This quiz works best with JavaScript enabled. Home > Cbse > Class 12 > Science > Mathematics > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 2 (60 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The growth of population y is described by the differential equation $\frac{dy}{dt}=ky$ A) 0.087. B) 4.351. C) 0.250. D) 0.271. Show Answer Correct Answer: A) 0.087. 2. What is the result of applying the reduction of order method? A) A solution to a higher order equation. B) No solution. C) A constant solution. D) A solution to a lower order equation. Show Answer Correct Answer: D) A solution to a lower order equation. 3. Which is one of the following are the bases for $P_2\left(R\right)?$ A) $\left\{1, 2x, 3x^2\right\}$. B) $\left\{1+2x+x^2, 3+x^2, x+x^2\right\}$. C) $\left\{1, x, 2x\right\}$. D) $\left\{1+x, 2x+2x^2, x-x^2\right\}$. Show Answer Correct Answer: A) $\left\{1, 2x, 3x^2\right\}$. 4. Please find the answer to this limit:$\lim_{x\rightarrow\infty}\frac{x^2+\sin x}{x^2}$ A) $\infty$. B) -1. C) 1. D) 0. Show Answer Correct Answer: C) 1. 5. What is the degree of the PDE ( (u ..... {x})^2 + u ..... {y} = 0 )? A) 1. B) 2. C) 4. D) 3. Show Answer Correct Answer: B) 2. 6. The integrating factor for the equation dy/dx-(3y)/(x+1) = (x+1)/4 is: A) $e^{3x}$. B) $\int_{x}^{3} dx$. C) I. D) 1/(x+1). Show Answer Correct Answer: A) $e^{3x}$. 7. The general solution of y" -5y'+6y=0 is: A) $c_1e^{5x}+c_2e^{6x}$. B) $c_1e^{2x}+c_2e^{3x}$. C) $c_1e^x+c_2e^{6x}$. D) $c_1e^{-2x}+c_2e^{-3x}$. Show Answer Correct Answer: B) $c_1e^{2x}+c_2e^{3x}$. 8. If C is the straight line joining (0, 0, 0) and (1, 1, 1) then $\int_C\overrightarrow{r}.d\overrightarrow{r}$ A) 3/2. B) 1/2. C) 2. D) 1. Show Answer Correct Answer: A) 3/2. 9. The roots of m$^{2}$-6m+13=0 are ..... A) 1, 1. B) 3+2i, 3-2i. C) 3, 2. D) 1+i, 1-i. Show Answer Correct Answer: B) 3+2i, 3-2i. 10. F(s) = L\{(e$^{at}$cos(bt))\} (s) A) B/(s$^{2}$ + b$^{2}$). B) 1/s. C) B/(s-a)$^{2 }$+ b$^{2}$. D) (s-a)/((s-a)$^{2}$+b$^{2}$). E) S/(s$^{2}$+b$^{2}$). Show Answer Correct Answer: D) (s-a)/((s-a)$^{2}$+b$^{2}$). 11. The standard form of a growth/decay equation is: A) Dy/dx = k y. B) $\frac{dy}{dx} = e^x$. C) $\frac{dy}{dx} = y^2$. D) Dy/dx = k. Show Answer Correct Answer: A) Dy/dx = k y. 12. Population y grows according to the equation dy/dx=ky, where k is a constant and t is measured in years. If the population doubles every 10 years, then the value of k is: A) 0.301. B) 5.000. C) 3.322. D) 0.200. E) 0.069. Show Answer Correct Answer: E) 0.069. 13. Which of the following is the general solution to $\frac{dy}{dx} =\cos x$ A) $y = \sin x + C$. B) $y =-\cos x + C$. C) $y =-\sin x + C$. D) $y =\cos x + C$. Show Answer Correct Answer: A) $y = \sin x + C$. 14. Find a solution to:y" + 8y' + 16y = 0 given y ' = 4 when y = 3 and x = 0 A) $e^{2x}(4+3x)$. B) $e^{2x}(3+4x)$. C) $e^{-4x}(4+3x)$. D) $e^{-4x}(3+4x)$. Show Answer Correct Answer: D) $e^{-4x}(3+4x)$. 15. Find the particular solution of the differential equation $\frac{dy}{dx}=x\sqrt{y}$ $y\left(-1\right)=\frac{25}{16}$ A) $y=\left(\frac{x^2}{2}+1\right)^2$. B) $y=-e^{x^2}$. C) $y=\left(\frac{3x^4}{4}+3\right)^{\frac{1}{3}}$. D) $y=\left(\frac{x^2}{4}+1\right)^2$. Show Answer Correct Answer: D) $y=\left(\frac{x^2}{4}+1\right)^2$. 16. The formula for sin 3x is A) 4 sinx + 3 sin$^{3}$x. B) 3 sinx-4 sin$^{3}$x. C) 4 sinx-3 sin$^{3}$x. D) 3 sinx + 4 sin$^{3}$x. Show Answer Correct Answer: B) 3 sinx-4 sin$^{3}$x. 17. If f(D)y = X is a Linear differential equation with constant coefficient in x and y of degree n then Particular Integral is given by A) P.I. = 1/f(D)y. B) P.I. = 1/f(D)X. C) I. = f(D)y. D) I. = f(D)X. Show Answer Correct Answer: B) P.I. = 1/f(D)X. 18. Solve the differential equation at x=1, y=0dy/dx =1+x+y+xy A) Log|1+y| =x+x$^{2}$/2-3/2. B) Log|1+y| =2x+x$^{2}$/2-3/2. C) Log|1-y| =x+x$^{2}$/2-3/2. D) Log|1+y| =x+x$^{2}$/2 +3/2. Show Answer Correct Answer: A) Log|1+y| =x+x$^{2}$/2-3/2. 19. Find the general solution for $\frac{d\theta}{dt}-3\theta=2e^{3t}$ A) $\theta=\frac{2+c}{e^{3t}}$. B) $\theta=e^{-3t}\left(2t+c\right)$. C) $\theta=e^{3t}\left(2t+a\right)$. D) None of the above. Show Answer Correct Answer: C) $\theta=e^{3t}\left(2t+a\right)$. 20. Find the order of the equation $\left(\frac{\text{d}^3y}{\text{d}x^3}\right)^4+2\frac{\text{d}^2y}{\text{d}x^2}=0$ A) 1. B) 4. C) 3. D) 2. Show Answer Correct Answer: C) 3. 21. Use implicit differentiation to find y' for the following equation:4x cos(y) = 1 A) Y' = cot(y). B) Y' = 4x sin(y). C) Y' = 4 / sec(y)tan(y). D) Y' = cos(y) / x sin(y). Show Answer Correct Answer: D) Y' = cos(y) / x sin(y). 22. The particular integral of the differential equation (D$^{2}$-4D+13)y=e$^{-3x}$ is ..... A) E$^{3x}$/34. B) E$^{-3x}$/34. C) E$^{3x}$. D) E$^{3x}$/9. Show Answer Correct Answer: B) E$^{-3x}$/34. 23. Now that we have separated, what would be the correct integration? $3y\cdot dy=\left(2x+1\right)dx$ A) $\frac{3}{2}y^2dy=x^2+x$. B) $3\ln\left|y\right|=x^2+x+C$. C) $\frac{3}{2}y^2=x^2+x+C$. D) $3y^2=\frac{1}{2}x^2+x+C$. Show Answer Correct Answer: C) $\frac{3}{2}y^2=x^2+x+C$. 24. What does 'i' represent in complex numbers? A) Imaginary part. B) Real part. C) Cube root of-1. D) Square root of 1. Show Answer Correct Answer: A) Imaginary part. 25. Let g be a function that is differentiable over the interval (2, 9) . Given g(3) = 5, g(6) =-2, and g(8) = 5, which of the following must be true?I. g has at least one horizontal tangent line.II. g has at least 2 zeros.III. For some c in the interval (3, 6), f'(c) =-7/3. A) II only. B) II and III. C) I and II. D) I, II, and III. Show Answer Correct Answer: D) I, II, and III. 26. The characteristic roots of a triangular matrix are just the ..... of the matrix. A) Column elements. B) Middle elements. C) Diagonal elements. D) Row elements. Show Answer Correct Answer: C) Diagonal elements. 27. Stoke's theorem connects A) Line integral and double integral. B) Line integral and Surface integral. C) Double integral and Surface integral. D) Volume integral and Surface integral. Show Answer Correct Answer: B) Line integral and Surface integral. 28. In equations solvable for dy/dx, the number of solutions is equal to the: A) Degree of derivative. B) Order of the equation. C) Number of variables. D) None. Show Answer Correct Answer: B) Order of the equation. 29. The following Differential Equation is $\frac{\text{d}y}{\text{d}x}=\frac{y}{x}$ A) Separable. B) Non Separable. C) All the above. D) None of the above. Show Answer Correct Answer: A) Separable. 30. $y" +2y'+16y=0$ $x=\frac{\pi}{2\sqrt{15}}$ $y=ie^{-\frac{\pi}{2\sqrt{15}}}$ A) $y=e^{-1}-e^{i\sqrt{15}}$. B) $y=e^{x\left(i\sqrt{15}-1\right)}$. C) $y=e^{x\left(i\sqrt{15}+1\right)}$. D) $y=e^{-1}+e^{i\sqrt{15}}$. Show Answer Correct Answer: B) $y=e^{x\left(i\sqrt{15}-1\right)}$. 31. The method of solving linear systems using matrix exponentials is based on ..... A) Eigenvalue decomposition. B) Fourier Transform. C) Integration by parts. D) Laplace Transform. Show Answer Correct Answer: A) Eigenvalue decomposition. 32. Determine the general solution of $y"-6y'+9y=0$ A) $y=C_1e^x+C_2xe^{3x}$. B) $y=e^{3x}\left(C_1\cos3x+C_2\sin3x\right)$. C) $C_1e^{3x}+C_2xe^{3x}$. D) $y=C_1e^{3x}+C_2e^{3x}$. Show Answer Correct Answer: C) $C_1e^{3x}+C_2xe^{3x}$. 33. For what kind of signals one sided Z-transfrom is unique A) All signals. B) Anti-causal signal. C) Causal signal. D) None of the above. Show Answer Correct Answer: C) Causal signal. 34. $\frac{\text{d}^2y}{\text{d}x^2}=2x$ A) Second order differential equation at second degree. B) First order differential equation at second degree. C) First order differential equation. D) Second order differential equation. Show Answer Correct Answer: D) Second order differential equation. 35. Variation of parameters is used to solve: A) Non-homogeneous linear equations. B) Homogeneous linear equations. C) Partial differential equations. D) Separable equations. Show Answer Correct Answer: A) Non-homogeneous linear equations. 36. Given $\frac{dy}{dx} = y^2$ A) $y = x^2 + C$. B) $y = Ce^x$. C) $y = \frac{1}{C-x}$. D) $y = Cx^2$. Show Answer Correct Answer: C) $y = \frac{1}{C-x}$. 37. Consider two differential equations(i) $e^ydx+\left(xe^y+2y\right)dy=0$ $xdy+2y^2dx=0$ A) Both I and II are exact differential equations. B) I is exact and II is not an exact differential equation. C) Neither I nor II are exact differential equations. D) I is not exact but II is an exact differential equation. Show Answer Correct Answer: B) I is exact and II is not an exact differential equation. 38. You draw a card at random from a standard deck of 52 cards. Find the probability that the card is a spade given that it is not a diamond. A) 0.077. B) 0.333. C) 0.5. D) 0.25. Show Answer Correct Answer: B) 0.333. 39. In half range Fourier series expansion, we know the nature of the function in its full time period. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 40. Which of the following equations has complex roots in its characteristic equation? A) $y" + 4y = 0$. B) $y" -2y' + y = 0$. C) $y" + 2y' + y = 0$. D) $y" -6y' + 9y = 0$. Show Answer Correct Answer: A) $y" + 4y = 0$. 41. If the number of constants to be eliminated is greater than the number of independent variables, then the result is ..... A) First order PDE. B) Second and higher order PDE. C) Second and higher order PDE. D) Only Second order linear PDE. Show Answer Correct Answer: B) Second and higher order PDE. 42. What is the general solution to the DE $\frac{\text{d}^2x}{\text{d}y^2}+7\frac{\text{d}x}{\text{d}y}-8y=0$ A) $y=Ce^{-x}+De^{7x}$. B) $y=Ce^x+De^{-8x}$. C) $y=Ce^{-x}+De^{8x}$. D) $y=Ce^x+De^{7x}$. Show Answer Correct Answer: B) $y=Ce^x+De^{-8x}$. 43. Polynomials are not analytic at all points. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 44. The general solution of a first-order PDE is: A) A constant function of the variables involved. B) A function of arbitrary functions of the variables involved. C) A polynomial function of fixed coefficients. D) A linear combination of the variables only. Show Answer Correct Answer: B) A function of arbitrary functions of the variables involved. 45. If Eigen values of a matrix are 0, 1, 2, then the matrix will be A) Non-singular. B) Singular. C) Both. D) None of these. Show Answer Correct Answer: B) Singular. 46. Solve dy/dx = x(y+5) A) $y=Ce^{\frac{1}{2}x^2}+5$. B) $y=Ce^{\frac{1}{2}x^2}-5$. C) $y=\frac{Ce^{\frac{1}{2}x^2}}{e^5}$. D) $y=5e^{\frac{1}{2}x^2}-C$. Show Answer Correct Answer: B) $y=Ce^{\frac{1}{2}x^2}-5$. 47. What is the general form of a second order ordinary differential equation (ODE)? A) A y" + b y' + c y = f(t). B) A y" + b y = 0. C) Y" + 2y' + y = f(t). D) Y" + y' + y = 0. Show Answer Correct Answer: A) A y" + b y' + c y = f(t). 48. Find the particular solution to the differential equation $\frac{dy}{dx}=\frac{2xy}{x^2+1}$ $\left(1, \-2\right)$ A) $y=3e^{2x^3}$. B) $y=-x^2-2$. C) $y=x^2+1$. D) $y=-x^2-1$. Show Answer Correct Answer: D) $y=-x^2-1$. 49. What is the definition of a separable differential equation? A) A differential equation with separable variables. B) An nth-order ordinary differential equation in one dependent variable. C) A differential equation where the unknown function depends on only one independent variable. D) An equation containing the derivatives of one or more unknown functions with respect to one or more independent variables. Show Answer Correct Answer: A) A differential equation with separable variables. 50. Apa metode untuk menyelesaikan persamaan diferensial homogen orde kedua dengan koefisien konstan? A) Gunakan metode numerik untuk mendekati solusi. B) Gunakan transformasi Laplace untuk menyelesaikan persamaan. C) Integrasikan persamaan secara langsung untuk menemukan solusi. D) Gunakan persamaan karakteristik untuk menemukan akar dan membangun solusi umum. Show Answer Correct Answer: D) Gunakan persamaan karakteristik untuk menemukan akar dan membangun solusi umum. 51. The particular integral of (D$^{2}$-9)y=cos3x is ..... A) Cos3x/18. B) Cos3x/9. C) Cos3x/-18. D) None of these. Show Answer Correct Answer: C) Cos3x/-18. 52. Which of the following is the solution to the differential equation $y^{" }-4y=0$ A) $y=e^{2x}$. B) $y=e^{-4x}$. C) $y=e^{2x^2}$. D) $y=2x^2$. Show Answer Correct Answer: A) $y=e^{2x}$. 53. $\left(\frac{dy}{dx}\right)^2+5\\frac{dy}{dx}+6=0$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 54. Solve the initial value problem. y" = $xe^{2x}$ A) Y = $\frac{1}{4}xe^{2x} + \frac{1}{8}e^{2x} + 3$. B) Y = $\frac{1}{4}xe^{2x}-\frac{1}{8}e^{2x} + 3$. C) Y = $\frac{1}{4}xe^{2x} + \frac{1}{8}e^{2x}-3$. D) Y = $\frac{1}{4}xe^{2x}-\frac{1}{8}e^{2x}-3$. Show Answer Correct Answer: D) Y = $\frac{1}{4}xe^{2x}-\frac{1}{8}e^{2x}-3$. 55. L\{(1/48b$^{6}$)((15-6(bt)$^{2}$sin bt-(15bt-(bt)$^{3}$)bt cos bt)\} A) B/(s$^{2}$+b$^{2}$)$^{4}$. B) B/(s$^{2}$+b$^{2}$)$^{2}$. C) B/(s$^{2}$+b$^{2}$). D) B/(s$^{2}$+b$^{2}$)$^{3}$. Show Answer Correct Answer: A) B/(s$^{2}$+b$^{2}$)$^{4}$. 56. State TWO types of solutions of Differential Equations A) General Solutions Only. B) General and Particular Solutions. C) Particular Solutions Only. D) No solutions. Show Answer Correct Answer: B) General and Particular Solutions. 57. $\frac{\text{d}^2y}{\text{d}x^2}-2\frac{\text{d}y}{\text{d}x}+y=0$ A) $y=Axe^{-2x}$. B) $y=e^x\left(A+Bx\right)$. C) $y=Ae^x$. D) $y=Ae^x+Bx$. Show Answer Correct Answer: B) $y=e^x\left(A+Bx\right)$. 58. The roots of m$^{3}$ + 3m$^{2}$ + 3m +1 = 0 are A) 1, 1, -1. B) 1, 2, 3. C) 1, 0, 1. D) 1, 1, 1. Show Answer Correct Answer: D) 1, 1, 1. 59. Determine the general solution of $9y"+6y'+y=0$ A) $y=e^{-\frac{x}{3}}\left(C_1\cos x+C_2\sin x\right)$. B) $y=C_1e^{-\frac{x}{3}}+C_2e^{-\frac{x}{3}}$. C) $y=C_1e^{-\frac{x}{3}}+C_2xe^{-\frac{x}{3}}$. D) $y=e^x\left(C_1\cos\frac{x}{3}+C_2\sin\frac{x}{3}\right)$. Show Answer Correct Answer: C) $y=C_1e^{-\frac{x}{3}}+C_2xe^{-\frac{x}{3}}$. 60. Milne's method consists of: A) Only predictor. B) Only corrector. C) Predictor and corrector. D) Taylor expansion. Show Answer Correct Answer: C) Predictor and corrector. ← PreviousNext →Related QuizzesScience QuizzesClass 12 QuizzesClass 12 Mathematics Chapter 9 Differential Equations Quiz 1Class 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 9 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books