This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 46 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 46 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. A population of rabbits grows according to the differential equation dp/dt = 0.08p, where p(0) = 50. What is the population after 5 years? A) 74.59. B) 45.12. C) 60.33. D) 100.25. Show Answer Correct Answer: A) 74.59. 2. Find the order of the differential equation:$\frac{d^2y}{dx^2} + 7\frac{dy}{dx}-2y = 0$ A) 0. B) 3. C) 1. D) 2. Show Answer Correct Answer: D) 2. 3. How can you mitigate Zeno behavior in system design? A) Increase the number of incremental tasks. B) Eliminate deadlines entirely. C) Use synchronous processing exclusively. D) Reduce incremental tasks, prioritize, batch processes, set deadlines, and use asynchronous processing. Show Answer Correct Answer: D) Reduce incremental tasks, prioritize, batch processes, set deadlines, and use asynchronous processing. 4. The differential equation $2ydx-\left(3y-2x\right)dy=0$ A) Exact and homogeneous but not linear. B) Exact, homogeneous and linear. C) Exact and homogeneous but not linear. D) Homogeneous and linear but not excat. Show Answer Correct Answer: B) Exact, homogeneous and linear. 5. What is a finite state machine in CPS? A) A finite state machine in CPS is a graphical representation of system architecture. B) A finite state machine in CPS is a type of algorithm that does not involve states. C) A finite state machine in CPS is a model that represents system behavior through a finite number of states and transitions based on inputs. D) A finite state machine in CPS is a model that uses an infinite number of states. Show Answer Correct Answer: C) A finite state machine in CPS is a model that represents system behavior through a finite number of states and transitions based on inputs. 6. How do the roots of the characteristic equation affect the complementary function? A) They only affect the non-homogeneous part. B) They dictate the form of the complementary function. C) They have no impact on the solution. D) They determine the coefficients of the particular solution. Show Answer Correct Answer: B) They dictate the form of the complementary function. 7. $\frac{dy}{dx}=\frac{x^2}{x^2-y^2}+\frac{y}{x}$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: D) Homogeneous. 8. Which of the following differential equations can be classified as separable and exact? A) $y^3dx+3xy^2dy=0$. B) $\frac{\text{d}y}{\text{d}x}=\frac{x+y}{x}$. C) $\frac{\text{d}y}{\text{d}x}=3\left(y+5\right)x$. D) $\left(x^2+1\right)dy+\left(xy+x\right)dx=0$. Show Answer Correct Answer: A) $y^3dx+3xy^2dy=0$. 9. What is the main focus of initial and boundary value problems in differential equations? A) Finding the solution at a specific point or along a specific curve. B) Dealing with non-linear equations. C) Working with partial differential equations. D) Setting conditions for the solution on a given curve or at certain points. Show Answer Correct Answer: D) Setting conditions for the solution on a given curve or at certain points. 10. I.F. of $\frac{\text{d}x}{\text{d}y}+Px=Q$ A) $e^{\int Pdx_{ }}$. B) $e^{\int Pdy_{ }}$. C) $e^{\int Qdy_{ }}$. D) $e^{\int Qdx_{ }}$. Show Answer Correct Answer: B) $e^{\int Pdy_{ }}$. 11. 5y" +3y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: C) UNDAMPED. 12. Solve dy/dx = (y+5)(x+2) given the point (0, 1) A) $y=6e^{\frac{1}{2}x^2+2x}-5$. B) $y=6e^{2x^2+2x}-5$. C) $y=3e^{\frac{1}{2}x^2+2x}-5$. D) $y=4e^{\frac{1}{2}x^2+2x}-5$. Show Answer Correct Answer: A) $y=6e^{\frac{1}{2}x^2+2x}-5$. 13. Page 397 #41 CALC A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: A) A. 14. What is the solution curve of a differential equation? A) A constant function. B) A line that intersects the x-axis. C) A function that satisfies the differential equation. D) A polynomial function. Show Answer Correct Answer: C) A function that satisfies the differential equation. 15. Part B. Find the particular solution under the given conditions:14. y" -5y' + 6y = 0, y(0) = 0, y'(0) = 3 A) $y =-2e^{2x} + 2e^{3x}$. B) Y = $2e^{2x}-2e^{3x}$. C) Y = $3e^{2x} + e^{3x}$. D) $y = e^{2x}-3e^{3x}$. Show Answer Correct Answer: A) $y =-2e^{2x} + 2e^{3x}$. 16. Find the degree for the differential equation. A) 2. B) 4. C) 1. D) 3. Show Answer Correct Answer: C) 1. 17. Find the general solution of the homogeneous equation:y" + 4y = 0. A) Y(t) = C1 e$^{2t}$ + C2 e$^{-2t}$. B) Y(t) = C1 cos(2t) + C2 sin(2t). C) Y(t) = C1 t + C2 t$^{2}$. D) Y(t) = C1 cos(t) + C2 sin(t). Show Answer Correct Answer: B) Y(t) = C1 cos(2t) + C2 sin(2t). 18. The solution of linear differential equation $x\frac{dy}{dx}+2y=x^2$ A) $y=\frac{x^2+c}{4x^2}$. B) $y=\frac{x^4+c}{4x^2}$. C) $y=\frac{x^4+c}{x^2}$. D) $y=\frac{x^2}{4}+c$. Show Answer Correct Answer: B) $y=\frac{x^4+c}{4x^2}$. 19. During a certain epidemic, the number of people that are infected at any time increases at a rate proportional to the number of people that are infected at that time. If 1, 000 people are infected when the epidemic is first discovered, and 1, 200 are infected 7 days later, how many people are infected 12 days after the epidemic is first discovered? A) 343. B) 1343. C) 1367. D) 1400. E) 2057. Show Answer Correct Answer: C) 1367. 20. If you're supposed to find the Average Value of $f\left(x\right)$ A) The same as the unit for $f\left(x\right)$. B) The units of the $\int_{ }f\left(x\right)$. C) The units of the derivative of $f\left(x\right)$. D) None of the above. Show Answer Correct Answer: A) The same as the unit for $f\left(x\right)$. 21. The solution of the system X = AX using the matrix exponential is ..... A) X(t) = A t X(0). B) $e^{At} X(0)$. C) X(t) = [I + At] X(0). D) $X(t) = A^t X(0)$. Show Answer Correct Answer: B) $e^{At} X(0)$. 22. The method of variation of parameters is mainly used to find: A) Complementary function only. B) Particular solution of a non-homogeneous differential equation. C) Order of a differential equation. D) General solution of homogeneous equations. Show Answer Correct Answer: B) Particular solution of a non-homogeneous differential equation. 23. Solve the homogeneous equation:y" + 6y' + 9y = 0. A) Y(t) = C1 e$^{-t}$ + C2 e$^{-2t}$. B) Y(t) = (C1 + C2t)e$^{-3t}$. C) Y(t) = C1e$^{2t}$ + C2e$^{-3t}$. D) Y(t) = C1e$^{3t}$. Show Answer Correct Answer: B) Y(t) = (C1 + C2t)e$^{-3t}$. 24. Which of the following is a correct way to verify that $y = e^{2x}$ $\frac{dy}{dx} = 2y$ A) Substitute $y$. B) Integrate both sides of the equation. C) Differentiate both sides of the equation. D) Substitute $x = 0$. Show Answer Correct Answer: A) Substitute $y$. 25. The solution of $\vec{X}' = A \vec{X}$ A) The eigenvalues of A. B) The determinant of A only. C) The trace of A only. D) The rank of A. Show Answer Correct Answer: A) The eigenvalues of A. ← 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