This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 25 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 25 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. CHOOSE THE CORRECT FORM OF PARTICULAR INTEGRAL FOR sin(ax) A) PI=e$^{ax+by }$/f(a, b). B) PI=sin$^{ax}$ / f(a, b). C) PI=sin$^{ax}$/ f(-a$^{2}$, -ab, -b$^{2}$). D) PI=1/ f(-a$^{2}$, -ab, -b$^{2}$). Show Answer Correct Answer: C) PI=sin$^{ax}$/ f(-a$^{2}$, -ab, -b$^{2}$). 2. What is the order and degree for the differential equation:$\left(\frac{\text{d}y}{\text{d}x}\right)^4-\left(\frac{\text{d}^2y}{\text{d}x^2}\right)=-y$ A) Order:4 Degree:1. B) Order:2 Degree:1. C) Order:1 Degree:4. D) Order:2 Degree:4. Show Answer Correct Answer: B) Order:2 Degree:1. 3. Choose the correct expansion of (1+x)$^{-1}$ A) 1-x+ x$^{2}$-x$^{3}$+x$^{5}$. B) 1+x+ x$^{2}$-x$^{3}$. C) 1-x+ x$^{2}$-x$^{3}$-x$^{4}$. D) 1-x+ x$^{2}$-x$^{3}$+x$^{4}$. Show Answer Correct Answer: D) 1-x+ x$^{2}$-x$^{3}$+x$^{4}$. 4. Any periodic motion can be written as sum of harmonic functions. A) Yes. B) No. C) All the above. D) None of the above. Show Answer Correct Answer: A) Yes. 5. For repeated roots m1=m2=m, the complementary function is: A) $c_1e^{mx}$. B) $(c_1+c_2)xe^{mx}$. C) $c_1e^{mx}+c_2xe^{mx}$. D) $(c_1+c_2e^{mx})$. Show Answer Correct Answer: C) $c_1e^{mx}+c_2xe^{mx}$. 6. The fundamental frequency corresponds to: A) The highest frequency of the signal. B) The first harmonic. C) The average of all harmonics. D) Zero frequency component. Show Answer Correct Answer: B) The first harmonic. 7. Which of the following is a first-order PDE? A) U x + u y = 0. B) U x-u y = 0. C) U x u y = 0. D) U x + 2u y = 1. Show Answer Correct Answer: A) U x + u y = 0. 8. Which of the following equations represents Clairaut's partial differential equation? A) Z=px+f(p, q). B) Z=f(p, q). C) Z=p+q+f(p, q). D) Z=px+qy+f(p, q). Show Answer Correct Answer: D) Z=px+qy+f(p, q). 9. If a substance decomposes at a rate proportional to the amount of the substance present, and if the amount decreases from 40 g to 5 g in 3 hours, then the constant of proportionality is A) $-\ln2$. B) $-\ln8$. C) $-\ln\left(\frac{1}{8}\right)$. D) $-\ln\left(\frac{1}{2}\right)$. Show Answer Correct Answer: A) $-\ln2$. 10. Find the general solution $\frac{\text{d}y}{\text{d}x}=4x$ A) $y=4x^2+c$. B) $y=2x+c$. C) $y=4x+c$. D) $y=2x^2+c$. Show Answer Correct Answer: D) $y=2x^2+c$. 11. What type of differential equations are Cauchy's and Euler's equations used to solve? A) First order linear. B) Nonlinear. C) Higher order linear with constant coefficients. D) Initial and boundary value problems. Show Answer Correct Answer: C) Higher order linear with constant coefficients. 12. When applying boundary conditions to a PDE, what is the primary goal? A) To find the general solution of the PDE. B) To determine specific values of the unknown function at the boundaries of the domain. C) To classify the PDE as linear or non-linear. D) To convert the PDE into an ordinary differential equation. Show Answer Correct Answer: B) To determine specific values of the unknown function at the boundaries of the domain. 13. The general solution of the DE $\frac{d^2y}{dx^{2}}+4\frac{dy}{dx}-5y=0$ A) $y=Ae^x+Be^{-5x}$. B) $y=Ae^x+Be^{5x}$. C) $y=Ae^{-x}+Be^{-5x}$. D) $y=Ae^{-x}+Be^{5x}$. Show Answer Correct Answer: A) $y=Ae^x+Be^{-5x}$. 14. Which of the following has the trial solution z=ax+by+c A) $z=px+qy+p^2$. B) $p+q=pq$. C) $p\left(1+q\right)=qz$. D) None of the above. Show Answer Correct Answer: B) $p+q=pq$. 15. A differential equation in which the function depends on more than one independent variabls is called a ..... A) Partial differential equation. B) Linear equation. C) Ordinary differential equation. D) Non linear equation. Show Answer Correct Answer: A) Partial differential equation. 16. Determine whether the functions $y_{1} = e^{4x}$ $y_{2} = xe^{4x}$ A) Yes, the functions are linearly independent. B) No, the functions are linearly dependent. C) The functions coincide. D) The functions are undefined. Show Answer Correct Answer: A) Yes, the functions are linearly independent. 17. A particular integral of y ''-4y=ex is A) 12ex. B) Xex. C) X2ex. D) E-x. Show Answer Correct Answer: B) Xex. 18. Integrating factor of $\frac{\text{d}y}{\text{d}x}+\frac{1}{x}=\frac{e^y}{x^2}$ A) X. B) $\frac{1}{x}$. C) $x^2$. D) $-\frac{1}{x}$. Show Answer Correct Answer: B) $\frac{1}{x}$. 19. Cross product is commutative. A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 20. If y satisfies $\frac{dy}{dt}=ky$ A) $3e^{kt}$. B) $3e^{kty}$. C) $e^{kt}+5$. D) $kty+7$. Show Answer Correct Answer: A) $3e^{kt}$. 21. How would you CORRECTLY separate the following differential equation? $\frac{dy}{dx}=\frac{2x+1}{3y}$ A) $3y\cdot dy=\left(2x+1\right)dx$. B) $\frac{dy}{3y}=\left(2x+1\right)dx$. C) $\frac{dy}{3y}=\frac{dx}{2x+1}$. D) $3y^{-1}dy=\left(2x+1\right)dx$. Show Answer Correct Answer: A) $3y\cdot dy=\left(2x+1\right)dx$. 22. $L^{-1}\left[\frac{1}{\left(s-a\right)^2}\right]=$ A) $xe^{-ax}$. B) $e^{ax}$. C) $xe^{ax}$. D) $e^x$. Show Answer Correct Answer: C) $xe^{ax}$. 23. Order and degree of the D.E. y$^{" }$+logy$^{" '}$-xy+(y" ')$^{3}$=0 A) 3, 1. B) 2, 3. C) Order-3, degree not defined. D) 3, 3. Show Answer Correct Answer: C) Order-3, degree not defined. 24. Using $v=xy$ $y+x\frac{dy}{dx}=1-xy$ A) $\frac{dv}{dx}=1-v$. B) $x\frac{dv}{dx}=v$. C) $\frac{v}{x}+\frac{dv}{dx}=1-v$. D) $\frac{dv}{dx}+x\\frac{dy}{dx}=1-v$. Show Answer Correct Answer: A) $\frac{dv}{dx}=1-v$. 25. There are two (2) types of conditions in a differential equation:Initial and Boundary. Identify the type of condition for the followings problems.a) $y\left(\pi\right)=-3$ $y'\left(\pi\right)=0$ $y\left(2\right)=1$ $y'\left(1\right)=0$ $y\left(0\right)=0$ $y'\left(0\right)=1.$ A) Initial.b) Boundary.c) Initial. B) Boundary.b) Initial.c) Boundary. C) Initial.b) Boundary.c) Boundary. D) Boundary.b) Initial.c) Initial. Show Answer Correct Answer: A) Initial.b) Boundary.c) Initial. ← 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