This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 34 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 34 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. The following are the requirements of a DE to be linear except one A) 1st order. B) 1st degree. C) No transcendental functions of the dependent variable and its derivatives. D) No product of the dependent variable and its derivatives. Show Answer Correct Answer: A) 1st order. 2. An equation that contains only ordinary derivatives of one or more dependent variables with respect to a single independent variable A) Dependent Differential Equation. B) First Order Differential Equation. C) Partial Differential Equation. D) Ordinary Differential Equation. Show Answer Correct Answer: D) Ordinary Differential Equation. 3. Differential equations in control systems are mainly used to describe ..... A) Static behavior of systems. B) Dynamic behavior of systems. C) Geometric modeling only. D) Stability of algebraic equations. Show Answer Correct Answer: B) Dynamic behavior of systems. 4. What is Euler's method used for? A) Measuring angles in a triangle. B) Approximating solutions to ordinary differential equations. C) Solving algebraic equations. D) Finding prime numbers. Show Answer Correct Answer: B) Approximating solutions to ordinary differential equations. 5. Solutions of differential equations are categorized into general and particular. Identify the type of solution of the equations shown below.a) $\frac{\text{d}y}{\text{d}x}=2e^x+5e^{2x}$ $\frac{\text{d}y}{\text{d}x}=Ae^x+5e^{2x}$ A) General.b) Particular. B) General.b) General. C) Particular.b) General. D) Particular.b) Particular. Show Answer Correct Answer: C) Particular.b) General. 6. Which of the following is a method for solving first-order differential equations? A) Partial fractions. B) Variable separation. C) Integration by substitution. D) Matrix method. Show Answer Correct Answer: B) Variable separation. 7. Solve dy/dx = 5x/y given the point (0, -1) A) $y=\sqrt[]{5x^2+1}$. B) $y=-\sqrt[]{\frac{5}{2}x^2+1}$. C) $y=-\sqrt[]{5x^2+1}$. D) $y=-\sqrt[]{5x^2+5}$. Show Answer Correct Answer: C) $y=-\sqrt[]{5x^2+1}$. 8. F(s) = L\{(e$^{at}$sin(bt))\} (s) A) 1/s. B) B/(s-a)$^{2 }$+ b$^{2}$. C) (s-a)/(s-a)$^{2}$+b$^{2}$. D) B/(s$^{2}$ + b$^{2}$). E) S/(s$^{2}$+b$^{2}$). Show Answer Correct Answer: B) B/(s-a)$^{2 }$+ b$^{2}$. 9. Let PDE c$^{2}$(u$_{xx }$+ u$_{yy }$)= u$_{tt}$, By is known as A) 2-D heat equation. B) 2-D wave equation. C) Laplace equation. D) None of these. Show Answer Correct Answer: B) 2-D wave equation. 10. Part B. Find the particular solution under the given conditions:15. y" + 3y' + 2y = 0, y(0) = 1, y'(0) = 1 A) $y = 2e^{-x}-e^{-2x}$. B) $y = e^{-x} + e^{-2x}$. C) $y = e^{x}-2e^{-2x}$. D) $y = e^{-x}-e^{-2x}$. Show Answer Correct Answer: A) $y = 2e^{-x}-e^{-2x}$. 11. Let A and B be two subspaces of a vector space V. Then A U B is a subspace of V if and only if A) $A\cap B=\left\{0\right\}$. B) $A\cup B=B$. C) $A\cap B=\phi$. D) $A\cap B=\left\{0, 1\right\}$. Show Answer Correct Answer: B) $A\cup B=B$. 12. Which of these is the correct complimentary function for the equation $2\frac{\text{d}^2y}{\text{d}x}+4\frac{\text{d}y}{\text{d}x}-6y=0$ A) $Ae^{3x}+Be^x$. B) $Ae^{3x}+Be^{-x}$. C) $Ae^{-3x}+Be^x$. D) $Ae^{-3x}+Be^{-x}$. Show Answer Correct Answer: C) $Ae^{-3x}+Be^x$. 13. If N(t) is the size of a population at time t, which of the following differential equations describes exponential growth in the size of the population? A) $\frac{dN}{dt}=300$. B) $\frac{dN}{dt}=300t$. C) $\frac{dN}{dt}=\frac{300}{N}$. D) $\frac{dN}{dt}=300N$. Show Answer Correct Answer: D) $\frac{dN}{dt}=300N$. 14. The general solution of Clairaut's equation involves: A) One arbitrary constant. B) Two arbitrary constants. C) No arbitrary constant. D) None. Show Answer Correct Answer: A) One arbitrary constant. 15. Find the general solution to the following non-homogeneous DE:$\frac{d^2y}{dx^2}+2\frac{dy}{dx}+y=\cos2x$ A) $y=(A+Bx)e^{-x}+(3/31)\cos2x+(4/31)\sin2x$. B) $y=(A+Bx)e^{-x}+P\cos2x+Q\sin2x$. C) $y=(A+Bx)e^x+(3/31)\cos2x+(4/31)\sin2x$. D) $y=Ae^{-x}+Be^x+(3/31)\cos2x+(4/31)\sin2x$. Show Answer Correct Answer: A) $y=(A+Bx)e^{-x}+(3/31)\cos2x+(4/31)\sin2x$. 16. Find the order for the differential equation. A) 4. B) 3. C) 2. D) 6. Show Answer Correct Answer: B) 3. 17. What do you understand by the term 'partial derivative'? A) A derivative of a function with respect to a constant. B) A derivative of a function with respect to one of its variables, with all other variables held constant. C) A derivative of a function with respect to a new variable. D) A derivative of a function with respect to all of its variables. Show Answer Correct Answer: B) A derivative of a function with respect to one of its variables, with all other variables held constant. 18. Solve the partial differential equation $\frac{\partial^2z}{\partial x\partial y}=0$ A) $z=f\left(y\right)+g\left(x\right)$. B) $z=xf\left(y\right)+g\left(x\right)$. C) $z=xf\left(x\right)+g\left(y\right)$. D) $z=f\left(y\right)g\left(x\right)$. Show Answer Correct Answer: A) $z=f\left(y\right)+g\left(x\right)$. 19. Given the differential equation $\frac{dP}{dt}=5P$ 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$^{5t}$. 20. Roots of the auxiliary equation determine: A) The method of solving algebraic equations. B) The form of the complementary solution. C) The Wronskian of the functions. D) The non-homogeneous term. Show Answer Correct Answer: B) The form of the complementary solution. 21. A solution obtained by giving particular values to the arbitrary constants in a complete integral is called ..... A) Complete integral. B) Particular integral. C) Singular integral. D) General integral. Show Answer Correct Answer: B) Particular integral. 22. Solve the differential equation. $\frac{dy}{dt}=\frac{\sqrt{t}}{y^3}$ A) $\frac{y^4}{4}=t^{\frac{3}{2}}+C$. B) $y=t^2+C$. C) $y^3=t^2+C$. D) $\frac{y^4}{4}=\frac{2}{3}t^{\frac{3}{2}}+C$. Show Answer Correct Answer: D) $\frac{y^4}{4}=\frac{2}{3}t^{\frac{3}{2}}+C$. 23. Find the order of the differential equation:$\frac{d^4y}{dx^4} + 2\frac{d^2y}{dx^2}-y = 0$ A) 3. B) 4. C) 2. D) 1. Show Answer Correct Answer: B) 4. 24. The power of the differential equation's highest derivative, after the equation has been made rational and integral in all of its derivatives A) Order. B) Degree. C) Exponent. D) Variable. Show Answer Correct Answer: B) Degree. 25. General solution of (D$^{2}$+9) y= 0 is A) Y =c$_{1}$ cos x + c$_{2}$ sin x +x. B) Y = x. C) Y = c$_{1}$ cos 3x + c$_{2}$ sin 3x. D) None. Show Answer Correct Answer: C) Y = c$_{1}$ cos 3x + c$_{2}$ sin 3x. ← 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