This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 7 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 7 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $L\left(e^{ax}\right)= ..... $ A) $\frac{a}{s+a}$. B) $\frac{a}{s-a}$. C) $\frac{1}{s+a}$. D) $\frac{1}{s-a}$. Show Answer Correct Answer: D) $\frac{1}{s-a}$. 2. The number of radioactive atoms, N, in a sample is described by the differential equation $\frac{dN}{dt}=-kN$ A) 0.545. B) 1.290. C) 1.835. D) 2.380. Show Answer Correct Answer: C) 1.835. 3. If Y is the complementary function and u is the particular integral then the general solution of (D$^{n}$ + a$_{1}$D$^{n-1}$ + a$_{2}$D$^{n-2}$ + ..... + a$_{n}$) y = X is of the form A) Y = c$_{1}$Y + c$_{2}$u. B) Y = Y + u. C) Y = y + u. D) Y = c$_{1}$y+ c$_{2}$u. Show Answer Correct Answer: B) Y = Y + u. 4. In a garden, the rate flowers bloom F with respect to time t is inversely proportional to the square of the amount of rain R (in inches). Approximately 8 flowers bloom per day with 2.6 inches of rain. A) $\frac{dF}{dt}=\frac{4.96}{R^2}$. B) $\frac{dF}{dt}=1.18\sqrt[]{R}$. C) $\frac{dF}{dt}=\frac{12.9}{\sqrt[]{R}}$. D) $\frac{dF}{dt}=\frac{54.08}{R^2}$. Show Answer Correct Answer: D) $\frac{dF}{dt}=\frac{54.08}{R^2}$. 5. Let $y=f(x)$ $\frac{dy}{dx}=x-2y$ $f(3)=2$ $f(4)$ $x=3$ A) $-1$. B) $\tfrac14$. C) $\tfrac34$. D) $\tfrac74$. Show Answer Correct Answer: D) $\tfrac74$. 6. $\frac{dy}{dx}=6y^2x$ $y\left(1\right)=\frac{1}{25}$ A) $y=28-3x^2$. B) $y=\frac{1}{28-3x^2}$. C) $y=\frac{1}{3x^2-28}$. D) None of the above. Show Answer Correct Answer: B) $y=\frac{1}{28-3x^2}$. 7. Please find $\lim_{x\rightarrow0}\frac{2x+\tan3x}{\sin x}$ A) 0. B) 2. C) 5. D) $\infty$. Show Answer Correct Answer: C) 5. 8. What is the order in the given differential equation:(1-x) y" -4xy' + 5y = cosx A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: B) 2. 9. Legendre's type equations are transformed into: A) Algebraic equations. B) First-order equations. C) Linear equations with constant coefficients. D) Separable differential equations. Show Answer Correct Answer: C) Linear equations with constant coefficients. 10. The general form of a linear differential equation with constant coefficients involves: A) Powers of derivatives with constant multipliers. B) Homogeneous functions only. C) Exponential terms. D) None. Show Answer Correct Answer: A) Powers of derivatives with constant multipliers. 11. Solve using Lagrange's multipliers(y-2)p+(z-x)q=(x-y) A) F(x+y+z, x$^{2}$+ y$^{2}$+z$^{2}$)=0. B) F(y+z, x$^{2}$+ y$^{2}$+z$^{2}$)=0. C) F(y+z, x$^{2}$+ y$^{2}$)=0. D) F(x+3y+2z, 6x$^{2}$+ y$^{2}$+z$^{2}$)=0. Show Answer Correct Answer: A) F(x+y+z, x$^{2}$+ y$^{2}$+z$^{2}$)=0. 12. At each point on a certain curve, the slope of the curve is $3x^2=\frac{\text{d}y}{\text{d}x}$ A) $y=8e^{x^3}$. B) $y=x^3+8$. C) $y=e^{x^3}+7$. D) $y=\ln\left(x+1\right)+8$. Show Answer Correct Answer: B) $y=x^3+8$. 13. For the system dx/dt=3x+4y, dy/dt=-4x+3y, the general solution is: A) Real exponentials. B) Oscillatory (sine and cosine terms). C) Polynomials. D) Constant solutions. Show Answer Correct Answer: B) Oscillatory (sine and cosine terms). 14. Which of the following is the graph of the solution to the differential equation $\frac{dy}{dx} =-2y$ A) A line with a positive slope. B) A line with a negative slope. C) An exponential decay curve. D) An exponential growth curve. Show Answer Correct Answer: C) An exponential decay curve. 15. At the point of discontinuity, sum of the series is equal to ..... A) 1/2[f(x+0)-f(x-0)]. B) 1/2[f(x+0)+f(x-0)]. C) 1/4[f(x+0)-f(x-0)]. D) 1/4[f(x+0)+f(x-0)]. Show Answer Correct Answer: B) 1/2[f(x+0)+f(x-0)]. 16. Now that we have separated, what would be the correct integration? $e^{-y}dy=e^xdx$ A) $e^y=e^x+c$. B) $e^{-y}=e^x+c$. C) $-e^{-y}=-e^x+c$. D) $-e^{-y}=e^x+C$. Show Answer Correct Answer: D) $-e^{-y}=e^x+C$. 17. The solution of y" '-y" -y'+y=0 is obtained by: A) Using separation of variables. B) Finding characteristic roots. C) Applying Laplace transforms. D) Direct integration. Show Answer Correct Answer: B) Finding characteristic roots. 18. What is the order & degree of the p.d.e $x^2\left(\frac{\partial z}{\partial x}\right)^2=z\left(x-y\frac{\partial z}{\partial y}\right)$ A) 1 & 2. B) 2 & 1. C) 2 & 2. D) None of the above. Show Answer Correct Answer: A) 1 & 2. 19. $\frac{\partial^2z}{\partial x^2}+\frac{\partial^2z}{\partial x\partial y}-2\frac{\partial^2z}{\partial y^2}=0$ 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) $Z=f_1\left(y+x\right)+f_2\left(y-2x\right)$. 20. (D$^{2}$-4)y=0 has particular integral alone as general solution. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 21. $\overrightarrow{a}\times\overrightarrow{b}=\overrightarrow{0}$ $\overrightarrow{a}$ $\overrightarrow{b}$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 22. If A has distinct real eigenvalues, then solution trajectories are A) Spiral. B) Straight line combination of eigenvalues. C) Circles. D) Always unstable. Show Answer Correct Answer: B) Straight line combination of eigenvalues. 23. The solution of y" -4y'+4y=0 is: A) $c_1e^{2x}+c_2e^{-2x}$. B) $c_1e^{2x}+c_2xe^{2x}$. C) $c_1e^{-2x}+c_2e^{2x}$. D) $c_1e^{4x}+c_2e^{-4x}$. Show Answer Correct Answer: B) $c_1e^{2x}+c_2xe^{2x}$. 24. Which of the following differential equations best models exponential growth? A) $\frac{dy}{dt} =-ky$. B) $\frac{dy}{dt} = ky$. C) $\frac{dy}{dt} = k$. D) $\frac{dy}{dt} = y^2$. Show Answer Correct Answer: B) $\frac{dy}{dt} = ky$. 25. What would the sign of the square root after finding c be given the initial condition g(1)=-5 A) Positive. B) Negative. C) All the above. D) None of the above. Show Answer Correct Answer: B) Negative. ← 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 8Class 12 Mathematics Chapter 9 Differential Equations Quiz 9Class 12 Mathematics Chapter 9 Differential Equations Quiz 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books