This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 37 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 37 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find the composite function of (D$^{3}$-4D$^{2}$D'+DD'$^{2}$)z=0 A) CF=f 1 (x)+f 2 (y+x)+f 3 (y+3x). B) CF=f 1 (y)+f 2 (y+x)+f 3 (y+4x). C) CF=f 1 (y)+f 2 (y+t). D) CF=f 1 (y)+f 2 (y+x)+f 3 (y+3x). Show Answer Correct Answer: D) CF=f 1 (y)+f 2 (y+x)+f 3 (y+3x). 2. If $x^{\alpha}y^{\beta}$ $\left(2x^2y-3y^4\right)dx-\left(3x^3+2xy^3\right)dy=0$ $\alpha$ $\beta$ A) $\alpha=-\frac{49}{13}, \\beta=-\frac{28}{13}$. B) $\alpha=\frac{49}{18}, \\beta=\frac{28}{18}$. C) $\alpha=\frac{49}{18}, \beta=-\frac{28}{18}$. D) $\alpha=-\frac{49}{13}, \\beta=\frac{28}{13}$. Show Answer Correct Answer: A) $\alpha=-\frac{49}{13}, \\beta=-\frac{28}{13}$. 3. Which method is suitable for solving a system of first-order linear ODEs? A) Cramer's Rule. B) Gaussian Elimination. C) Matrix exponentials. D) Taylor series only. Show Answer Correct Answer: C) Matrix exponentials. 4. Newton's Law of Cooling states that the rate at which an object cools is proportional to what? A) Difference in temperature of the object and the temperature of its surroundings. B) Temperature of surroundings. C) Temperature of the object. D) Object's mass. Show Answer Correct Answer: A) Difference in temperature of the object and the temperature of its surroundings. 5. If the roots of A. E are real and equal then C. F is C$_{1}$e$^{m1x}$+C$_{2}$e$^{m2x}$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 6. Differential equation representing the curve y=cx+c$^{2}$ where c being arbitrary constant is A) Y=xy$^{'}$+(y)$^{2}$. B) Y=xy$^{'}$ +y$^{2}$. C) Y=xy$^{'}$+(y$^{' }$)$^{2}$. D) Y=xy+(y$^{'}$)$^{2}$. Show Answer Correct Answer: C) Y=xy$^{'}$+(y$^{' }$)$^{2}$. 7. A differential equation is said to be ..... if it can be expressed as $f(x)dx=g(y)dy$ $f$ $g$ $x$ $y, $ A) Differentiable. B) Integrable. C) Solved. D) Separable. Show Answer Correct Answer: D) Separable. 8. Part B. Find the particular solution under the given conditions:13. y" + y'-6y = 0, y(0) = 2, y'(0) =-1 A) $y = e^{2x} + e^{-3x}$. B) Y = $2e^{2x}-e^{-3x}$. C) $y = e^{2x}-2e^{-3x}$. D) Y = $-e^{2x} + 2e^{-3x}$. Show Answer Correct Answer: A) $y = e^{2x} + e^{-3x}$. 9. What is the role of constants in linear combinations of functions? A) They determine the order of the equation. B) They are always zero. C) They can be any real numbers. D) They must be integers. Show Answer Correct Answer: C) They can be any real numbers. 10. A particle has acceleration given by a(t)=12t-4 with initial velocity-10. What is the velocity equation? A) 12t-14. B) 2t$^{3}$-2t$^{2}$. C) 6t$^{2}$-4t. D) 6t$^{2}$-4t-10. Show Answer Correct Answer: D) 6t$^{2}$-4t-10. 11. The Auxiliary equation of x$^{2}$y" -xy'+4y=cos(logx)+xsin(logx) is ..... A) M$^{2}$+2m+4=0. B) M$^{2}$+2m+2=0. C) M$^{2-}$2m+4=0. D) M$^{2}$+2m-4=0. Show Answer Correct Answer: C) M$^{2-}$2m+4=0. 12. Greenium has a half-life of 23 years and decays following the Law of Exponential Change. After how many years will 80% of an original amount have decayed? A) T = 7.4143 years. B) T = 10.2646. C) T = 53.4043 years. D) T = 74.0341 years. Show Answer Correct Answer: C) T = 53.4043 years. 13. It is an equation that contains derivatives A) Differential Equation. B) Linear Equation. C) Polynomial Equation. D) Differential Calculus. Show Answer Correct Answer: A) Differential Equation. 14. The solution of $\frac{dy}{dx}-y = e^{2x}$ A) $y = Ce^{x} + e^{2x}$. B) $y = Ce^{x}-e^{2x}$. C) Y = $Ce^{x} + \frac{1}{3}e^{2x}$. D) Y = $Ce^{-x} + \frac{1}{3}e^{2x}$. Show Answer Correct Answer: C) Y = $Ce^{x} + \frac{1}{3}e^{2x}$. 15. If the number of arbitrary function is n then the pde obtained is of order A) B) >n. C) =n. D) 1. Show Answer Correct Answer: C) =n. 16. How do differential equations apply to CPS? A) Differential equations are used to model dynamic behaviors and interactions in Cyber-Physical Systems. B) Differential equations are primarily for static systems analysis. C) Differential equations are only used in financial modeling. D) Differential equations have no relevance to system dynamics. Show Answer Correct Answer: A) Differential equations are used to model dynamic behaviors and interactions in Cyber-Physical Systems. 17. What is the order of a differential equation? A) The number of variables in the equation. B) The highest power of the dependent variable. C) The number of solutions to the equation. D) The highest order derivative present in the equation. Show Answer Correct Answer: D) The highest order derivative present in the equation. 18. Find the particular solution of the differential equation $\frac{dy}{dx}=12x^3y$ $y\left(0\right)=3$ A) $y=2e^{3x^4}$. B) $y=e^{x^4}$. C) $y=e^{2x^4}$. D) $y=3e^{3x^4}$. Show Answer Correct Answer: D) $y=3e^{3x^4}$. 19. $\left(1+x^2\right)\frac{\text{d}y}{\text{d}x}+xy=0$ A) $\ln\left|y\right|=-\frac{1}{2}\ln\left|1+x^2\right|+c$. B) $\ln\left|y\right|=\frac{1}{2}\ln\left|1+x^2\right|+c$. C) $-\frac{1}{y^2}=2\ln\left|1+x\right|+c$. D) $-\frac{1}{y^2}=\frac{1}{2}\ln\left|1+x\right|+c$. Show Answer Correct Answer: A) $\ln\left|y\right|=-\frac{1}{2}\ln\left|1+x^2\right|+c$. 20. A function $y=f\left(x\right)$ $y\frac{\text{d}y}{\text{d}x}=x$ $f\left(0\right)=1$ A) $f\left(x\right)=x$. B) $f\left(x\right)=e^x$. C) $f\left(x\right)=\sqrt{x^2+1}$. D) $f\left(x\right)=\sqrt{1-x^2}$. Show Answer Correct Answer: C) $f\left(x\right)=\sqrt{x^2+1}$. 21. $\frac{\partial x}{\partial y}$ A) Yes. B) No. C) Neither. D) Either. Show Answer Correct Answer: A) Yes. 22. How does feedback influence CPS behavior? A) Feedback decreases the adaptability of CPS behavior. B) Feedback has no impact on CPS behavior. C) Feedback enhances the adaptability and efficiency of CPS behavior. D) Feedback complicates the efficiency of CPS behavior. Show Answer Correct Answer: C) Feedback enhances the adaptability and efficiency of CPS behavior. 23. The general solution of (D$^{2}$-4)y=0 is ..... A) C$_{1}$e$^{-2x}$+c$_{2}$e$^{-2x}$. B) C$_{1}$e$^{-2x}$+c$_{2}$e$^{2x}$. C) C$_{1}$e$^{x}$+c$_{2}$e$^{2x}$. D) C$_{1}$e$^{3x}$+c$_{2}$e$^{2x}$. Show Answer Correct Answer: B) C$_{1}$e$^{-2x}$+c$_{2}$e$^{2x}$. 24. Find the particular solution of the differential equation $\frac{dy}{dx} = 6x$ $y(0) = 5$ A) $y = 3x^2 + 5$. B) $y = 3x^2 + C$. C) $y = 6x^2 + 5$. D) $y = 6x^2 + C$. Show Answer Correct Answer: A) $y = 3x^2 + 5$. 25. The formula for u'1 in Variation of Parameters is: A) U'1=-y2 f(x)/W(y1, y2). B) U'1=-y1 f(x)/W(y1, y2). C) U'1=y'2 f(x)/W(y1, y2). D) U'1=y" 2 f(x)/W(y1, y2). Show Answer Correct Answer: A) U'1=-y2 f(x)/W(y1, y2). ← 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