This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 31 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 31 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Y" =-$\pi$ A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: C) UNDAMPED. 2. The expansion for s A) $\frac{\partial^2z}{\partial y^2}$. B) $\frac{\partial^2z}{\partial x^2}$. C) $\frac{\partial^2z}{\partial x\partial y^{ }}$. D) None of the above. Show Answer Correct Answer: C) $\frac{\partial^2z}{\partial x\partial y^{ }}$. 3. A rod of length 10 m has temperature 30$^{0 }$C and 40$^{0 }$C at end points. What is the temperature gradient A) 1$^{0}$C per cm. B) 3$^{0}$C per cm. C) 2$^{0}$C per cm. D) None of these. Show Answer Correct Answer: A) 1$^{0}$C per cm. 4. The PDE u$_{xx }$+ u$_{yy }$= 0, is known as A) 1-D heat equation. B) 1-D wave equation. C) Laplace equation. D) None of these. Show Answer Correct Answer: C) Laplace equation. 5. What is the integral factor, $V\left(x\right)$ $x\frac{dy}{dx}-2y=x^3\ln x$ A) $e^{2x}$. B) $e^{-2x}$. C) $\frac{1}{x^2}$. D) $x^2$. Show Answer Correct Answer: C) $\frac{1}{x^2}$. 6. Find the general solution to $y" -2y' + y = 0$ A) $y(x) = Ce^{x} + Dxe^{x}$. B) $y(x) = Ce^{x} + De^{-x}$. C) $y(x) = C\sin(x) + D\cos(x)$. D) $y(x) = Ce^{2x} + De^{-2x}$. Show Answer Correct Answer: A) $y(x) = Ce^{x} + Dxe^{x}$. 7. The complete solution(or complete integral ) of Linear Differential equations involves A) Complete function + particular integral. B) Complementary function + particular integral. C) Complementary function + definite integral. D) Complete function + indefinite integral. Show Answer Correct Answer: B) Complementary function + particular integral. 8. What are the values of $\alpha$ $\beta$ $dF\left(x, y\right)=\left(\frac{1}{x^2+2}+\frac{\alpha}{y}\right)dx+\left(xy^{\beta}+1\right)dy$ A) $\alpha=-1, \beta=-2$. B) $\alpha=1, \beta=-2$. C) $\alpha=-1, \beta=2$. D) $\alpha=-2, \beta=-1$. Show Answer Correct Answer: A) $\alpha=-1, \beta=-2$. 9. If $f\left(x\right)$ $x^2\sqrt[]{x^3+1}$ $f\left(2\right)=0, $ $f\left(0\right)=$ A) $\frac{52}{9}$. B) $-\frac{52}{9}$. C) $\frac{56}{9}$. D) $-\frac{56}{9}$. Show Answer Correct Answer: B) $-\frac{52}{9}$. 10. The value of f ..... x(1, 2) for f(x, y) = $4x^2y-3y$ A) 8. B) 16. C) 4. D) 13. Show Answer Correct Answer: B) 16. 11. What is the solution to dy/dx = 3? A) Y = x + C. B) Y = 3x + C. C) Y = 3x. D) Y = 3x + 1. Show Answer Correct Answer: B) Y = 3x + C. 12. Dy/dx = x + 3y and y(2) = 3. Use Euler's Method with a step size of 1 to approximate y(5). A) 11. B) 181. C) 45. D) 240. Show Answer Correct Answer: D) 240. 13. For the function f(x, y) = $(x^2 + y^2)(y^2 + 1)$ A) 10. B) 8. C) 12. D) 16. Show Answer Correct Answer: A) 10. 14. Given the differential equation $\frac{dy}{dx} = 3x^2$ A) $y = x^3 + C$. B) $y = 3x^2 + C$. C) $y = x^2 + C$. D) $y = 6x + C$. Show Answer Correct Answer: A) $y = x^3 + C$. 15. The total differential of z = f(x, y) is: A) Dz = f x dx + f y dy. B) Dz = dfdy. C) Dz = f dx + f dy. D) Dz = dx + dy. Show Answer Correct Answer: A) Dz = f x dx + f y dy. 16. Solve $\left(D^2-3DD'+2D'^2\right)z=0$ A) $Z=f_1\left(y+x\right)+f_2\left(y+2x\right)$. B) $Z=f_1\left(y\right)+f_2\left(y+x\right)$. C) $Z=f_2\left(y-x\right)+f_3\left(y-2x\right)$. D) $Z=xf_1\left(y\right)+xf_2\left(y+x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y+x\right)+f_2\left(y+2x\right)$. 17. Given $\frac{\text{d}^2x}{\text{d}y^2}+4\frac{\text{d}x}{\text{d}y}+3y=2e^{-x}.$ $y_p$ A) $Ce^{-x}$. B) $C\cos x+D\sin x$. C) $Ce^x$. D) $Cxe^{-x}$. Show Answer Correct Answer: D) $Cxe^{-x}$. 18. $\int_{ }^{ }3te^{2t}dt$ A) $\frac{3te^{2t}}{2}-\frac{e^{2t}}{4}+C$. B) $3e^{2t}-\frac{e^{2t}}{4}+C$. C) $6te^{2t}-12e^{2t}+C$. D) $\frac{3te^{2t}}{2}-\frac{3e^{2t}}{4}+C$. Show Answer Correct Answer: D) $\frac{3te^{2t}}{2}-\frac{3e^{2t}}{4}+C$. 19. How can Zeno behavior affect system performance? A) Zeno behavior improves system performance by increasing efficiency. B) Zeno behavior can negatively impact system performance by causing delays and inefficiencies. C) Zeno behavior has no effect on system performance whatsoever. D) Zeno behavior only affects hardware, not system performance. Show Answer Correct Answer: B) Zeno behavior can negatively impact system performance by causing delays and inefficiencies. 20. A stone is thrown straight up from the top of a building with initial velocity $40\\frac{ft}{\sec}$ $32\\frac{ft}{\sec^2}$ A) 88. B) 96. C) 112. D) 128. Show Answer Correct Answer: B) 96. 21. Integrate $\int_{ }^{ }\left(\frac{1-\sin x}{\cos^2x}\right)dx$ A) $\tan x-\sec x+c$. B) $\tan x+\sec x+c$. C) $\cot x-\operatorname{cosec}x+c$. D) $\cot x+\operatorname{cosec}x+c$. Show Answer Correct Answer: A) $\tan x-\sec x+c$. 22. Classify the PDE:u ..... xx + u ..... yy = 0. A) Linear. B) Elliptic. C) Parabolic. D) Hyperbolic. Show Answer Correct Answer: B) Elliptic. 23. There were 7 wolves introduced to a reserve in Colorado. The rate of growth of the population of wolves W over time is assumed to be proportional to the number of wolves. A) $W=\sqrt[]{2kt+49}$. B) $W=\sqrt[]{2kt+14}$. C) $W=6e^{kt}$. D) $W=7e^{kt}$. Show Answer Correct Answer: D) $W=7e^{kt}$. 24. $x\frac{dy}{dx}-2y=2x^2\ln\left(x\right)$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: A) Linear. 25. What type of differential equations are of the form y' = f(x)g(y)? A) Differential equations with separable variables. B) Differential equations with polynomial solutions. C) Differential equations with linear coefficients. D) Differential equations with constant functions. Show Answer Correct Answer: A) Differential equations with separable variables. ← 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