This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 23 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 23 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Determine the general solution of $4y"+12y'+9y=0$ A) $y=C_1e^{-\frac{3}{2}x}+C_2xe^{-\frac{3}{2}x}$. B) $y=C_1e^{-\frac{3}{2}}+C_2xe^{-\frac{3}{2}}$. C) $y=e^{-\frac{3}{2}x}\left(C_1\cos\frac{3}{2}x+C_2\sin\frac{3}{2}x\right)$. D) $C_1e^{-\frac{3}{2}x}+C_2e^{-\frac{3}{2}x}$. Show Answer Correct Answer: A) $y=C_1e^{-\frac{3}{2}x}+C_2xe^{-\frac{3}{2}x}$. 2. A slope field is a pictorial representation of all of the possible solutions to a given differential equation. A) True. B) False. C) I don't know. D) None of the above. Show Answer Correct Answer: A) True. 3. Pick out the even function. A) $\sin x$. B) $\tan x$. C) $x^2$. D) $x^3$. Show Answer Correct Answer: C) $x^2$. 4. It is a type of differential equation wherein every term has the same degree. A) Variable Separable. B) Exact D.E. C) Non-exact D.E. D) Homogenous D.E. Show Answer Correct Answer: D) Homogenous D.E. 5. The main idea behind equations of first order but higher degree is to reduce them to: A) Linear equations. B) Standard solvable forms. C) Exact equations. D) None. Show Answer Correct Answer: B) Standard solvable forms. 6. The vector $\overrightarrow{f}$ $x^2\overrightarrow{i}+y^2\overrightarrow{j}+z^2\overrightarrow{k}$ A) Solenoidal. B) Irrotational. C) Harmonic. D) Neither solenoidal or irrotational. Show Answer Correct Answer: B) Irrotational. 7. The integrating factor is required when: A) Equation is already exact. B) Equation is not exact. C) Equation is linear. D) Equation is separable. Show Answer Correct Answer: B) Equation is not exact. 8. If $h'\left(x\right)=k\left(x\right)$ $\int_{-1}^1k\left(5x\right)dx=$ A) $\frac{1}{5}h\left(5\right)-\frac{1}{5}h\left(-5\right)$. B) $\frac{1}{5}h\left(5\right)+\frac{1}{5}h\left(-5\right)$. C) $5h\left(5\right)-5h\left(-5\right)$. D) $5h\left(5\right)+5h\left(-5\right)$. Show Answer Correct Answer: A) $\frac{1}{5}h\left(5\right)-\frac{1}{5}h\left(-5\right)$. 9. Find y' for y= sin(2x$^{2}$) A) 4sin(2x$^{2}$). B) 4xcos(2x$^{2}$). C) 2xcos(2x$^{2}$). D) Xcos(4x$^{2}$). Show Answer Correct Answer: B) 4xcos(2x$^{2}$). 10. RK4 method is used to solve: A) Algebraic equations. B) Ordinary differential equations. C) Integral equations. D) Matrices. Show Answer Correct Answer: B) Ordinary differential equations. 11. Determine the general solution of $y"-2y'+5y=0$ A) $y=C_1e^x+C_2xe^{2x}$. B) $y=C_1e^x+C_2e^{2x}$. C) $y=C_1e^x\cos2x+C_2e^x\sin2x$. D) $y=C_1e^{2x}\cos x+C_2e^{2x}\sin x$. Show Answer Correct Answer: C) $y=C_1e^x\cos2x+C_2e^x\sin2x$. 12. $\int_{ }^{ }\sec^2xdx=?$ A) $\frac{\sec^3x}{3}+c$. B) $\sec x+c$. C) $\tan x+c$. D) $\sec x\tan x+c$. Show Answer Correct Answer: C) $\tan x+c$. 13. Pick out one of the conditions of Dirichlet's condition. A) $f\left(x\right)$. B) $f\left(x\right)$. C) $f\left(x\right)$. D) $f\left(x\right)$. Show Answer Correct Answer: A) $f\left(x\right)$. 14. Which type of differential equations can be solved using the method of separation of variables? A) First order linear. B) Nonlinear. C) Higher order linear with constant coefficients. D) Partial differential equations. Show Answer Correct Answer: A) First order linear. 15. Evaluate the definite integral \( \int ..... 1^4 (4x-1) \, dx \). A) 15. B) 32. C) 27. D) 20. Show Answer Correct Answer: C) 27. 16. Find the order and degree of the differential equation + A) 4, 2. B) 4, 3. C) 4, 4. D) 4, 1. Show Answer Correct Answer: D) 4, 1. 17. If dy/dt=-2y and if y=1 when t=0, what is the value of t for what y=1/2? A) -ln(2)/2. B) -1/4. C) Ln(2)/2. D) Sqrt(2)/2. E) Ln2. Show Answer Correct Answer: C) Ln(2)/2. 18. L\{(1/48b$^{6}$)(3bt-(bt)$^{3}$(sin bt)-3(bt)$^{2}$cosbt)\} A) S/(s$^{2}$+b$^{2}$). B) S/(s$^{2}$+b$^{2}$)$^{2}$. C) S/(s$^{2}$+b$^{2}$)$^{3}$. D) S/(s$^{2}$+b$^{2}$)$^{4}$. Show Answer Correct Answer: D) S/(s$^{2}$+b$^{2}$)$^{4}$. 19. Classify the PDE:u ..... xx + 2u ..... xy + u ..... yy = 0. A) Hyperbolic. B) Parabolic. C) Elliptic. D) Linear. Show Answer Correct Answer: B) Parabolic. 20. Write an equation for the description:The rate of change of y with respect to x is proportional to the difference of x and z. A) $\frac{\text{d}y}{\text{d}x}=k\left(x-z\right)$. B) $\frac{\text{d}y}{\text{d}x}=\left(x-z\right)$. C) $\frac{\text{d}y}{\text{d}x}=\frac{k}{x-z}$. D) $\frac{\text{d}y}{\text{d}x}=k\left(\frac{x}{z}\right)$. Show Answer Correct Answer: A) $\frac{\text{d}y}{\text{d}x}=k\left(x-z\right)$. 21. $\int_{ }^{ }f'\left(\frac{1}{2}x\right)dx$ A) $\frac{1}{2}f\left(\frac{1}{2}x\right)$. B) $2f" \left(\frac{1}{2}x\right)$. C) $2f\left(\frac{1}{2}x\right)$. D) $\frac{1}{2}f" \left(\frac{1}{2}x\right)$. Show Answer Correct Answer: C) $2f\left(\frac{1}{2}x\right)$. 22. Which of the following differential equation CAN NOT be separated? A) $\frac{dy}{dx}+1=4x$. B) $y^2\frac{dy}{dx}=\sqrt{xy}-2x^2\sqrt{y}$. C) $\frac{dy}{dx}+\frac{2}{x}y=\frac{1}{x+1}$. D) $\frac{dy}{dx}-e^xy=e^x$. Show Answer Correct Answer: C) $\frac{dy}{dx}+\frac{2}{x}y=\frac{1}{x+1}$. 23. $\int\frac{1}{\csc x}dx$ A) $-\cos x+c$. B) $\sin x+c$. C) $\cot^2x+c$. D) $\sec x+c$. Show Answer Correct Answer: A) $-\cos x+c$. 24. The formation of differential equation can be done by eliminating arbitrary constants in a given expression. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 25. Which of the following differential equations is separable? A) $\frac{dy}{dx} = xy$. B) $\frac{dy}{dx} + y = x$. C) $\frac{dy}{dx} = y + \sin(x)$. D) $\frac{dy}{dx} = \frac{y}{x} + x$. Show Answer Correct Answer: A) $\frac{dy}{dx} = xy$. ← 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