This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 3 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 3 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Y" +8y'+12y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: B) OVERDAMPED. 2. The following Differential Equation is $\frac{\text{d}y}{\text{d}x}=\frac{e^y}{e^x}$ A) Separable. B) Non Separable. C) All the above. D) None of the above. Show Answer Correct Answer: A) Separable. 3. The population $P(t)$ $\frac{dP}{dt}=3P\Big(4-\frac{P}{6000}\Big)$ A) $\tfrac13$. B) $4$. C) $6000$. D) $24000$. Show Answer Correct Answer: D) $24000$. 4. $2\frac{\text{d}^2y}{\text{d}x^2}+\frac{\text{d}y}{\text{d}x}-y=2x^2+1$ A) $y=Ae^{-x}+Be^{x/2}-2x^2-4x-13$. B) $y=Ae^x+Be^{-x/2}-2x^2-4x-13$. C) $y=Ae^{-x}+Be^{x/2}+2x^2+4x-13$. D) $y=Ae^x+Be^{-x/2}+2x^2+4x-13$. Show Answer Correct Answer: A) $y=Ae^{-x}+Be^{x/2}-2x^2-4x-13$. 5. The particular solution of the differential equation $\frac{\text{d}y}{\text{d}x}+2y=x$ A) $y=\frac{1}{2}x^2e^{-2x}$. B) $y=\frac{e^{-2x}+2x-1}{4}$. C) $y=1-e^{-2x}$. D) $y=\frac{1-e^{-2x}}{2}$. Show Answer Correct Answer: B) $y=\frac{e^{-2x}+2x-1}{4}$. 6. The population of the little town of Scorpion Gulch is now 1000 people. The population is presently growing at about 5% per year.Find the general solution. A) P=.05e$^{1000t}$. B) P=1000e$^{ln(5)t}$. C) P=1000e$^{ln(1.05)t}$. D) P=lne$^{1000t}$. Show Answer Correct Answer: C) P=1000e$^{ln(1.05)t}$. 7. 83% of a certain airline's flights depart on time. Of these flights, 90% also arrive on time. 30% of flights from this airline that depart late manage to make up time in the air to still arrive on time.You see a flight from this airline arriving on time. What is the probability that it departed on time? A) 0.9361. B) 0.9608. C) 0.9721. D) 0.8532. Show Answer Correct Answer: A) 0.9361. 8. Which of the following is an application of PDEs in engineering? A) Calculating stress in structural beams. B) Modeling heat conduction in materials. C) Simulating fluid flow in pipes. D) Analyzing electrical circuits in devices. Show Answer Correct Answer: B) Modeling heat conduction in materials. 9. Find the general solution of the differential equation y" +6y'-16y=10x-32 A) $y=Ae^{2x}+Be^{-8x}$. B) $y=Ae^2+Be^{-8}-x+2$. C) $y=Ae^{2x}+Be^{-8x}-x+2$. D) $y=\left(e^{2x}+e^{-8x}\right)\left(A+Bx\right)$. Show Answer Correct Answer: C) $y=Ae^{2x}+Be^{-8x}-x+2$. 10. The nature of PDE u$_{xx }$+4 u$_{xy }$+3 u$_{yy}$, =0 A) Circular. B) Elliptic. C) Hyperbolic. D) Parabolic. Show Answer Correct Answer: C) Hyperbolic. 11. What is the method of reduction of order used for? A) To convert a linear differential equation to a lower order. B) To find the Wronskian. C) To solve non-linear equations. D) To determine linear independence. Show Answer Correct Answer: A) To convert a linear differential equation to a lower order. 12. The growth of population y is described by the differential equation $\frac{dy}{dt}=ky$ A) 0.087. B) 0.250. C) 0.271. D) 4.351. Show Answer Correct Answer: A) 0.087. 13. What is the result of applying the reduction of order method? A) A solution to a higher order equation. B) A solution to a lower order equation. C) No solution. D) A constant solution. Show Answer Correct Answer: B) A solution to a lower order equation. 14. Which is one of the following are the bases for $P_2\left(R\right)?$ A) $\left\{1, x, 2x\right\}$. B) $\left\{1, 2x, 3x^2\right\}$. C) $\left\{1+x, 2x+2x^2, x-x^2\right\}$. D) $\left\{1+2x+x^2, 3+x^2, x+x^2\right\}$. Show Answer Correct Answer: B) $\left\{1, 2x, 3x^2\right\}$. 15. Please find the answer to this limit:$\lim_{x\rightarrow\infty}\frac{x^2+\sin x}{x^2}$ A) 0. B) 1. C) -1. D) $\infty$. Show Answer Correct Answer: B) 1. 16. What is the degree of the PDE \( (u ..... \{x\})^2 + u ..... \{y\} = 0 \)? A) 2. B) 1. C) 3. D) 4. Show Answer Correct Answer: A) 2. 17. The integrating factor for the equation dy/dx-(3y)/(x+1) = (x+1)/4 is: A) I. B) $e^{3x}$. C) $\int_{x}^{3} dx$. D) 1/(x+1). Show Answer Correct Answer: B) $e^{3x}$. 18. The general solution of y" -5y'+6y=0 is: A) $c_1e^{2x}+c_2e^{3x}$. B) $c_1e^{-2x}+c_2e^{-3x}$. C) $c_1e^x+c_2e^{6x}$. D) $c_1e^{5x}+c_2e^{6x}$. Show Answer Correct Answer: A) $c_1e^{2x}+c_2e^{3x}$. 19. If C is the straight line joining (0, 0, 0) and (1, 1, 1) then $\int_C\overrightarrow{r}.d\overrightarrow{r}$ A) 1/2. B) 1. C) 3/2. D) 2. Show Answer Correct Answer: C) 3/2. 20. The roots of m$^{2}$-6m+13=0 are ..... A) 3+2i, 3-2i. B) 3, 2. C) 1+i, 1-i. D) 1, 1. Show Answer Correct Answer: A) 3+2i, 3-2i. 21. F(s) = L\{(e$^{at}$cos(bt))\} (s) A) 1/s. B) B/(s-a)$^{2 }$+ b$^{2}$. C) (s-a)/((s-a)$^{2}$+b$^{2}$). D) B/(s$^{2}$ + b$^{2}$). E) S/(s$^{2}$+b$^{2}$). Show Answer Correct Answer: C) (s-a)/((s-a)$^{2}$+b$^{2}$). 22. The standard form of a growth/decay equation is: A) $\frac{dy}{dx} = y^2$. B) Dy/dx = k y. C) Dy/dx = k. D) $\frac{dy}{dx} = e^x$. Show Answer Correct Answer: B) Dy/dx = k y. 23. Population y grows according to the equation dy/dx=ky, where k is a constant and t is measured in years. If the population doubles every 10 years, then the value of k is: A) 5.000. B) 3.322. C) 0.301. D) 0.200. E) 0.069. Show Answer Correct Answer: E) 0.069. 24. Which of the following is the general solution to $\frac{dy}{dx} =\cos x$ A) $y = \sin x + C$. B) $y =\cos x + C$. C) $y =-\sin x + C$. D) $y =-\cos x + C$. Show Answer Correct Answer: A) $y = \sin x + C$. 25. Find a solution to:y" + 8y' + 16y = 0 given y ' = 4 when y = 3 and x = 0 A) $e^{-4x}(4+3x)$. B) $e^{-4x}(3+4x)$. C) $e^{2x}(3+4x)$. D) $e^{2x}(4+3x)$. Show Answer Correct Answer: B) $e^{-4x}(3+4x)$. ← 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 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 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books