This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 32 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 32 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. What is the integral for $e^{-2t}$ A) $\frac{1}{2}$. B) $\frac{1}{2-e}$. C) $\frac{2}{e^2}$. D) $\frac{1}{2}-\frac{\frac{ }{1}}{2e^2}$. Show Answer Correct Answer: D) $\frac{1}{2}-\frac{\frac{ }{1}}{2e^2}$. 2. By separation of variables, solve the resulting equations $\int\\frac{v}{v+1}dv=\int_{ }^{ }\\frac{1}{y}dy\text{}$ A) $\frac{x}{y}-\ln\left|\frac{x}{y}+1\right|=\ln y+C$. B) $\frac{x}{y}+\ln\left|\frac{x}{y}+1\right|=\ln y+C$. C) $\frac{x}{y}+\frac{x^2}{2y^2}=\ln y+C$. D) $\frac{x}{y}-\frac{x^2}{2y^2}=\ln y+C$. Show Answer Correct Answer: A) $\frac{x}{y}-\ln\left|\frac{x}{y}+1\right|=\ln y+C$. 3. Why are initial or boundary conditions important in solving second order ODEs? A) They only apply to first order ODEs. B) They are not relevant to the solution. C) They help find the constants of the complementary function. D) They determine the form of the non-homogeneous term. Show Answer Correct Answer: C) They help find the constants of the complementary function. 4. The complete solution of Linear Differential equations involves A) Complete function + particular integral. B) Complementary function + particular integral. C) Complementary function + definite integral. D) Complete function + indefinite integral. Show Answer Correct Answer: B) Complementary function + particular integral. 5. Unit normal to the surface $\phi\left(x, y, z\right)=c$ A) $\left|\nabla\phi\right|$. B) $\frac{\nabla\phi}{\left|\nabla\phi\right|}$. C) $\nabla$. D) $\nabla\phi$. Show Answer Correct Answer: B) $\frac{\nabla\phi}{\left|\nabla\phi\right|}$. 6. Y is proportional to the difference of x and z A) Y= x-z. B) Y= k(z-x). C) Y= k(x-z). D) Y= z-x. Show Answer Correct Answer: C) Y= k(x-z). 7. Determine the degree of the differential equation:$\left(\frac{d^2y}{dx^2}\right)^3 + \frac{dy}{dx} + y = 0$ A) 4. B) 3. C) 2. D) 1. Show Answer Correct Answer: B) 3. 8. What is the general solution to Cauchy's and Euler's equations? A) Exponential functions. B) Trigonometric functions. C) Polynomial functions. D) Power series. Show Answer Correct Answer: D) Power series. 9. State the order and degree for differential equation below:$\left(\frac{\text{d}^2y}{\text{d}x^2}\right)^3+5\left(\frac{\text{d}y}{\text{d}x}\right)^4=\cos3x$ A) Order:2Degree:4. B) Order:3Degree:2. C) Order:2Degree:3. D) Order:4Degree:2. Show Answer Correct Answer: C) Order:2Degree:3. 10. If $f\left(x\right)=\int_1^xt\left(t^3+1\right)^{\frac{3}{2}}dt, $ $f'\left(2\right)$ A) $2^{\frac{3}{2}}$. B) 18. C) 54. D) 135. Show Answer Correct Answer: C) 54. 11. Given a differential equation as $y\frac{\text{d}y}{\text{d}x}=3$ A) $\frac{y^2}{2}=3x+\frac{1}{2}$. B) $y^2=3+\frac{1}{2}$. C) $\frac{y^2}{2}=3x+c$. D) $\frac{y^2}{2}=\frac{3x^2}{3}+\frac{1}{2}$. Show Answer Correct Answer: A) $\frac{y^2}{2}=3x+\frac{1}{2}$. 12. Find the particular solution to the differential equation $\frac{dy}{dx}=2xy+x^2y$ $\left(-3, -1\right)$ A) $y=-e^{x^2+\frac{x^3}{3}}$. B) $y=-2e^{x^2+\frac{x^3}{3}}$. C) $y=e^{\frac{x^2}{2}+\frac{x^3}{3}}$. D) $y=-e^{\frac{x^2}{2}+\frac{x^3}{3}}$. Show Answer Correct Answer: A) $y=-e^{x^2+\frac{x^3}{3}}$. 13. If we eliminate a and b from z = (x+a)(y+b) A) Z = p/q. B) Z = p-q. C) Z = p + q. D) Z = pq. Show Answer Correct Answer: D) Z = pq. 14. What is the condition for a system of equations to have infinitely many solutions? A) All equations are independent. B) Determinant of coefficients is zero. C) At least one equation is redundant. D) Determinant of coefficients is non-zero. Show Answer Correct Answer: B) Determinant of coefficients is zero. 15. The roots of m$^{2}$+1=0 are real and equal. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 16. What does it mean if a function is analytic at a point? A) It has a Taylor series representation. B) It is not defined at that point. C) It is a constant function. D) It has a discontinuity. Show Answer Correct Answer: A) It has a Taylor series representation. 17. What type of PDE is the heat equation? A) Elliptic partial differential equation. B) Linear ordinary differential equation. C) Parabolic partial differential equation. D) Hyperbolic partial differential equation. Show Answer Correct Answer: C) Parabolic partial differential equation. 18. $L\left(\cosh ax\right)= ..... $ A) $\frac{a}{s^2+1}$. B) $\frac{a}{s^2-1}$. C) $\frac{s}{s^2+1}$. D) $\frac{s}{s^2-a^2}$. Show Answer Correct Answer: D) $\frac{s}{s^2-a^2}$. 19. What is the degree of the equation $(y" ')^2+2y'+3=0$ A) 2. B) 3. C) 1. D) 4. Show Answer Correct Answer: A) 2. 20. How is a PDE formed by eliminating arbitrary constants? A) A PDE is formed by differentiating a family of functions and eliminating arbitrary constants. B) A PDE is formed by substituting values into a constant equation. C) A PDE is formed by integrating a single function and adding constants. D) A PDE is formed by multiplying two functions and introducing variables. Show Answer Correct Answer: A) A PDE is formed by differentiating a family of functions and eliminating arbitrary constants. 21. If $3x^2 + 2y$ $2x + 4y$ A) Exact. B) Not exact. C) Linear. D) Homogeneous. Show Answer Correct Answer: A) Exact. 22. Find the solution of the second order differential equation y ''+y=0 is A) Y= C1 ex+ C2e-2x. B) Y= C1 e2x+ C2e-2x. C) Y= C1 + C2x. D) Y= C1sinx+ C2cosx. Show Answer Correct Answer: A) Y= C1 ex+ C2e-2x. 23. RK4 method is: A) Exact method. B) Numerical method. C) Graphical method. D) Analytical method. Show Answer Correct Answer: B) Numerical method. 24. The solution of the differential equation x$^{2}$y" +xy'-y=0 is y=c$_{1}$x+c$_{2}$x$^{-1}$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: A) True. 25. Which of the following functions is a solution of the equation $y" -y = 0$ $y(t) = Ce^{t}$ $C$ $y(t) = Ce^{-t} + 2$ $C$ $y(t) =\cos t$ A) (i) and (ii). B) (i) and (iii). C) (i). D) None of the above. Show Answer Correct Answer: C) (i). ← 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