, sine, cosine RHS. 15. What are the factors affecting heat conduction according to Fourier's law? A) Shape, texture, and weight. B) Color, density, and volume. C) Time, pressure, and velocity. D) Temperature gradient, cross-sectional area, distance, and material's thermal conductivity. Show Answer Correct Answer: D) Temperature gradient, cross-sectional area, distance, and material's thermal conductivity. 16. If $\phi$ $\nabla\phi$ A) Normal. B) Tangent plane. C) Tangent line. D) Surface. Show Answer Correct Answer: A) Normal. 17. How would you CORRECTLY separate the following differential equation? $\frac{dy}{dx}=2y-xy$ A) $\frac{1}{y}dy=\left(2-x\right)dx$. B) $y\cdot dy=\left(2-x\right)dx$. C) $\frac{dy-2y}{y}=xdx$. D) $\frac{-2y+dy}{y}=x\cdot dx$. Show Answer Correct Answer: A) $\frac{1}{y}dy=\left(2-x\right)dx$. 18. Sinx is analytic at which point? A) 1. B) 0. C) -1. D) 2. Show Answer Correct Answer: B) 0. 19. A company selling Teslas has been using the logistic differential equation to model sales over the last 3 years. That is, $\frac{dN}{dt}=kN\left(2-N\right)$ $\frac{2}{N\left(2-N\right)}$ A) $-\frac{1}{N}-\frac{1}{2-N}$. B) $\frac{1}{N}-\frac{2}{2-N}$. C) $\frac{3}{N}-\frac{1}{2-N}$. D) $\frac{1}{N}+\frac{1}{2-N}$. Show Answer Correct Answer: D) $\frac{1}{N}+\frac{1}{2-N}$. 20. Why do we add a constant $C$ A) To make answers unique. B) Because derivatives are unique. C) Many functions can have the same derivative. D) To satisfy boundary conditions only. Show Answer Correct Answer: C) Many functions can have the same derivative. 21. What is the method of solution for homogeneous differential equations? A) Linear Differential Equation. B) Method of Solution of Homogeneous Differential Equation. C) Exact differential equation. D) Separable differential equation. Show Answer Correct Answer: B) Method of Solution of Homogeneous Differential Equation. 22. Which method is used to solve nonlinear differential equations? A) Separation of variables. B) Integrating factor. C) Exact equations. D) Substitution. Show Answer Correct Answer: D) Substitution. 23. Solve the following differential equations:$\frac{\text{d}y}{\text{d}x}=e^x$ A) $1=e^x+1$. B) $y=\frac{e^x}{2}+1$. C) $y=e^x+C$. D) $0=e^x+C$. Show Answer Correct Answer: A) $1=e^x+1$. 24. Solve dy/dx = 2x/y A) $y=\pm\sqrt[]{2x^2+C}$. B) $y=\pm\sqrt[]{4x^2+C}$. C) $y=\pm\sqrt[]{x^2+C}$. D) $y=\pm\sqrt[]{4x+C}$. Show Answer Correct Answer: A) $y=\pm\sqrt[]{2x^2+C}$. 25. The annihilator of sin bx is A) D2-b2. B) D2+ b2. C) D2+D. D) D-b. Show Answer Correct Answer: A) D2-b2. ← 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