This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 16 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 16 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Green's theorem connects A) Line integral and double integral. B) Line integral and Surface integral. C) Double integral and Surface integral. D) Surface integral and volume integral. Show Answer Correct Answer: A) Line integral and double integral. 2. Which among the following statements is true? A) A subset of linearly dependent is linear dependent. B) The union of two subspaces is a subspace. C) A spanning set should be a basis for a vector space. D) A subset of a linearly independent is linearly independent. Show Answer Correct Answer: D) A subset of a linearly independent is linearly independent. 3. Which of the following is the solution to the differential equation $\frac{dy}{dx}=3\cos x$ $y\!\left(\frac{\pi}{2}\right)=-1$ A) $y=3\sin x+2$. B) $y=3\sin x-4$. C) $y=-3\sin x+2$. D) $y=-3\sin x-4$. Show Answer Correct Answer: B) $y=3\sin x-4$. 4. If $\frac{dy}{dx}=2y^2$ A) -2/3. B) -1/3. C) 1/3. D) 2/3. Show Answer Correct Answer: B) -1/3. 5. Solve $\left(D^3-DD'^2-D'^3\right)z=0$ A) $Z=f_1\left(y+x\right)+f_2\left(y-x\right)+xf_3\left(y-x\right)$. B) $Z=f_1\left(y-2x\right)+xf_2\left(y-2x\right)+f_3\left(y+x\right)$. C) $Z=f_1\left(y\right)+xf_2\left(y\right)+f_3\left(y-x\right)$. D) $Z=f_1\left(y+x\right)+f_2\left(y-x\right)+f_3\left(y-x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y+x\right)+f_2\left(y-x\right)+xf_3\left(y-x\right)$. 6. For the differential equation (D$^{2}$-4D+4)y=0, the auxiliary equation is: A) $m^2-2m+2=0$. B) $m^2-4m-4=0$. C) $m^2+4m+4=0$. D) $m^2-4m+4=0$. Show Answer Correct Answer: D) $m^2-4m+4=0$. 7. If a slope field for $\frac{dy}{dx} = x-y$ $(x, y)$ A) The value of $y$. B) The slope $x-y$. C) The value of $x$. D) The solution curve passing through that point. Show Answer Correct Answer: B) The slope $x-y$. 8. $L^{-1}\left(\frac{1}{s-a}\right)$ A) $e^{-ax}$. B) $e^{-x}$. C) $e^{ax}$. D) 1. Show Answer Correct Answer: C) $e^{ax}$. 9. A vector $\overrightarrow{f}$ A) $\nabla^2\overrightarrow{f}=0$. B) $\nabla^2\overrightarrow{f}=\overrightarrow{0}$. C) $\nabla\overrightarrow{f}=0$. D) $\nabla\overrightarrow{f}=\overrightarrow{0}$. Show Answer Correct Answer: A) $\nabla^2\overrightarrow{f}=0$. 10. What is DE A) Contains variables. B) Have constants. C) Contains variables and its derivatives. D) Has image. Show Answer Correct Answer: C) Contains variables and its derivatives. 11. Eigen values of the matrix [ 1 1 1 ; 1 1 1 ; 1 1 1 ] are A) 0, 0, 0. B) 0, 0, 3. C) 1, 1, 1. D) 0, 0, 1. Show Answer Correct Answer: B) 0, 0, 3. 12. The C.F. of the equation $\left(D^2-4\right)y=\sin^2x$ A) $c_1e^{-x}+c_2e^{2x}$. B) $c_1e^x+c_2e^{-2x}$. C) $c_1e^x+c_2e^{2x}$. D) $c_1e^{4x}+c_2e^{2x}$. Show Answer Correct Answer: C) $c_1e^x+c_2e^{2x}$. 13. What is meant by P.I. in solution of a linear differential equation? A) Solution of Auxiliary equation. B) Effect of the terms of equation that are not attached to any dependent variable or its derivatives. C) Proper Involvement. D) Power and Intensity. Show Answer Correct Answer: B) Effect of the terms of equation that are not attached to any dependent variable or its derivatives. 14. In a series LR circuit connected to a DC source (E), the governing differential equation is: A) L (di/dt) + Ri = E. B) R (di/dt) + Li = E. C) L (di/dt)-Ri = E. D) R (di/dt)-Li = E. Show Answer Correct Answer: A) L (di/dt) + Ri = E. 15. The highest derivative in the given pde is called A) Order. B) Degree. C) All the above. D) None of the above. Show Answer Correct Answer: A) Order. 16. What type of differential equations involve finding the solution at a specific point or along a specific curve? A) Initial and boundary value problems. B) Partial differential equations. C) First order linear. D) Nonlinear. Show Answer Correct Answer: A) Initial and boundary value problems. 17. On what interval(s) is the function $f\left(x\right)=x^3+6x^2$ A) $\left(-\infty, -4\right)$. B) $\left(-\infty, -2\right)$. C) $\left(-2, \infty\right)$. D) $\left(0, \infty\right)$. Show Answer Correct Answer: B) $\left(-\infty, -2\right)$. 18. L$^{-1 }$\{1/s\} A) 1. B) T$^{n}$. C) E$^{at}$. D) T$^{n }$e$^{at}$. E) Cos bt. Show Answer Correct Answer: A) 1. 19. The solution of y '" =0 is A) Y= C1 +C2x+ C3x2. B) Y= C1 ex+C2e-x+ C3. C) Y= C1 sinx+C2cosx+ C3. D) Y=C1 +C2x+ C3x2 ex. Show Answer Correct Answer: A) Y= C1 +C2x+ C3x2. 20. Separate the variables for the equation $\frac{dy}{dx}=3y+2$ A) $\frac{dy}{(3y+2)}=dx$. B) $\frac{dy}{3y}=dx$. C) $\frac{dy}{y+2}=3dx$. D) $\left(3y+2\right)dx=dy$. Show Answer Correct Answer: A) $\frac{dy}{(3y+2)}=dx$. 21. $L\left(\sinh ax\right)= ..... $ A) $\frac{a}{s^2+1}$. B) $\frac{a}{s^2-a^2}$. C) $\frac{s}{s^2+1}$. D) $\frac{s}{s^2-1}$. Show Answer Correct Answer: B) $\frac{a}{s^2-a^2}$. 22. The derivative of $e^{3x}$ A) Power rule. B) Product rule. C) Chain rule. D) Quotient rule. Show Answer Correct Answer: C) Chain rule. 23. If P(t) is the size of a population at time t, which of the following differential equations describes linear growth in the size of the population. A) $\frac{dP}{dt}=200$. B) $\frac{dP}{dt}=200t$. C) $\frac{dP}{dt}=100t^2$. D) $\frac{dP}{dt}=200P$. E) $\frac{dP}{dt}=100P^2$. Show Answer Correct Answer: A) $\frac{dP}{dt}=200$. 24. Giving particular values for arbitrary constants in the complete integral is called A) Particular solution. B) General solution. C) Singular solution. D) None of the above. Show Answer Correct Answer: A) Particular solution. 25. Parametric equation of the line joining (0, 0, 0) and (2, 1, 1) can be taken as ..... A) X = 2t, y=t, z = t where $0\le t\le1$. B) X=t, y = t, z = t where $0\le t\le1$. C) X = 2, y = 1, z = 1. D) X = 2t, y=t, z = t where $0\le t\le2$. Show Answer Correct Answer: A) X = 2t, y=t, z = t where $0\le t\le1$. ← 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