This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 40 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 40 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Part C. Find the equation (inverse method) from the general solution:19. y = $C_{1}e^{4x} + C_{2}e^{-x}$ A) Y" -3y'-4y = 0. B) Y" + 3y' + 4y = 0. C) Y" -4y' + 3y = 0. D) Y" + y'-4y = 0. Show Answer Correct Answer: A) Y" -3y'-4y = 0. 2. What does the Hessian matrix of a function f(x, y) consist of? A) First-order partial derivatives of f. B) Second-order partial derivatives of f. C) Gradient vector of f. D) Integral of f. Show Answer Correct Answer: B) Second-order partial derivatives of f. 3. The integrating factor of y(1+xy)dx + (2y-x)dy =0 [s A) X$^{2}$y$^{2}$. B) Y$^{2}$. C) Y$^{-2}$. D) X$^{2}$. Show Answer Correct Answer: C) Y$^{-2}$. 4. If the roots of differential equation are real and equal then C. F is C$_{1}$e$^{m1x}$+C$_{2}$e$^{m2x}$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 5. Methods to solve DE are ..... A) Integration and Differentiation. B) Integration and Separable Variable Method. C) Integrating Factor and Separable Variable Methods. D) Separable Variable Methods only. Show Answer Correct Answer: C) Integrating Factor and Separable Variable Methods. 6. For what value of k, if any, is $y=e^{2x}+ke^{-3x}$ $4y-y"=10e^{-3x}$ A) -2. B) 10/3. C) 10. D) There is no such value of k. Show Answer Correct Answer: A) -2. 7. Y" = 12x; y'(-1) = 10 and y(2) = 22Find 2y" + 3y'-y A) $-2x^3+18x^2+20x+14$. B) $-2x^3+18x^2+28x+10$. C) $-3x^3+18x^2+20x+22$. D) $-3x^3+6x^2+20x-6$. Show Answer Correct Answer: A) $-2x^3+18x^2+20x+14$. 8. A non-empty set W of V(F) is a subspace V if and only if $u, v\\in W$ $\alpha, \\beta\\in F$ A) $\alpha u+\beta v\\in W$. B) $u+v\\in W$. C) $\alpha u\\in W$. D) $\beta u\\in W$. Show Answer Correct Answer: A) $\alpha u+\beta v\\in W$. 9. Find the Partial derivative of f with respect to y for $f\left(x, y\right)=\frac{y^2}{x+y}$ A) $\frac{2x+y}{\left(x+y\right)^2}$. B) $\frac{2xy+y^2}{\left(x+y\right)^2}$. C) $\frac{2}{\left(x+y\right)^{ }}$. D) $\frac{2x^2+y^2}{\left(x+y\right)^2}$. Show Answer Correct Answer: B) $\frac{2xy+y^2}{\left(x+y\right)^2}$. 10. What is a partial differential equation? A) An equation involving derivatives with respect to one variable. B) An equation involving derivatives with respect to multiple variables. C) An equation that has no solutions. D) An equation that is always true. Show Answer Correct Answer: B) An equation involving derivatives with respect to multiple variables. 11. Find N(T) if $T:R^3\longrightarrow R^2$ $T\left(x, y, z\right)=\left(x-y, 2z\right)$ A) $N\left(T\right)=\left\{\left(a, 0, 0\right):a\text{ }\in R\right\}$. B) $N\left(T\right)=\left\{0\text{ }\right\}$. C) $N\left(T\right)=R^2$. D) $N\left(T\right)=\left\{\left(a, a, 0\right):a\in R\text{ }\right\}$. Show Answer Correct Answer: D) $N\left(T\right)=\left\{\left(a, a, 0\right):a\in R\text{ }\right\}$. 12. The derivative of the matrix exponential is ..... A) $d/dt e^{At} = A$. B) $d/dt e^{At} = Ae^{At}$. C) $d/dt e^{At}$. D) $d/dt e^{At} = e^{At} + A$. Show Answer Correct Answer: B) $d/dt e^{At} = Ae^{At}$. 13. Solve the differential equation. $y'=x^2y$ A) $y=\frac{x^2}{2}+C$. B) $\ln\left|y\right|=\frac{x^2}{2}+C$. C) $\ln\left|y\right|=\frac{x^3}{3}+C$. D) $\left|y\right|=x^2+C$. Show Answer Correct Answer: C) $\ln\left|y\right|=\frac{x^3}{3}+C$. 14. Water flows continuously from a large tank at a rate proportional to the amount of water in the tank, modeled by $\frac{dy}{dt}=ky$ $ft^3$ $t=0$ $ft^3$ $k$ A) -0.050. B) -0.056. C) -.169. D) -.200. Show Answer Correct Answer: B) -0.056. 15. Using the separation of variables, what is the solution of the differential equation $y'=-\frac{x}{y}$ $y\left(1\right)=4$ A) $y^2=14+2x^2$. B) $y^2=18-2x^2$. C) $y^2=15+x^2$. D) $y^2=17-x^2$. Show Answer Correct Answer: D) $y^2=17-x^2$. 16. Write a differential equation that describes each relationship. If necessary, use k as the constant of proportionality. The number of packets, p, Mr. Sullivan completes for Pre-Calculus is increasing as he nears the end of the school year. The rate of change of p with respect to time t is inversely proportional to the natural log of t. A) Dp/dt = k * ln(t). B) Dp/dt = k / ln(t). C) Dp/dt = k * t. D) Dp/dt = k / t. Show Answer Correct Answer: B) Dp/dt = k / ln(t). 17. The expression 12(1.015)$^{t}$ models the population of elephants in a wildlife refuge after t years since 1975.What does the value 1.015 represent? A) The number of elephants was 1, 015 in 1975. B) The number of elephants increases by 1.5% each year. C) The number of elephants increases by 101.5% each year. D) The number of elephants is multiplied by 1.015 each year. Show Answer Correct Answer: B) The number of elephants increases by 1.5% each year. 18. What is the notation for the first derivative of y with respect to x? A) Y'. B) Dy/dx. C) D/dx(y). D) D(y)/d(x). Show Answer Correct Answer: A) Y'. 19. $L\left[f" \left(x\right)\right]=s^2L\left[f\left(x\right)\right]-f\left(0\right)-f'\left(0\right)$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 20. The value of $j\times k$ A) -i. B) 1. C) 0. D) I. Show Answer Correct Answer: D) I. 21. If the characteristic equation has a repeated root $r$ A) $y(x) = Ce^{rx}$. B) $y(x) = Ce^{rx} + De^{rx}$. C) $y(x) = Ce^{rx} + Dxe^{rx}$. D) $y(x) = Cx^r + Dx^r$. Show Answer Correct Answer: C) $y(x) = Ce^{rx} + Dxe^{rx}$. 22. Find the solution of y' + y = 0. A) $y = Ce^{x}$. B) $y = Ce^{-x}$. C) $y = e^{x}$. D) Y = Cx. Show Answer Correct Answer: B) $y = Ce^{-x}$. 23. What is the first step in forming a partial differential equation? A) Set the equation equal to zero. B) Identify the independent and dependent variables. C) Solve for the constants. D) Differentiate the equation. Show Answer Correct Answer: B) Identify the independent and dependent variables. 24. Find the area under the curve of \( f(x) = x^3 \) from \( x = 1 \) to \( x = 2 \). A) 3.75. B) 5.0. C) 4.0. D) 2.5. Show Answer Correct Answer: A) 3.75. 25. A virus has infected 1.8% of a population. A test detects this virus 95% of the time when it is actually present, but it returns a false positive 3% of the time when the virus is not present.If a person selected at random from this population tests positive for the virus, what is the probability that this person is actually infected? [Round to the nearest percent.] A) 37%. B) 63%. C) 34%. D) 66%. Show Answer Correct Answer: A) 37%. ← 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