This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 17 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 17 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the definition of differential equations? A) Equations with unknown functions and their derivatives. B) Equations with known functions and their integrals. C) Equations with constant values and their derivatives. D) Equations with variables and their limits. Show Answer Correct Answer: A) Equations with unknown functions and their derivatives. 2. Is the differential equation dy/dx = sin(x) linear or nonlinear? A) Quadratic. B) Cubic. C) Nonlinear. D) Linear. Show Answer Correct Answer: C) Nonlinear. 3. Find the complementary function of $\frac{\partial^3z}{\partial x^3}-3\frac{\partial^3z}{\partial x^2\partial y}+4\frac{\partial^3z}{\partial y^3}=0$ A) $Z=f_1\left(y-x\right)+f_2\left(y+2x\right)+xf_3\left(y+2x\right)$. B) $Z=f_1\left(y-x\right)+f_2\left(y+2x\right)+f_3\left(y-2x\right)$. C) $Z=f_1\left(y-x\right)+f_2\left(y+2x\right)+f_3\left(y+2x\right)$. D) $Z=f_1\left(y+x\right)+f_2\left(y+2x\right)+xf_3\left(y+2x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y-x\right)+f_2\left(y+2x\right)+xf_3\left(y+2x\right)$. 4. The number of bacteria increases at a rate proportional to the present amount. After 5 hours, there were 80 bacteria and after 8 hours, there were 120 bacteria. How many bacteria were present initially? A) 1. B) About 16. C) About 40. D) About 53. Show Answer Correct Answer: C) About 40. 5. Solve the following differential equations:$\frac{\text{d}y}{\text{d}x}=\frac{1}{\cos y}$ A) $\sin y=1+C$. B) $\sin y=x+C$. C) $-\sin y=\frac{x^2}{2}+C$. D) $\sin y=0+C$. Show Answer Correct Answer: B) $\sin y=x+C$. 6. How are partial differential equations different from ordinary differential equations? A) Partial differential equations have no variables. B) Partial differential equations are the same as ordinary differential equations. C) Partial differential equations involve only one variable. D) Partial differential equations involve functions of multiple variables. Show Answer Correct Answer: D) Partial differential equations involve functions of multiple variables. 7. Solve $\left(D^2-5D+6\right)y=0$ A) $y=c_1e^x+c_2e^{2x}$. B) $y=c_1e^{3x}+c_2e^{2x}$. C) $y=c_1e^{-3x}+c_2e^{2x}$. D) $y=c_1e^{-3x}+c_2e^{-2x}$. Show Answer Correct Answer: B) $y=c_1e^{3x}+c_2e^{2x}$. 8. What type of differential equations can be solved using the method of undetermined coefficients? A) First order linear. B) Nonlinear. C) Higher order linear with constant coefficients. D) Partial differential equations. Show Answer Correct Answer: A) First order linear. 9. F(s) = L\{(t$^{n}$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: D) N!/(s-a)$^{(n+1)}$. 10. What do conjugate pairs in complex numbers involve? A) Numbers with the same real part and same imaginary part. B) Numbers with different real parts and different imaginary parts. C) Numbers with the same real part but opposite imaginary parts. D) Numbers with opposite real parts but same imaginary parts. Show Answer Correct Answer: C) Numbers with the same real part but opposite imaginary parts. 11. The population P(t) of a species satisfies the logistic differential equation dP/dt=P(2-P/5000), Where the initial population P(0)=3000 and t is time in years. What is lim(t$\rightarrow$infinity)P(t)? A) 2500. B) 3000. C) 4200. D) 5000. E) 10000. Show Answer Correct Answer: A) 2500. 12. Determine the general solution of $y"+5y'+6y=0$ A) $y=C_1e^{-3x}+C_2xe^{-2x}$. B) $y=C_1e^{-3x}+C_2e^{-2x}$. C) $y=e^{-3x}\left(C_1\cos2x+C_2\sin2x\right)$. D) $y=C_1e^{3x}+C_2e^{-2x}$. Show Answer Correct Answer: B) $y=C_1e^{-3x}+C_2e^{-2x}$. 13. Water flows continuously from a large tank at a rate proportional to the amount of water in the tank, modeled by dy/dt = ky. There was initially 10, 000 ft$^{3}$ at t=0. After 4 hours there were 8000 ft$^{3}$ remaining.What is the value of k in the differential equation? A) -0.050. B) -0.056. C) -.169. D) -.200. Show Answer Correct Answer: B) -0.056. 14. The value of $\int_{ }\int_{ }dxdy$ A) 2. B) 0. C) 3. D) 4. Show Answer Correct Answer: D) 4. 15. What is the number of arbitrary constant in a particular solution of a differential equation of order 3 and degree2? A) 2. B) 3. C) 3$^{2}$. D) 0. Show Answer Correct Answer: D) 0. 16. Find the complementary function of $\left(D^3-7DD'^2-6D'^3\right)z=0$ A) $Z=f_1\left(y-x\right)+f_2\left(y-2x\right)+f_3\left(y+3x\right)$. B) $Z=f_1\left(y+x\right)+f_2\left(y+2x\right)+f_3\left(y-3x\right)$. C) $Z=f_1\left(y+x\right)+f_2\left(y-2x\right)+xf_3\left(y+3x\right)$. D) $Z=f_1\left(y-x\right)+f_2\left(y\right)+f_3\left(y+3x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y-x\right)+f_2\left(y-2x\right)+f_3\left(y+3x\right)$. 17. The velocity function is $v(t) = 4t-5$ $s(t)$ $s(0) = 2$ A) $s(t) = 2t^2-5t + 2$. B) $s(t) = 2t^2-5t$. C) $s(t) = 2t^2 + 5t + 2$. D) $s(t) = 2t^2 + 5t$. Show Answer Correct Answer: A) $s(t) = 2t^2-5t + 2$. 18. What are the challenges in modeling Zeno behavior? A) Zeno behavior is easily modeled with simple equations. B) There are no significant challenges in understanding Zeno behavior. C) The challenges in modeling Zeno behavior include dealing with infinite divisibility, reconciling discrete and continuous motion, and addressing philosophical implications of paradoxes. D) Zeno behavior only applies to physical objects in motion. Show Answer Correct Answer: C) The challenges in modeling Zeno behavior include dealing with infinite divisibility, reconciling discrete and continuous motion, and addressing philosophical implications of paradoxes. 19. Given that the acceleration of an object satisfies the differential equation $e^t\frac{dv}{dt}=2\sqrt{v}$ $v=1.$ A) $v=\left(2-e^{-t}\right)^2$. B) $v=\left(3-2e^{-t}\right)^2$. C) $v=\left(2e^{-t}-1\right)^2$. D) None of the above. Show Answer Correct Answer: A) $v=\left(2-e^{-t}\right)^2$. 20. Y" =-12y A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: C) UNDAMPED. 21. If eigenvalues of system matrix have negative real parts, the system is ..... A) Stable. B) Unstable. C) Saddle. D) Neutral. Show Answer Correct Answer: A) Stable. 22. The nature of PDE 4u$_{xx }$+3 u$_{xy }$+3 u$_{yy}$=0 A) Parabolic. B) Hyperbolic. C) Elliptic. D) Laplace. Show Answer Correct Answer: C) Elliptic. 23. $\frac{dy}{dt}+y=e^t$ A) Linear. B) Nonlinear. C) Not sure. D) None of the above. Show Answer Correct Answer: A) Linear. 24. In the steady state, 2-D heat equation reduces to A) 1-D heat equation. B) 1-D wave equation. C) Laplace equation. D) None of these. Show Answer Correct Answer: C) Laplace equation. 25. Determine the degree of the differential equation:$\left(\frac{d^3y}{dx^3}\right)^4 + \left(\frac{d^2y}{dx^2}\right)^2 + \frac{dy}{dx} = 0$ A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: D) 4. ← 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