This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 30 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 30 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Solve the homogeneous equation:y" -5y' + 6y = 0. A) Y(t) = C1 e$^{2t}$ + C2 e$^{3t}$. B) Y(t) = C1 + C2 e$^{6t}$. C) Y(t) = C1 e$^{t}$ + C2 e$^{4t}$. D) Y(t) = C1 e$^{3t}$ + C2 e$^{5t}$. Show Answer Correct Answer: A) Y(t) = C1 e$^{2t}$ + C2 e$^{3t}$. 2. Solve $\left(D^3-3D^2D'+2DD^{'2}\right)Z=0$ A) $Z=f_1\left(y\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. B) $Z=f_1\left(y-x\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. C) $Z=f_1\left(y\right)+xf_2\left(y+x\right)+f_3\left(y+2x\right)$. D) $Z=f_1\left(y\right)+f_2\left(y-x\right)+f_3\left(y-2x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. 3. The complete integral of $z=px+qy+f\left(p, q\right)$ A) $z=px+qy$. B) $z=ax+by+f\left(a, b\right)$. C) $z=f\left(a, b\right)$. D) None of the above. Show Answer Correct Answer: B) $z=ax+by+f\left(a, b\right)$. 4. Apply the initial condition $y(1) = 3$ $y = Cx^2$ $\frac{dy}{dx} = \frac{2y}{x}$ $C$ A) $C = 1$. B) $C = 2$. C) $C = 3$. D) $C = 4$. Show Answer Correct Answer: C) $C = 3$. 5. Find the complementary function for the differential equation A) . B) Y=. C) . D) . Show Answer Correct Answer: B) Y=. 6. The roots of the auxiliary equation $\frac{\text{d}x}{\text{d}y}+16y=0$ A) $y=A\cos16x+B\sin16x$. B) $y=A+Be^{-16x}$. C) $y=A\cos4x+B\sin4x$. D) $y=Ae^{4x}+Be^{-4x}$. Show Answer Correct Answer: C) $y=A\cos4x+B\sin4x$. 7. The general solution of $y'(t) + 8y(t) = 0$ A) $y = Ce^{8t}$. B) $y = Ce^{-8t}$. C) $y = e^{8t} + C$. D) None of the above. Show Answer Correct Answer: B) $y = Ce^{-8t}$. 8. What is the order of an equation in differential equations? A) The degree of the unknown function in the equation. B) The highest power of the unknown function's derivative in the equation. C) The number of variables in the equation. D) The sum of the coefficients in the equation. Show Answer Correct Answer: B) The highest power of the unknown function's derivative in the equation. 9. Solve the homogeneous equation 2y" + 3y' + y = 0. A) $y_c=Ae^{0.5x}+Be^x$. B) $y_c=Ae^{2x}+Be^x$. C) $y_c=Ae^{-0.5x}+Be^{-x}$. D) $y_c=Ae^{2x}+Be^{-x}$. Show Answer Correct Answer: C) $y_c=Ae^{-0.5x}+Be^{-x}$. 10. Y is proportional to the product of z and the square root of x A) $y=zx^2$. B) $y=kzx^2$. C) $y=kz\sqrt{x}$. D) $y=zkx$. Show Answer Correct Answer: C) $y=kz\sqrt{x}$. 11. A puppy weighs 2.0 pounds at birth and 3.5 pounds two months later. If the weight of the puppy during its first 6 months is increasing at a rate proportional to its weight, then how much will the puppy 3weigh when it is 3 months old? A) 4.6 pounds. B) 6.5 pounds. C) 4.8 pounds. D) 5 pounds. Show Answer Correct Answer: A) 4.6 pounds. 12. How can you represent a CPS using state diagrams? A) A CPS can only be represented using flowcharts. B) CPS representation requires only physical components without computational aspects. C) A CPS can be represented using state diagrams by defining states, transitions, and interactions between physical and computational components. D) State diagrams are not applicable to CPS representation. Show Answer Correct Answer: C) A CPS can be represented using state diagrams by defining states, transitions, and interactions between physical and computational components. 13. In the heat equation, the constant c2represents: A) Velocity of wave. B) Thermal diffusivity. C) Amplitude. D) Frequency. Show Answer Correct Answer: B) Thermal diffusivity. 14. If the number of arbitrary constants is less than or equal to number of independent variables then the pde obtained is of order A) >1. B) =1. C) <1. D) None of the above. Show Answer Correct Answer: B) =1. 15. $\int_{ }^{ }\frac{\left(\ln x\right)^2}{x}dx=$ A) $\left(\ln x\right)^2+C$. B) $\left(\ln x\right)^3+C$. C) $2\ln x+C$. D) $\frac{\left(\ln x\right)^3}{3}+C$. Show Answer Correct Answer: D) $\frac{\left(\ln x\right)^3}{3}+C$. 16. Which method is commonly used to find the particular solution when f(t) is a polynomial? A) Method of Variation of Parameters. B) Substitution Method. C) Method of Undetermined Coefficients. D) Laplace Transform Method. Show Answer Correct Answer: C) Method of Undetermined Coefficients. 17. Which of the following is a characteristic of a second-order linear PDE? A) It can only have one solution. B) It involves the second derivatives of the unknown function. C) It cannot be solved using separation of variables. D) It is always non-linear. Show Answer Correct Answer: B) It involves the second derivatives of the unknown function. 18. $y=\frac{5}{\sqrt{x-3}}$ A) $x>3$. B) $x<3$. C) $-3 D) $x\ne3$. Show Answer Correct Answer: A) $x>3$. 19. The curl of a vector valued function is a scalar valued function. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 20. $\frac{dy}{dx}=\frac{x+1}{y+2}$ A) Homogeneous. B) Nonhomogeneous. C) Not sure. D) None of the above. Show Answer Correct Answer: B) Nonhomogeneous. 21. Which of the following is the formula for growth and decay? A) $y=mx+b$. B) $y=e^{kt}$. C) $y=Ce^t$. D) $y=Ce^{kt}$. Show Answer Correct Answer: D) $y=Ce^{kt}$. 22. If $\frac{\text{d}y}{\text{d}x}=e^y$ A) $y=\ln\left|x\right|$. B) $y=\ln\left|2-x\right|$. C) $y=-\ln\left|x\right|$. D) $y=-\ln\left|2-x\right|$. Show Answer Correct Answer: D) $y=-\ln\left|2-x\right|$. 23. What is the characteristic of first order linear differential equations? A) They involve finding the solution at a specific point or along a specific curve. B) They are non-linear. C) They are partial differential equations. D) They involve initial and boundary value problems. Show Answer Correct Answer: D) They involve initial and boundary value problems. 24. In control theory, the stability of a system modeled by differential equations is determined by ..... A) Eigenvalues of the system matrix A. B) Determinant of A. C) Rank of A. D) Dimension of state vector. Show Answer Correct Answer: A) Eigenvalues of the system matrix A. 25. What is the method of characteristics? A) A technique for solving PDEs by transforming them into ODEs along characteristic curves. B) A process for integrating differential equations directly. C) A method for solving algebraic equations. D) A technique for graphing functions in three dimensions. Show Answer Correct Answer: A) A technique for solving PDEs by transforming them into ODEs along characteristic curves. ← 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