This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 44 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 44 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If the PDE is of the type f(z, p, q)=0, then we will take ..... A) F(x, p)=a. B) P=aq. C) P=a. D) P=q. Show Answer Correct Answer: B) P=aq. 2. The initial guess for $f\left(x\right)-4\cos3x+2x^2$ A) $y_p=\left(C\cos3x+Fx^2\right)$. B) $y_p=\left(C\cos3x+D\sin3x+Fx^2+Gx+H\right)$. C) $y_p=\left(C\cos3x+D\sin3x+Fx^2\right)$. D) $y_p=\left(C\cos3x-D\sin3x+Fx^2+G\right)$. Show Answer Correct Answer: B) $y_p=\left(C\cos3x+D\sin3x+Fx^2+Gx+H\right)$. 3. State the order and degree of the differential function $\frac{\text{d}y}{\text{d}x}+\frac{\text{d}^2y}{\text{d}x^2}=10$ A) 2nd order and degree 1. B) 1st order and degree 2. C) 2nd order and degree 2. D) 1st order and degree 1. Show Answer Correct Answer: A) 2nd order and degree 1. 4. The particular integral represents the solution of the: A) Non-homogeneous part. B) Homogeneous part. C) Exact part. D) None. Show Answer Correct Answer: A) Non-homogeneous part. 5. If the roots of A.E are real and equal then C.F is $y=e^{m_1x}\left(c_1+c_2\right)$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 6. The particular integral of (D$^{3}$+3D$^{2}$+3D+1)y=e$^{-x}$ is ..... A) X$^{3}$e$^{-2x}$/6. B) X$^{3}$e$^{-3x}$/6. C) X$^{3}$e$^{-x}$/3. D) X$^{3}$e$^{-x}$/6. Show Answer Correct Answer: D) X$^{3}$e$^{-x}$/6. 7. Let the function $y=f\left(x\right)$ $\frac{dy}{dx}=4-x$ $y\left(-1\right)=2.$ A) $y=2x+\frac{x^2}{2}-\frac{11}{2}$. B) $y=2x-\frac{x^2}{2}-\frac{11}{2}$. C) $y=4x-\frac{x^2}{2}+\frac{13}{2}$. D) $y=-4x+\frac{x^2}{2}-\frac{13}{2}$. Show Answer Correct Answer: C) $y=4x-\frac{x^2}{2}+\frac{13}{2}$. 8. What is the form of a first-order linear differential equation? A) Dy/dx + P(x)y = Q(x). B) Dy/dx = P(x)y + Q(x). C) Dy/dx = P(y)x + Q(y). D) Dy/dx = Q(x) + P(y). Show Answer Correct Answer: A) Dy/dx + P(x)y = Q(x). 9. Consider the differential equation $\frac{dy}{dx}=e^y\left(4x^2-5x\right)$ A) Y=x-1. B) Y=2(x-1). C) Y=-(x-1). D) Y=-2(x-1). Show Answer Correct Answer: C) Y=-(x-1). 10. If $\frac{dy}{dx}=2y^2$ $y=-1$ $x=1, $ $x=2$ $y=?$ A) $-\frac{2}{3}$. B) $-\frac{1}{3}$. C) $0$. D) $\frac{1}{3}$. E) $\frac{2}{3}$. Show Answer Correct Answer: B) $-\frac{1}{3}$. 11. Sum of the Eigen values of a matrix is equal to ..... of the matrix A) Determinant. B) Product. C) Trace. D) Sum. Show Answer Correct Answer: C) Trace. 12. Which of the following statements is true about slope fields? A) Slope fields show the exact solution to a differential equation. B) Slope fields provide a graphical representation of the slopes of solutions at given points. C) Slope fields are only used for linear differential equations. D) Slope fields are used to solve algebraic equations. Show Answer Correct Answer: B) Slope fields provide a graphical representation of the slopes of solutions at given points. 13. The complementary function of the equation $\frac{d^3y}{dx^3}+\frac{d^2y}{dx^2}=0$ A) $\left(c_1+c_2x\right)+c_3e^x$. B) $\left(c_1+c_2x\right)+c_3e^{-x}$. C) $\left(c_1+c_2\right)+c_3e^x$. D) $\left(c_1+c_2x\right)+c_3e^{-2x}$. Show Answer Correct Answer: B) $\left(c_1+c_2x\right)+c_3e^{-x}$. 14. Evaluate the integral \( \int ..... 0^\{\pi\} \sin(x) \, dx \). A) 3. B) \(\frac\{\pi\}\{2\}\). C) 1. D) 2. Show Answer Correct Answer: D) 2. 15. $\frac{dy}{dx}=x+y$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 16. If y satisfies $\frac{dy}{dx}=\frac{1}{2y}$ A) $\tfrac12\ln|x|+3$. B) $\tfrac12\ln|y|+3$. C) $\sqrt{x+3}$. D) $\sqrt{x}+3$. Show Answer Correct Answer: C) $\sqrt{x+3}$. 17. If $f'\left(a\right)=0$ $f'\left(x\right)$ $x=a$ $f\left(x\right)$ A) A relative maximum at x=a. B) A relative minimum at x=a. C) No relative extrema at x=a. D) A vertical tangent line at x=a. Show Answer Correct Answer: A) A relative maximum at x=a. 18. If u is homogeneous function of order n then $\frac{\partial u}{\partial x}\, \\frac{\partial u}{\partial y}$ A) N. B) N-1. C) N+1. D) N-2. Show Answer Correct Answer: B) N-1. 19. If $\frac{dy}{dx}=\sin x\\cos^2x$ $\frac{\pi}{2}$ A) -1. B) -1/3. C) 1/3. D) 1. Show Answer Correct Answer: B) -1/3. 20. Use separation of variables to solve the differential equation $\frac{dy}{dx} = \frac{y}{x}$ A) $y = Cx$. B) $y = Cx^2$. C) $y = C\ln(x)$. D) $y = Cx^3$. Show Answer Correct Answer: A) $y = Cx$. 21. Clairaut's equation geometrically represents: A) A set of tangents. B) A set of circles. C) Straight lines with slope p. D) None. Show Answer Correct Answer: A) A set of tangents. 22. $L^{-1}\left[\frac{1}{\left(s+3\right)^2+25}\right]=$ A) $\frac{1}{3}e^{-3x}\sin5x$. B) $\frac{1}{5}e^{-3x}\sin5x$. C) $e^{-2x}\left(1-2x\right)$. D) $e^{-x}\left(1-x\right)$. Show Answer Correct Answer: B) $\frac{1}{5}e^{-3x}\sin5x$. 23. Degree of Differential equation is A) Power of highest order derivative. B) Highest power. C) Highest order derivative in DE. D) None of above. Show Answer Correct Answer: A) Power of highest order derivative. 24. A puppy weighs 2.0 pounds at birth and 3.5 pounds two months later. If the weight of the puppy during its first 6 months is increasing at a rate proportional to its weight, then how much will the puppy weigh when it is 3 months old? A) 4.2 Pounds. B) 4.6 Pounds. C) 4.8 Pounds. D) 5.6 Pounds. E) 6.5 Pounds. Show Answer Correct Answer: B) 4.6 Pounds. 25. Suppose $y(x)$ $\frac{dy}{dx} = 2y$ $y(0) = 3$ A) $y = 2x + 3$. B) $y = 3e^{2x}$. C) $y = 2e^{3x}$. D) $y = 3x^2$. Show Answer Correct Answer: B) $y = 3e^{2x}$. ← 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