This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 18 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 18 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which of the following is a solution to the differential equation $\frac{dy}{dx} = x^2y$ A) $y = Ce^{x^3/3}$. B) $y = Ce^{x^2}$. C) $y = Cx^2$. D) $y = Cx^3$. Show Answer Correct Answer: A) $y = Ce^{x^3/3}$. 2. What are some common techniques used to solve partial differential equations? A) Euler's method, Newton's method, Runge-Kutta method. B) Separation of variables, method of characteristics, finite difference method, finite element method, and spectral methods. C) Taylor series method, Bisection method, Secant method. D) Gaussian elimination, LU decomposition, Cholesky decomposition. Show Answer Correct Answer: B) Separation of variables, method of characteristics, finite difference method, finite element method, and spectral methods. 3. Findthe general solution to the following DE:$\frac{dy}{dx}-\frac{2y}{x+1}=3x^4$ A) $y=\left(x+1\right)^2\left(\frac{3}{5}x^5+c\right)$. B) $y=\left(x+1\right)^2\left(\frac{3}{5}x^5\right)+c$. C) $y=\left(x+1\right)^3\left(3x^4+c\right)$. D) $y=\left(x+1\right)^2\left(3x^4+c\right)$. Show Answer Correct Answer: A) $y=\left(x+1\right)^2\left(\frac{3}{5}x^5+c\right)$. 4. The value of $\int_0^a\int_0^axdxdy$ A) 1/2. B) $\frac{a^3}{2}$. C) $\frac{a^3}{3}$. D) $\frac{a^2}{2}$. Show Answer Correct Answer: B) $\frac{a^3}{2}$. 5. For the equation y" +y'+y=0, the roots of the auxiliary equation are: A) Real and distinct. B) Real and equal. C) Complex conjugates. D) All imaginary. Show Answer Correct Answer: C) Complex conjugates. 6. What is the order of the equation y" + 3y'-4y = 0? A) 3. B) 1. C) 2. D) 4. Show Answer Correct Answer: C) 2. 7. What is a second order differential equation? A) Is a differential equation whose highest derivative is to power two. B) Is an equation that is differentiated twice. C) Is a differential equation that is equated to two. D) Is any equation that is differentiable. Show Answer Correct Answer: A) Is a differential equation whose highest derivative is to power two. 8. If the characteristic equation has two distinct real roots $r_1$ $r_2$ $y" + ay' + by = 0$ A) $y(x) = Ce^{r_1x} + De^{r_2x}$. B) $y(x) = Ce^{rx}$. C) $y(x) = C\sin(rx) + D\cos(rx)$. D) $y(x) = Ce^{r_1x} + De^{r_1x}$. Show Answer Correct Answer: A) $y(x) = Ce^{r_1x} + De^{r_2x}$. 9. $\frac{\partial^2f}{\partial x^2}+\frac{\partial^2f}{\partial y^2}=0$ A) $f\left(x, t\right)$. B) $f\left(x, y\right)$. C) $y\left(f, x\right)$. D) $x=f\left(y, t\right)$. Show Answer Correct Answer: B) $f\left(x, y\right)$. 10. Which function grows the fastest as $x$ A) $x^2$. B) $\ln x$. C) $\sin x$. D) $e^x$. Show Answer Correct Answer: D) $e^x$. 11. What are the boundary conditions in the context of solving partial differential equations? A) Conditions specified at the initial time step. B) Conditions specified at random points in the domain. C) Conditions specified on the boundaries of the domain. D) Conditions specified inside the domain. Show Answer Correct Answer: C) Conditions specified on the boundaries of the domain. 12. A set of linear differential equations of first order with constant coefficients, $\frac{d\vec{x}}{dt}=A\\vec{x}$ A) It is inhomogeneous. B) The matrix A must always be invertible. C) You mainly have to compute the eigenvalues of the matrix. D) I don't know. Show Answer Correct Answer: C) You mainly have to compute the eigenvalues of the matrix. 13. $\left(\tan x\right)y'+y=2\sin(x)$ A) $y=\frac{(k-2\cos(x))}{(\sin(2x))}$. B) $y=\frac{(k-2\cos(x))}{\sin(x)}$. C) $y=\frac{(k-2\cos(2x))}{2\sin(x)}$. D) $y=\frac{(k-\cos(x))}{2\sin(2x)}$. Show Answer Correct Answer: C) $y=\frac{(k-2\cos(2x))}{2\sin(x)}$. 14. Page 392 # 13 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: E) E. 15. What is the degree of a differential equation? A) The number of solutions to the equation. B) The highest order derivative present. C) The highest power of the highest order derivative. D) The number of variables in the equation. Show Answer Correct Answer: C) The highest power of the highest order derivative. 16. Consider the differential equation $\frac{dy}{dx}=x+4y+2$ $y=f\left(x\right)$ $f\left(0\right)=k$ $f\left(1\right)\approx\frac{11}{4}$ A) $-\frac{19}{60}$. B) $-\frac{1}{6}$. C) $-\frac{5}{36}$. D) $\frac{3}{20}$. Show Answer Correct Answer: B) $-\frac{1}{6}$. 17. A bacteria culture grows at a constant relative growth rate. The count was 400 after 2 hours and 25, 600 after 6 hours. Find the value of k, the constant relative growth rate. A) $\frac{\ln\left(64\right)}{4}$. B) $\frac{\ln\left(64\right)}{6}$. C) $\frac{e^{64}}{4}$. D) $\frac{\ln25, 600}{4}$. Show Answer Correct Answer: A) $\frac{\ln\left(64\right)}{4}$. 18. Determine whether the functions $y_{1} = e^{2x}$ $y_{2} = e^{-4x}$ A) Yes, they are linearly independent. B) No, they are linearly dependent. C) They are orthogonal. D) Not defined. Show Answer Correct Answer: A) Yes, they are linearly independent. 19. Standard form for a pair of ordinary simultaneous equation of the first order but first degree A) Dx/p=dY/Q=dz/R. B) Dx/l=dy/m=dz/n. C) Dx/p=dy/Q=dz/R. D) Dx/l+dy/m+dz+n. Show Answer Correct Answer: A) Dx/p=dY/Q=dz/R. 20. If dy/dt = ky and k is a nonzero constant, then y could be A) $kt+5$. B) $e^{kt}+3$. C) $69e^{kt}$. D) $2e^{kty}$. Show Answer Correct Answer: C) $69e^{kt}$. 21. Find the complementary function of $\frac{\partial^2z}{\partial x^2}+\frac{\partial^2z}{\partial x\partial y}-2\frac{\partial^2z}{\partial y^2}=0$ A) $Z=f_1\left(y+x\right)+f_2\left(y-2x\right)$. B) $Z=f_1\left(y-x\right)+f_2\left(y+2x\right)$. C) $Z=f_1\left(y\right)+f_2\left(y+2x\right)$. D) $Z=f_1\left(y+x\right)+xf_2\left(y-2x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y+x\right)+f_2\left(y-2x\right)$. 22. Dy/dx= tanx+15x$^{2}$+e$^{x}$+1/x A) Y=-ln|sinx| + 5x$^{3}$ + e$^{x}$ + ln|x| + c. B) Y= secxtanx + 5x$^{3}$ + e$^{x}$ + ln|x| + c. C) Y=-ln|cosx| + 5x$^{3}$ + e$^{x}$ + ln|x| + c. D) Y= sec$^{2}$(x) + 5x$^{3}$ + e$^{x}$ + ln|x| + c. Show Answer Correct Answer: C) Y=-ln|cosx| + 5x$^{3}$ + e$^{x}$ + ln|x| + c. 23. " +140y'+49y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: D) CRITICALLY DAMPED. 24. Number of arbitrary constant in the general solution of a differential equation of degree 3 and order 4 is A) 3. B) 4. C) 0. D) 4$^{3}$. Show Answer Correct Answer: B) 4. 25. Solve the differential equation xdy/dx =y-xtan(y/x) A) Sin(y/x) =c/x. B) -sin(y/x) =c/x. C) Cos(y/x) =c/x. D) Tan(y/x) =c/x. Show Answer Correct Answer: A) Sin(y/x) =c/x. ← 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