This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 42 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 42 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Separate the variables for the equation $\frac{dy}{dx}=\frac{(x^2+x-1)}{y^2}$ A) $(x^2+x-1)dx=\frac{1}{y^2}dy$. B) $\frac{y^2}{(x^2+x-1)}dy=dx$. C) $\left(y^2-1\right)dy=(x^2-1)dx$. D) $y^2dy=(x^2+x-1)dx$. Show Answer Correct Answer: D) $y^2dy=(x^2+x-1)dx$. 2. Gemma is ready for her driving test. The probability of her passing the first time is 0.65. If she fails her first test, the probability of her passing on the second attempt is 0.85.Calculate the probability Gemma passes in exactly two attempts. A) 0.85. B) .2975. C) .0525. D) .9475. Show Answer Correct Answer: B) .2975. 3. The following Differential Equation is $\frac{\text{d}y}{\text{d}x}=x^2y+x$ A) Separable. B) Non Separable. C) All the above. D) None of the above. Show Answer Correct Answer: B) Non Separable. 4. Which of the following mathematical models CANNOT be solved by using separation of variables A) $\frac{\text{d}P}{\text{dt}}=kP$. B) $\frac{dT}{dt}=k\left(T-Tm\right)$. C) $\frac{dA}{dt}=kA$. D) $L\\frac{dI}{dt}+RI=E\left(t\right)$. Show Answer Correct Answer: D) $L\\frac{dI}{dt}+RI=E\left(t\right)$. 5. Let $y=g\left(x\right)$ $\frac{dy}{dx}=xy-2$ $g\left(2\right)=-1$ A) -6.25. B) 1.25. C) 1.50. D) 3.00. Show Answer Correct Answer: B) 1.25. 6. An equation containing derivatives of one or more dependent variables with one or more independent variables? A) Partial Equation. B) Different Equation. C) Differential Equation. D) Ordinary Equation. Show Answer Correct Answer: C) Differential Equation. 7. The general solution of the equation $y' + 4y = 8$ $y(t) = Ce^{-4t} + 2$ $y(0)=9$ A) $y(t) = 7e^{-4t} + 2$. B) $y(t) = 9e^{-4t} + 2$. C) $y(t) = 11e^{-4t} + 2$. D) None of the above. Show Answer Correct Answer: A) $y(t) = 7e^{-4t} + 2$. 8. Average value is ..... A) $\frac{1}{b-a}\int_a^bf\left(x\right)dx$. B) $\frac{f\left(b\right)-f\left(a\right)}{b-a}$. C) $\int_a^bf\left(x\right)dx$. D) $y-y_1=m\left(x-x_1\right)$. Show Answer Correct Answer: A) $\frac{1}{b-a}\int_a^bf\left(x\right)dx$. 9. Y" +40y'+391y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: B) OVERDAMPED. 10. The equation $y=e^x-2$ A) Y'-y =-2. B) Y'-y = 2. C) Y' + y =-2. D) Y' + y = 2. Show Answer Correct Answer: B) Y'-y = 2. 11. What does the complementary function (CF) represent in the context of a second order ODE? A) The specific solution to the non-homogeneous equation. B) The solution to the characteristic equation. C) The general solution to the associated homogeneous equation. D) The derivative of the particular solution. Show Answer Correct Answer: C) The general solution to the associated homogeneous equation. 12. $.$ $\left(D^2-4DD'+4D'^2\right)Z=e^{\left(2x+y\right)}$ A) $\\frac{y^2}{2}e^{\left(2x+y\right)}$. B) $\frac{xy^{ }}{2}e^{\left(2x+y\right)}$. C) $\frac{x^2}{2}e^{\left(2x+y\right)}$. D) $\frac{x^2}{2}e^{\left(2y+x\right)}$. Show Answer Correct Answer: C) $\frac{x^2}{2}e^{\left(2x+y\right)}$. 13. If R(x) is an increasing concave up function, then a Trapezoidal Riemann sum will be an ..... A) Underapproximation. B) Overapproximation. C) All the above. D) None of the above. Show Answer Correct Answer: B) Overapproximation. 14. Number of arbitrary constant in particular solution of the differential equation x(y$^{" '}$)$^{4}$-y(y$^{" " }$)$^{3}$=xy is A) 4. B) 3. C) 1. D) 0. Show Answer Correct Answer: D) 0. 15. $.$ $\left(\frac{\partial^2u}{\partial x^2}\right)^3+\left(\frac{\partial u}{\partial y}\right)^4=0$ A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: B) 2. 16. Determine the complementary solution for:y" + 2y' + y = 0. A) F= C1 e$^{x}$ + C2 x e$^{x}$. B) F = (C1 + C2 x )e$^{-x}$. C) F= C1 e$^{-2x}$+ C2 e$^{-x}$. D) F= C1 + C2 x. Show Answer Correct Answer: B) F = (C1 + C2 x )e$^{-x}$. 17. What is the degree in the given differential equation:(1-x) y" -4xy' + 5y = cosx A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: A) 1. 18. (D$^{2}$+4D+4)y=0 has no complementary function. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 19. The complete solution of partial differential equation involves A) Complete function + indefinite integral. B) Complete function + Particular Integral. C) Complementary function + Particular Integral. D) Complementary function + definite integral. Show Answer Correct Answer: C) Complementary function + Particular Integral. 20. Define a variable separable equation. A) A linear equation that relates x and y without derivatives. B) A function that describes the rate of change of y with respect to x. C) An equation that cannot be separated into two distinct variables. D) A differential equation that can be written as f(y) dy = g(x) dx. Show Answer Correct Answer: D) A differential equation that can be written as f(y) dy = g(x) dx. 21. Solve the differential equation. $y'=\frac{-2x}{\sin y}$ A) $\cos y=-x^2+C$. B) $-\cos y=-x^2+C$. C) $\cos y=x+C$. D) $\cos y=x^3+C$. Show Answer Correct Answer: B) $-\cos y=-x^2+C$. 22. $L\left[f'\left(x\right)\right]=$ A) $sL\left[f\left(x\right)\right]-sf\left(0\right)-f'\left(0\right)$. B) $L\left[f\left(x\right)\right]-sf\left(0\right)$. C) $sL\left[f\left(x\right)\right]-f'\left(0\right)$. D) $sL\left[f\left(x\right)\right]-f\left(0\right)$. Show Answer Correct Answer: D) $sL\left[f\left(x\right)\right]-f\left(0\right)$. 23. Find the complementary function of $\left(D^3-3D^2+3D-1\right)y=x^2e^x$ A) $C.F=e^x\left(c_1+c_2x+c_3x^2\right)$. B) $C.F=e^{-x}\left(c_1+c_2x+c_3x^2\right)$. C) $C.F=e^x\left(c_1x+c_2x^2+c_3x^3\right)$. D) $C.F=e^{-x}\left(c_1x+c_2x^2+c_3x^3\right)$. Show Answer Correct Answer: A) $C.F=e^x\left(c_1+c_2x+c_3x^2\right)$. 24. Determine the order of the differential equation:$\frac{d^6y}{dx^6} + \left(\frac{dy}{dx}\right)^2 + y = 0$ A) 6. B) 2. C) 4. D) 5. Show Answer Correct Answer: A) 6. 25. What is the order of the differential equation:$\frac{d^4y}{dx^4} + \left(\frac{d^3y}{dx^3}\right)^2 + \left(\frac{dy}{dx}\right)^5 = 0$ 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