This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 4 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 4 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the particular solution of the differential equation $\frac{dy}{dx}=x\sqrt{y}$ $y\left(-1\right)=\frac{25}{16}$ A) $y=\left(\frac{x^2}{4}+1\right)^2$. B) $y=\left(\frac{x^2}{2}+1\right)^2$. C) $y=-e^{x^2}$. D) $y=\left(\frac{3x^4}{4}+3\right)^{\frac{1}{3}}$. Show Answer Correct Answer: A) $y=\left(\frac{x^2}{4}+1\right)^2$. 2. 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: D) 3 sinx-4 sin$^{3}$x. 3. 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. 4. 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: C) Log|1+y| =x+x$^{2}$/2-3/2. 5. 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) $\theta=e^{3t}\left(2t+a\right)$. 6. 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) 2. B) 3. C) 1. D) 4. Show Answer Correct Answer: B) 3. 7. Use implicit differentiation to find y' for the following equation:4x cos(y) = 1 A) Y' = cos(y) / x sin(y). B) Y' = 4x sin(y). C) Y' = cot(y). D) Y' = 4 / sec(y)tan(y). Show Answer Correct Answer: A) Y' = cos(y) / x sin(y). 8. The particular integral of the differential equation (D$^{2}$-4D+13)y=e$^{-3x}$ is ..... A) E$^{3x}$/9. B) E$^{3x}$. C) E$^{3x}$/34. D) E$^{-3x}$/34. Show Answer Correct Answer: D) E$^{-3x}$/34. 9. Now that we have separated, what would be the correct integration? $3y\cdot dy=\left(2x+1\right)dx$ A) $3\ln\left|y\right|=x^2+x+C$. B) $\frac{3}{2}y^2dy=x^2+x$. 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) $\frac{3}{2}y^2=x^2+x+C$. 10. What does 'i' represent in complex numbers? A) Square root of 1. B) Imaginary part. C) Real part. D) Cube root of-1. Show Answer Correct Answer: B) Imaginary part. 11. 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. 12. The characteristic roots of a triangular matrix are just the ..... of the matrix. A) Diagonal elements. B) Row elements. C) Column elements. D) Middle elements. Show Answer Correct Answer: A) Diagonal elements. 13. 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. 14. 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. 15. 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. 16. $y" +2y'+16y=0$ $x=\frac{\pi}{2\sqrt{15}}$ $y=ie^{-\frac{\pi}{2\sqrt{15}}}$ A) $y=e^{x\left(i\sqrt{15}-1\right)}$. B) $y=e^{x\left(i\sqrt{15}+1\right)}$. C) $y=e^{-1}-e^{i\sqrt{15}}$. D) $y=e^{-1}+e^{i\sqrt{15}}$. Show Answer Correct Answer: A) $y=e^{x\left(i\sqrt{15}-1\right)}$. 17. The method of solving linear systems using matrix exponentials is based on ..... A) Fourier Transform. B) Eigenvalue decomposition. C) Laplace Transform. D) Integration by parts. Show Answer Correct Answer: B) Eigenvalue decomposition. 18. Determine the general solution of $y"-6y'+9y=0$ A) $y=C_1e^{3x}+C_2e^{3x}$. B) $y=C_1e^x+C_2xe^{3x}$. C) $y=e^{3x}\left(C_1\cos3x+C_2\sin3x\right)$. D) $C_1e^{3x}+C_2xe^{3x}$. Show Answer Correct Answer: D) $C_1e^{3x}+C_2xe^{3x}$. 19. 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. 20. $\frac{\text{d}^2y}{\text{d}x^2}=2x$ A) Second order differential equation. B) First order differential equation. C) First order differential equation at second degree. D) Second order differential equation at second degree. Show Answer Correct Answer: A) Second order differential equation. 21. Variation of parameters is used to solve: A) Homogeneous linear equations. B) Non-homogeneous linear equations. C) Partial differential equations. D) Separable equations. Show Answer Correct Answer: B) Non-homogeneous linear equations. 22. Given $\frac{dy}{dx} = y^2$ A) $y = Ce^x$. B) $y = \frac{1}{C-x}$. C) $y = x^2 + C$. D) $y = Cx^2$. Show Answer Correct Answer: B) $y = \frac{1}{C-x}$. 23. 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. 24. 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) 0.333. B) 0.077. C) 0.5. D) 0.25. Show Answer Correct Answer: A) 0.333. 25. 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. ← 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 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 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books