This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 21 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 21 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. $\int_{ }^{ }\frac{dx}{x}=$ A) $y=e^x+C$. B) $y=\ln\left|x\right|+C$. C) $y=\sin x+C$. D) $y=\frac{-1}{x^2}+C$. Show Answer Correct Answer: B) $y=\ln\left|x\right|+C$. 2. Which statement of differential equation is true? A) An equation that relates one or more functions and their derivatives. B) An equation that has multiple terms made up of numbers and variables. C) All the above. D) None of the above. Show Answer Correct Answer: A) An equation that relates one or more functions and their derivatives. 3. The standard form of a linear differential equation with constant coefficients is: A) $y" +p(x)y'+q(x)y=r(x)$. B) $y" +py'+qy=r(x)$. C) $y'+p(x)y=q(x)$. D) $y" +p(x)y'+qy=r(x)$. Show Answer Correct Answer: B) $y" +py'+qy=r(x)$. 4. Y" +y'+10y=0 A) UNDERDAMPED. B) OVERDAMPED. C) UNDAMPED. D) CRITICALLY DAMPED. Show Answer Correct Answer: A) UNDERDAMPED. 5. An integrating factor of the differential equation $\frac{\text{d}y}{\text{d}x}-\frac{2y}{x}=3x^2$ A) $e^{-2x}$. B) $-\ln\left(x^2\right)$. C) $x^2$. D) $\frac{1}{x^2}$. Show Answer Correct Answer: D) $\frac{1}{x^2}$. 6. What is the general solution of a second order differential equation with independent solutions? A) A constant function. B) A polynomial of degree two. C) An exponential function. D) A linear combination of the solutions. Show Answer Correct Answer: D) A linear combination of the solutions. 7. $D^2 + 4$ A) Y = Acos2x + Bsin2x. B) Y = Acos2x-iBsin2x. C) $e^{2x}i$. D) None of these. Show Answer Correct Answer: A) Y = Acos2x + Bsin2x. 8. What is the general solution for $\frac{\text{d}^2y}{\text{d}x^2}-2y=0$ A) $y=Ae^{\sqrt{2}x}+Be^{\sqrt{2}x}$. B) $y=Ae^{\sqrt{2}x}+Be^{-\sqrt{2}x}$. C) $y=\left(Ax+B\right)e^{\sqrt{2}x}$. D) $y=\left(Ax+B\right)e^{-\sqrt{2}x}$. Show Answer Correct Answer: B) $y=Ae^{\sqrt{2}x}+Be^{-\sqrt{2}x}$. 9. Eliminate the arbitrary function from z = f(x$^{2}$+y$^{2}$) A) Px = qy. B) Py+qx=0. C) Px+qy=0. D) Py = qx. Show Answer Correct Answer: D) Py = qx. 10. According to Newton's law of cooling, the rate at which an object cools (or warms) is directly proportional to the temperature difference between the environment and the object itself. If a pot of boiling water (100$^\circ$C) is left at room temperature (22$^\circ$C) and after five minutes the water is only 70$^\circ$C, find its temperature after another 5 minutes. A) 51$^\circ$C. B) 52$^\circ$C. C) 61$^\circ$C. D) 62$^\circ$C. E) 63$^\circ$C. Show Answer Correct Answer: B) 52$^\circ$C. 11. If $\frac{dy}{dx} = ky$ A) 100 $e^{k}$. B) $300e^{k}$. C) $100e^{3k}$. D) $300e^{3k}$. Show Answer Correct Answer: C) $100e^{3k}$. 12. Given the differential equation $\frac{\text{d}P}{\text{d}t}=5P$ A) P=Ce$^{5t}$B) P= 5e$^{418t}$. B) P=Ce$^{5t}$B) P= 418e$^{5t}$. C) P=Ce$^{t}$B) P= 418e$^{t}$. D) P=Ce$^{10t}$B) P= 418e$^{10t}$. Show Answer Correct Answer: B) P=Ce$^{5t}$B) P= 418e$^{5t}$. 13. Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^3}{y}$ $y(2)=-3$ A) $y=3e^{\frac{x^4}{4}-4}$. B) $y=-3e^{\frac{x^4}{4}-4}$. C) $y=\sqrt{\frac{x^4}{2}+1}$. D) $y=-\sqrt{\frac{x^4}{2}+1}$. Show Answer Correct Answer: D) $y=-\sqrt{\frac{x^4}{2}+1}$. 14. The general solution of the DE $\frac{d^2y}{dx^{2}}+7\frac{dy}{dx}-8y=0$ A) $y=Ae^x+Be^{-8x}$. B) $y=Ae^{-x}+Be^{8x}$. C) $y=Ae^{-x}+Be^{7x}$. D) $y=Ae^x+Be^{7x}$. Show Answer Correct Answer: A) $y=Ae^x+Be^{-8x}$. 15. $\frac{\text{d}x}{\text{d}y}-4y-5+e^{-2x}=0$ A) $y=-20+6e^{-2x}+Ce^{4x}$. B) $y=-\frac{5}{4}e^{-4x}+\frac{1}{6}e^{-2x}+Ce^{4x}$. C) $y=-20e^{-8x}+e^{-10x}+Ce^{-4x}$. D) $y=-\frac{5}{4}+\frac{1}{6}e^{-2x}+Ce^{-4x}$. Show Answer Correct Answer: B) $y=-\frac{5}{4}e^{-4x}+\frac{1}{6}e^{-2x}+Ce^{4x}$. 16. Hence, roots $r_1$ $r_2$ A) Real and distinct. B) Real and equal. C) Complex numbers. D) None of the above. Show Answer Correct Answer: C) Complex numbers. 17. Which of the following differential equations is linear? (i) $y' = 10y + 1$ $y'-4y = 0$ $y' + \sin y = 1$ A) (i). B) (i) and (iii). C) (i) and (ii). D) None of the above. Show Answer Correct Answer: C) (i) and (ii). 18. What type of differential equation is dy/dx = y + x? A) First-order linear differential equation. B) Partial differential equation. C) Nonlinear differential equation. D) Second-order linear differential equation. Show Answer Correct Answer: A) First-order linear differential equation. 19. Which of the following differential equations is separable? (i) $y' = \dfrac{12t}{y}$ $t^2 y'-y^2 \sin t = 0$ $y' + ty = 9$ A) (i). B) (i) and (iii). C) (i) and (ii). D) None of the above. Show Answer Correct Answer: C) (i) and (ii). 20. Given the differential equation $\frac{dy}{dx} = 2x + 1$ $y(0) = 3$ A) $y = x^2 + x + 3$. B) $y = x^2 + x$. C) $y = 2x + 3$. D) $y = x^2 + 3$. Show Answer Correct Answer: A) $y = x^2 + x + 3$. 21. What is the characteristic equation for $y" -5y' + 6y = 0$ A) $r^2-5r + 6 = 0$. B) $r^2 + 5r + 6 = 0$. C) $r^2-6r + 5 = 0$. D) $r^2 + 6r + 5 = 0$. Show Answer Correct Answer: A) $r^2-5r + 6 = 0$. 22. What is the method to solve a linear differential equation? A) Employ numerical methods and approximations. B) Use integrating factors and integration. C) Apply substitution and differentiation. D) Use Laplace transforms and series. Show Answer Correct Answer: B) Use integrating factors and integration. 23. If the auxiliary equation has equal roots, the complementary function involves: A) Polynomial factor multiplied by exponential. B) Trigonometric terms. C) Only constants. D) None. Show Answer Correct Answer: A) Polynomial factor multiplied by exponential. 24. CHOOSE THE CORRECT FORM OF PARTIAL DIFFERENTIAL EQUATION BY ELIMINATING ARBITARY FUNCTIONz=f(sinx+cosy) A) Tanxpq=0. B) -cosx+siny=0. C) -Sinyp+cosxq=0. D) Cosxp-sinyq=0. Show Answer Correct Answer: C) -Sinyp+cosxq=0. 25. The complementary function of (D$^{2}$-6D+9)y=0 is ..... A) E$^{-3x}$(ax+b). B) E$^{3x}$(ax+b). C) E$^{3x}$(ax-b). D) Ax+b. Show Answer Correct Answer: B) E$^{3x}$(ax+b). ← 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