This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 11 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Dy/dx = 2x/e$^{2y }$ find the general solution A) $y=\frac{1}{2}\ln\left|2x^2+c\right|$. B) $y=\ln\left|2x^2+c\right|$. C) Y = e$^{2x}$+c. D) Y = mx+b. Show Answer Correct Answer: A) $y=\frac{1}{2}\ln\left|2x^2+c\right|$. 2. Find the particular integral of (D$^{3}$-3DD'+D'+4)3=e$^{2x+y}$ A) 1/7. B) F(y+z, x$^{2}$+ +z$^{2}$)=0. C) E$^{2x}$. D) 1/7 e$^{2x+y}$. Show Answer Correct Answer: D) 1/7 e$^{2x+y}$. 3. For y" +y=0, y(0)=0, y'(0)=1, the solution is: A) $\sin x$. B) $\cos x$. C) $e^x$. D) None of these. Show Answer Correct Answer: A) $\sin x$. 4. Find the general solution of dy/dx = (x + y)/(x-y). A) X + y = k(x-y). B) Dy/dx = (x-y)/(x + y). C) Y = kx + c. D) X-y = k(x + y). Show Answer Correct Answer: A) X + y = k(x-y). 5. The differential equations are useful to describe anything that changes in time or in space.Is this statement TRUE or FALSE A) TRUE. B) FALSE. C) NOT SURE. D) None of the above. Show Answer Correct Answer: A) TRUE. 6. What is the solution of the differential equation $y'=-3x$ $P\left(3, -4\right)$ A) $y=2x+\frac{12}{5}$. B) $y=-2x+\frac{12}{5}$. C) $y=-\frac{3}{2}x^2-\frac{19}{2}$. D) $y=-\frac{3}{2}x^2+\frac{19}{2}$. Show Answer Correct Answer: D) $y=-\frac{3}{2}x^2+\frac{19}{2}$. 7. Differential equation of family of lines y=mx, where m is arbitrary constant is A) Y"=0. B) Y=xy'. C) Y=x+y". D) Y$^{'}$=0. Show Answer Correct Answer: B) Y=xy'. 8. Let $y=f(x)$ $\frac{dy}{dx}=x-y+1$ $f(0)=3$ $f(2)$ $x=0$ A) $-2$. B) $-1$. C) $2$. D) $5$. Show Answer Correct Answer: C) $2$. 9. The solution of Clairaut's equation usually consists of: A) A family of straight lines. B) A family of curves. C) Only one curve. D) None. Show Answer Correct Answer: A) A family of straight lines. 10. If $\dfrac{dy}{dx}=2x$ $y$ A) $x$. B) $x^2+C$. C) $2x^2$. D) $\ln x$. Show Answer Correct Answer: B) $x^2+C$. 11. What are the applications of partial differential equations in real life? A) Building construction. B) Modeling physical phenomena in various fields. C) Social media marketing. D) Cooking recipes. Show Answer Correct Answer: B) Modeling physical phenomena in various fields. 12. The solution to the given differential equation (y + xy2)dx + (2y-x)dy = 0 is $\frac{x^2}{2}$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 13. $\frac{dy}{dx}+y\cot\left(x\right)=y^3\sin^3\left(x\right)$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: C) Bernoulli. 14. $\left(\frac{d^2u}{dt^2}\right)^2+\left(\frac{du}{dt}\right)^3+u=t$ A) Second order, second degree. B) Second order, third degree. C) First order, second degree. D) First order, third degree. Show Answer Correct Answer: A) Second order, second degree. 15. Page 396 #34 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: D) D. 16. In the differential equation $\frac{dy}{dx}=x^ky^2$ A) $y=\frac{k+1}{k+1-x^{k+1}}$. B) $y=\frac{k+1}{k+1+x^{k+1}}$. C) $y=\sqrt[3]{\frac{k+1-3x^{k+1}}{k+1}}$. D) $y=\sqrt[3]{\frac{k+1+3x^{k+1}}{k+1}}$. Show Answer Correct Answer: A) $y=\frac{k+1}{k+1-x^{k+1}}$. 17. You draw a card at random from a standard deck of 52 cards. Find the probability that the card is a diamond given that it is a queen. A) 0.5. B) 0.25. C) 0.333. D) 0.077. Show Answer Correct Answer: B) 0.25. 18. For $y" + 2y' + y = 0$ A) Two distinct real roots. B) Two complex conjugate roots. C) A repeated real root. D) No real roots. Show Answer Correct Answer: C) A repeated real root. 19. Clairaut's form of a differential equation is written as: A) Y=px+f(p). B) Y=f(x). C) Y=f(p)only. D) None. Show Answer Correct Answer: A) Y=px+f(p). 20. $5\frac{dy}{dx}=3\frac{dy}{dx}+3xy$ A) YES. B) NO. C) All the above. D) None of the above. Show Answer Correct Answer: A) YES. 21. $L\left(x^n\right)=\frac{\Gamma\left(n\right)}{s^{\left(n+1\right)}}$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 22. Find the general solution of the non-homogeneous equation:y" -y = e$^{-x}$ A) Y = C1 e$^{x}$-C2 e$^{-x}$-x e$^{-x}$. B) Y = C1 e$^{x}$-C2 e$^{-x}$ +(1/2) e$^{-x}$. C) Y = C1 e$^{x}$ + C2 e$^{-x}$-(1/2)x e$^{-x}$. D) Y = C1 e$^{-x}$ +C2 e$^{2x}$-(1/2) x$^{2}$ e$^{-x}$. Show Answer Correct Answer: C) Y = C1 e$^{x}$ + C2 e$^{-x}$-(1/2)x e$^{-x}$. 23. Find the integrating factor to solve the equation $\frac{dy}{dx}-y=x^3.$ A) $-y$. B) $x^3$. C) $e^{-x}$. D) $e^y$. Show Answer Correct Answer: C) $e^{-x}$. 24. Solve dy/dx = (y+5)(x+2) A) $y=Ce^{x^2+x}+5$. B) $y=Ce^{x^2+2x}$. C) $y=Ce^{\frac{1}{2}x^2+2x}-5$. D) $y=Ce^{x+2}-5$. Show Answer Correct Answer: C) $y=Ce^{\frac{1}{2}x^2+2x}-5$. 25. The particular solution of $y" =e^x$ A) $e^{-x}$. B) $e^x$. C) $x^2$. D) $xe^x$. Show Answer Correct Answer: B) $e^x$. ← 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