This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 35 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 35 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which type of differential equations involve finding the solution at a specific point or along a specific curve? A) Nonlinear differential equations. B) First order linear differential equations. C) Partial differential equations. D) Initial and boundary value problems. Show Answer Correct Answer: B) First order linear differential equations. 2. When can the method of separation of variables be used to solve differential equations? A) When the equation is linear. B) When the equation is nonlinear. C) When the equation is homogeneous. D) When the equation is non-homogeneous. Show Answer Correct Answer: A) When the equation is linear. 3. Which of the following is the solution to the differential equation $\frac{dy}{dx}=3y^2$ $y\left(0\right)=3$ A) $y=\sqrt{9e^{3x}}$. B) $y=\sqrt{\frac{1}{9}e^{3x}}$. C) $y=\frac{3}{1-9x}$. D) $y=\frac{3}{9x-1}$. Show Answer Correct Answer: C) $y=\frac{3}{1-9x}$. 4. An equation containing partial derivatives of one or more dependent variables of two or more independent variables A) Ordinary Partial Differential Equation. B) Partial Differential Equation. C) Ordinary Differential Equation. D) Partially Ordinary Differential Equation. Show Answer Correct Answer: B) Partial Differential Equation. 5. The value of $\int_0^1\int_0^1\left(x^2+y^2\right)dxdy$ A) 2/3. B) 2. C) 1/2. D) 2. Show Answer Correct Answer: A) 2/3. 6. Find the roots of $m^3-m^2+m-1=0$ A) 1, i, -i. B) 1, -1, i. C) I, -i, 0. D) 1, -1, 0. Show Answer Correct Answer: A) 1, i, -i. 7. If $\frac{dy}{dx}=y\\sec^2x$ A) $e^{\tan x}+4$. B) $e^{\tan x}+5$. C) $5e^{\tan x}$. D) $\tan x+5$. Show Answer Correct Answer: C) $5e^{\tan x}$. 8. P. 392 #11 A) A. B) B. C) C. D) D. E) E. Show Answer Correct Answer: A) A. 9. Choose the Differential Equations A) $3x-4y+xy=1$. B) $5y+3y" -x^2=1$. C) $\frac{x}{y}+1=xy$. D) $6x^3+2y^4=xy-4$. Show Answer Correct Answer: B) $5y+3y" -x^2=1$. 10. For y" -y=0, y(0)=2, y'(0)=0, the solution is: A) $2\cosh x$. B) $2\sinh x$. C) $2e^x$. D) $2e^{-x}$. Show Answer Correct Answer: A) $2\cosh x$. 11. The general solution of the differential equation $\frac{\text{d}y}{\text{d}x}-\left(\cot x\right)y=\sin\left(2x\right)$ A) $y=\frac{1}{2}\sin\left(2x\right)+A\sin x$. B) $y=2\sin^2\left(x\right)+\sin x+A$. C) $y=\frac{2}{3}\sin^2\left(x\right)+A\operatorname{cosec}\left(x\right)$. D) $y=2\sin^2\left(x\right)+A\sin x$. Show Answer Correct Answer: D) $y=2\sin^2\left(x\right)+A\sin x$. 12. Solve the differential equation sec$^{2}$xtanydx+sec$^{2}$ytanxdy=0 A) -sinx tany=c. B) Sinx tany=c. C) Tanx tany=c. D) -tanx tany=c. Show Answer Correct Answer: C) Tanx tany=c. 13. $\left(\frac{\text{d}y}{\text{d}x}\right)^2-\tan x=0$ A) Second order differential equation. B) First order differential equation. C) First order differential equation at second degree. D) Second order differential equation at first degree. Show Answer Correct Answer: C) First order differential equation at second degree. 14. What is the degree of the differential equation:$\left(\frac{d^2y}{dx^2}\right)^5 + 4\frac{dy}{dx}-3y = 0$ A) 2. B) 3. C) 5. D) 4. Show Answer Correct Answer: C) 5. 15. Analyze the stability of the equilibrium solution $y = 2$ $\frac{dy}{dt} = (y-2)(y+1)$ A) Stable. B) Unstable. C) Semi-stable. D) Cannot be determined. Show Answer Correct Answer: A) Stable. 16. Based on the slope field, what can you infer about the behavior of the solution curves for the differential equation dy/dx = x-y? A) The behavior of the solution curves is oscillating between two values. B) The behavior of the solution curves is diverging to infinity. C) The behavior of the solution curves is random and unpredictable. D) The behavior of the solution curves is approaching a stable equilibrium. Show Answer Correct Answer: D) The behavior of the solution curves is approaching a stable equilibrium. 17. The other name of characteristic roots A) Eigen value. B) Eigen vector. C) Root. D) Zero. Show Answer Correct Answer: A) Eigen value. 18. The value of $\int_0^1\int_x^1\left(x^2+y^2\right)dydx$ A) 1/2. B) 1. C) 2/3. D) 1/3. Show Answer Correct Answer: D) 1/3. 19. Dp/dy = (4y)$^{-1}$find the general solution A) P= 1/5y$^{5/4}$ + c. B) P= 1/4ln|4y| + c. C) P= 1/8y$^{2}$ + c. D) P= 1 + c 4y. Show Answer Correct Answer: B) P= 1/4ln|4y| + c. 20. What is the standard form of a first order linear differential equation? A) Y + P(x)y + Q(x)y = 0. B) Y + P(x)y = Q(x). C) Y = f(y). D) Y + y = 0. Show Answer Correct Answer: B) Y + P(x)y = Q(x). 21. What is the significance of boundary conditions in PDEs? A) Boundary conditions are irrelevant in PDEs. B) Boundary conditions only affect linear equations. C) Boundary conditions are used to simplify PDEs without affecting solutions. D) Boundary conditions determine the uniqueness and behavior of solutions in PDEs. Show Answer Correct Answer: D) Boundary conditions determine the uniqueness and behavior of solutions in PDEs. 22. What would the sign of the square root solution to a differential equation be given the initial condition g(1)=-5? A) Positive. B) Negative. C) All the above. D) None of the above. Show Answer Correct Answer: B) Negative. 23. What is the order of the PDE \( u ..... \{xx\} + u ..... \{yy\} = 0 \)? A) 2. B) 4. C) 3. D) 1. Show Answer Correct Answer: A) 2. 24. $L^{-1}\left[\frac{1}{s^2}\right]=$ A) $x$. B) $1$. C) $0$. D) $x^2$. Show Answer Correct Answer: A) $x$. 25. What is the antiderivative of sine x in the context of separation of variables? A) Cosine x. B) -cosine x. C) Tangent x. D) Secant x. Show Answer Correct Answer: B) -cosine x. ← 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