This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 47 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 47 (18 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The degree of a differential equation is define by a A) Positive real number. B) Positive rational number. C) Positive integer. D) All the above. Show Answer Correct Answer: C) Positive integer. 2. If $\frac{\text{d}y}{\text{d}x}=3x^2-2$ $y\left(1\right)=4$ A) $y=x^3-2x$. B) $y=x^3-2x+4$. C) $y=x^3-2x+5$. D) $y=x^3-2x+1$. Show Answer Correct Answer: C) $y=x^3-2x+5$. 3. What is the linear span L(S) of the set $S=\left\{e_1, e_2, \frac{e_1+e_2}{2}\right\}$ $R^3$ A) Xy-plane. B) X-axis. C) Y-axis. D) Yz-plane. Show Answer Correct Answer: A) Xy-plane. 4. If the roots of the auxiliary equation in an ODE are 5 and 6, then complementary function is y= ..... A) $Ae^{5x}+Be^{6x}$. B) $Ae^{-5x}+Be^{-6x}$. C) $Ae^{5x}+xBe^{6x}$. D) None of the above. Show Answer Correct Answer: A) $Ae^{5x}+Be^{6x}$. 5. When sketching a solution curve on a slope field, what does the curve represent? A) The set of all possible slopes at each point. B) A particular solution to the differential equation passing through a given point. C) The general solution to the differential equation. D) The direction of increasing $x$. Show Answer Correct Answer: B) A particular solution to the differential equation passing through a given point. 6. Explain the concept of boundary conditions in PDEs. A) Boundary conditions are irrelevant in determining the solution's behavior in PDEs. B) Boundary conditions in PDEs define the behavior of solutions at the domain's edges, ensuring uniqueness and stability. C) Boundary conditions in PDEs only apply to linear equations, limiting their use. D) Boundary conditions in PDEs are solely concerned with initial values, not edges. Show Answer Correct Answer: B) Boundary conditions in PDEs define the behavior of solutions at the domain's edges, ensuring uniqueness and stability. 7. What type of differential equation is y" + y = 0? A) Second-order linear homogeneous differential equation with constant coefficients. B) Second-order non-linear homogeneous differential equation. C) Third-order linear non-homogeneous differential equation. D) First-order linear homogeneous differential equation with constant coefficients. Show Answer Correct Answer: A) Second-order linear homogeneous differential equation with constant coefficients. 8. What is a regular singular point? A) A point where the function has a discontinuity. B) A point where the Wronskian is zero. C) A point where the function is analytic. D) A point where the function is not analytic. Show Answer Correct Answer: D) A point where the function is not analytic. 9. CHOOSE THE CORRECT FORM OF PARTICULAR INTEGRAL FOR e$^{ax}$ A) PI=e$^{ax+by}$/f(a, b). B) PI=sinax / f(a, b). C) PI=cos$^{ax}$/f(-a$^{2}$, -ab, -b$^{2}$). D) PI=1f(-a$^{2}$, -ab, -b$^{2}$). Show Answer Correct Answer: A) PI=e$^{ax+by}$/f(a, b). 10. The purpose of state feedback in control is to ..... A) Modify eigenvalues of closed loop system. B) Increase system order. C) Make the system nonlinear. D) Reduce number of states. Show Answer Correct Answer: A) Modify eigenvalues of closed loop system. 11. Solve the Differential equation of ordwer 2y" -4y' + 3y = e$^{2x}$ for y(0) = 2 and y'(0) = 3 and find y when x =1 A) E$^{3x}$+2e$^{x}$. B) E$^{3}$+2e-e$^{2}$. C) E$^{3x}$+2e$^{x}$-e$^{2x}$. D) 2e$^{3}$. Show Answer Correct Answer: B) E$^{3}$+2e-e$^{2}$. 12. A Vector function $\overrightarrow{f}$ A) Grad $\overrightarrow{f}$. B) Curl $\overrightarrow{f}$. C) Div $\overrightarrow{f}\ne0$. D) Div $\overrightarrow{f}$. Show Answer Correct Answer: D) Div $\overrightarrow{f}$. 13. $\frac{dy}{dx}=x^2+3$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 14. The nature of PDE 4u$_{xx }$+3 u$_{xy }$=0 A) Circular. B) Elliptic. C) Hyperbolic. D) Parabolic. Show Answer Correct Answer: C) Hyperbolic. 15. The general form of a first order linear differential equation is: A) Dy/dx + P(x)y = Q(x). B) $\frac{d^2y}{dx^2} + P(x)\frac{dy}{dx} = Q(x)$. C) $\frac{dy}{dx} = P(x)y^2 + Q(x)$. D) $dy/dx + P(x)y^2 = Q(x)$. Show Answer Correct Answer: A) Dy/dx + P(x)y = Q(x). 16. A partial differential equation is formed by eliminating: A) Independent variables. B) Dependent variables. C) Arbitrary constants or functions. D) Coefficients. Show Answer Correct Answer: C) Arbitrary constants or functions. 17. The nature of the one-dimensional wave equation is A) Hyperbolic. B) Parabolic. C) Elliptic. D) None of These. Show Answer Correct Answer: A) Hyperbolic. 18. The complementary function of the equation $\frac{d^2y}{dx^2}+2\frac{\text{d}y}{\text{d}x}+y=0$ A) $c_1e^x+c_2e^{-x}$. B) $c_1e^{-x}+c_2e^{-x}$. C) $c_1e^x+c_2e^x$. D) $\left(c_1+c_2x\right)e^{-x}$. Show Answer Correct Answer: D) $\left(c_1+c_2x\right)e^{-x}$. ← PreviousRelated 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