This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 14 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 14 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the integral of for $f\left(t\right)=t^3$ A) $\frac{1}{4}$. B) $\frac{2}{3}$. C) $\frac{6}{ }$. D) $3$. Show Answer Correct Answer: A) $\frac{1}{4}$. 2. Consider the vector u = (1, 2, 3) and v = (2, 3, 1) in R$^{3}$. If w = (1, k, 4) is a linear combination of u and v, then k= A) 11/5. B) 2. C) 3. D) 11. Show Answer Correct Answer: A) 11/5. 3. Given $y" + 2y' + 5y = 0$ A) $y(x) = Ce^{-x} + De^{-5x}$. B) $y(x) = Ce^{-x}\sin(2x) + De^{-x}\cos(2x)$. C) $y(x) = Ce^{-x}\sin(2x) + De^{-x}\cos(2x)$. D) $y(x) = Ce^{2x} + De^{-2x}$. Show Answer Correct Answer: B) $y(x) = Ce^{-x}\sin(2x) + De^{-x}\cos(2x)$. 4. From the following partial differential equations, the seperableequation is ..... A) $p-x=q-y$. B) $p-z=q-y$. C) $p-x=q-y$. D) $p+q=pq$. Show Answer Correct Answer: A) $p-x=q-y$. 5. $\frac{d^2y}{dx^2}+y=e^xx$ A) $\frac{e^xx}{2}$. B) $\frac{e^x\left(x-1\right)}{2}$. C) $\frac{e^xx}{3}$. D) $\frac{e^x\left(x+1\right)}{2}$. Show Answer Correct Answer: B) $\frac{e^x\left(x-1\right)}{2}$. 6. Suppose that $T:R^2\longrightarrow R^2$ A) (2, 5). B) (5, 11). C) (5, 2). D) (8, 5). Show Answer Correct Answer: B) (5, 11). 7. What is the order of the differential equation $y" +xy'+x^2y=\sin x$ A) 4. B) 3. C) 2. D) 1. Show Answer Correct Answer: C) 2. 8. What is a common error when trying to separate variables in differential equations? A) Subtracting variables instead of dividing. B) Adding instead of multiplying by dy/dx. C) Incorrectly applying the chain rule. D) Forgetting to add the constant of integration. Show Answer Correct Answer: B) Adding instead of multiplying by dy/dx. 9. Dy/dx = x-y-2 and f(-1) = 3. Use Euler's Method with three steps to approximate f(2). A) -1. B) 1. C) 0. D) 2. Show Answer Correct Answer: A) -1. 10. For $y" -y=e^x, $ A) $Ae^x$. B) $Axe^x$. C) $12xe^x$. D) $Ae^{-x}$. Show Answer Correct Answer: B) $Axe^x$. 11. What is the solution method for Bernoulli differential equations? A) Orthogonal trajectories. B) Linear Differential Equation. C) Separable differential equation. D) Method of Solution of Homogeneous Differential Equation. Show Answer Correct Answer: A) Orthogonal trajectories. 12. Solve the homogeneous equation y" -6y' + 9y = 0. A) $y_c=A+Bxe^{-3x}$. B) $y_c=Ae^{3x}+Bxe^{3x}$. C) $y_c=Ae^{3x}+Be^{3x}$. D) $y_c=Ae^x+Be^{3x}$. Show Answer Correct Answer: B) $y_c=Ae^{3x}+Bxe^{3x}$. 13. What is the first step in the method of variation of parameters? A) Solving the homogeneous equation. B) Determining the roots of the equation. C) Finding the general solution. D) Finding the Wronskian. Show Answer Correct Answer: A) Solving the homogeneous equation. 14. What is the general solution for the system of equations represented by dx/P=dy/Q=dz/R? A) Dx=ldx+mdy+ndz. B) Dx/P=dy/Q=dz/R. C) Dx=Qdy+Rdz. D) Dx=ky+lz. Show Answer Correct Answer: B) Dx/P=dy/Q=dz/R. 15. The unit normal to the surface $x^3-xyz+z^3=1$ A) $\frac{1}{3}\left(2i-j+2k\right)$. B) $\frac{2}{3}\left(2i-j+2k\right)$. C) $\frac{1}{3}\left(2i-2j+2k\right)$. D) $\frac{1}{3}\left(2i-j+k\right)$. Show Answer Correct Answer: A) $\frac{1}{3}\left(2i-j+2k\right)$. 16. Which of the following is true about the Cayley-Hamilton theorem? A) It reduces higher powers of A to linear combinations of lower powers. B) It Avoids the need for eigenvalues. C) It makes the determinant zero. D) It diagonalizes any matrix. Show Answer Correct Answer: A) It reduces higher powers of A to linear combinations of lower powers. 17. $L^{-1}\left(\frac{a}{s^2+a^2}\right)$ A) $e^{ax}$. B) Sin ax. C) Cos ax. D) $e^{-ax}$. Show Answer Correct Answer: B) Sin ax. 18. The particular integral of the equation $\left(D-1\right)y=e^{3x}$ A) $\frac{e^{3x}}{2}$. B) $\frac{e^{-3x}}{2}$. C) $\frac{e^{3x}}{4}$. D) $\frac{e^x}{2}$. Show Answer Correct Answer: A) $\frac{e^{3x}}{2}$. 19. What is a first order differential equation? A) A first order differential equation is an equation involving the first derivative of a function. B) A first order differential equation is an equation with no derivatives. C) A first order differential equation is a polynomial equation without variables. D) A first order differential equation involves second derivatives of a function. Show Answer Correct Answer: A) A first order differential equation is an equation involving the first derivative of a function. 20. The value of $curl\\overrightarrow{r}$ A) 0. B) $\overrightarrow{r}$. C) 1. D) $\overrightarrow{0}$. Show Answer Correct Answer: D) $\overrightarrow{0}$. 21. A differential equation in which the function depends on only one independent variable is called a ..... A) Partial differential equation. B) Linear equation. C) Ordinary differential equation. D) Non linear equation. Show Answer Correct Answer: C) Ordinary differential equation. 22. The auxiliary equation of the following ODE $\left(D^2-3D+5\right)y=0$ A) $m^2-3m+5=0$. B) $m^2+3m-5=0$. C) $m^2-3m+5$. D) $\left(m^2-3m+5\right)y=0$. Show Answer Correct Answer: A) $m^2-3m+5=0$. 23. In the method of multipliers, what is the primary goal? A) To analyze the behavior of functions in different dimensions. B) To simplify linear equations for easier calculations. C) To solve constrained optimization problems by transforming them into unconstrained problems. D) To identify the maximum value of a function without constraints. Show Answer Correct Answer: C) To solve constrained optimization problems by transforming them into unconstrained problems. 24. F(s) = L\{(e$^{at}$)\} (s) A) 1/s. B) N!/s$^{(n+1)}$. C) 1/(s-a). D) N!/(s-a)$^{(n+1)}$. E) S/(s$^{2}$+b$^{2}$). Show Answer Correct Answer: C) 1/(s-a). 25. Which of the following equations solves dy/dt = ky? A) $y=y_0e^{kt}$. B) $y=mx+b$. C) $y=a\left(x-h\right)^2+k$. D) $y=A\sin\left[B\left(x-C\right)\right]+D$. Show Answer Correct Answer: A) $y=y_0e^{kt}$. ← 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