This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 29 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 29 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. If S=\{(1, 0, 0), (2, 0, 0), (3, 0, 0)\} is a subset of R$^{3}$, the dim(L(S))= A) 1. B) 2. C) 3. D) 4. Show Answer Correct Answer: A) 1. 2. The complementary function of x$^{2y" -3xy'-5y=sin(logx) is ..... }$ A) C$_{1}$x$^{5}$+c$_{2}$x$^{-1}$. B) C$_{1}$cos5x+c$_{2}$sinx. C) C$_{1e}$$^{5x}$+c$_{2}$x$^{-1}$. D) C$_{1}$x$^{5}$+c$_{2e}$$^{-x}$. Show Answer Correct Answer: A) C$_{1}$x$^{5}$+c$_{2}$x$^{-1}$. 3. Which is Bernoulli's equation? A) Y' + p(x)y = q(x). B) $y' + p(x)y = q(x)y^n$. C) $y = \frac{(x^2 + y^2)}{xy}$. D) None. Show Answer Correct Answer: B) $y' + p(x)y = q(x)y^n$. 4. $L\left(1\right)=$ A) $\frac{1}{s^2}$. B) $\frac{1}{s}$. C) $1$. D) $0$. Show Answer Correct Answer: B) $\frac{1}{s}$. 5. Which of the following is NOT a step in Euler's Method? A) Choose a step size $h$. B) Use the formula $y_{n+1} = y_n + h f(x_n, y_n)$. C) Find the exact analytical solution. D) Update $x$ $y$. Show Answer Correct Answer: C) Find the exact analytical solution. 6. For system $\vec{X}' = A \vec{X}$ A) Any constant vector. B) $\vec{X} = 0$. C) Determined by det(A). D) Always unstable. Show Answer Correct Answer: B) $\vec{X} = 0$. 7. Differential equation of the ellipses having centre at the origin and foci on x axis is A) Xy.y$^{"}$+x (y$^{' }$)$^{2}$=0. B) Xy.y$^{"}$+x (y$^{' }$)$^{2}$=y.y$^{'}$. C) Xy.y$^{" }$-x (y$^{' }$)$^{2}$=y.y$^{'}$. D) Xy.y$^{"}$+x (y$^{' }$)$^{2}$=y$^{'}$. Show Answer Correct Answer: B) Xy.y$^{"}$+x (y$^{' }$)$^{2}$=y.y$^{'}$. 8. Integrating factor of $\frac{d^2y}{dx^2}+\frac{dy}{dx}\tan x=\sec x+\cos x$ A) Cos x. B) Sin x. C) Tan x. D) Sec xTags5. Show Answer Correct Answer: D) Sec xTags5. 9. An integrating factor of the differential equation $\left(e^{2x}+1\right)\frac{\text{d}y}{\text{d}x}+4e^{2x}y=x$ A) $e^{2x}+1$. B) $e^{2e^{2x}}$. C) $\left(e^{2x}+1\right)^2$. D) $\left(e^{2x}+1\right)^4$. Show Answer Correct Answer: C) $\left(e^{2x}+1\right)^2$. 10. Identify the linearly independent set among the following in R$^{3}$. A) \{(1, 2, 3), (2, 4, 6), (1, 3, 0)\}. B) \{(1, -1, 0), (1, 1, 2)\}. C) \{(1, 1, 0), (0, 1, 1), (1, 0, 1), (1, 1, 1)\}. D) \{(1, 1, 2), (1, 0, 3), (0, 0, 0)\}. Show Answer Correct Answer: B) \{(1, -1, 0), (1, 1, 2)\}. 11. What is the order of the equation $y'+y^2=0$ A) 1. B) 3. C) 0. D) 2. Show Answer Correct Answer: A) 1. 12. If dy/dx = 2xy and y = 6 when x = 0, then y= A) $x^2y^2+6$. B) $e^{x^2}$. C) $\sqrt[]{x^2+16}$. D) $6e^{x^2}$. Show Answer Correct Answer: D) $6e^{x^2}$. 13. In differential equations, integration is mainly used to ..... A) Find slopes. B) Simplify algebra. C) Recover the function from its rate of change. D) Compute area. Show Answer Correct Answer: C) Recover the function from its rate of change. 14. Give an example of type III of a PDE A) F(z, p, q, a)=0. B) P(1-q$^{2}$)=q(1-z). C) P-x$^{2}$=q+y$^{2}$. D) P$^{2}$-q$^{2}$=1. Show Answer Correct Answer: B) P(1-q$^{2}$)=q(1-z). 15. The derivative of $\ln x$ A) $x$. B) $\dfrac{1}{x}$. C) $e^x$. D) $x^{-2}$. Show Answer Correct Answer: B) $\dfrac{1}{x}$. 16. Solve the partial differential equation $\frac{\partial z}{\partial y}=0.$ A) Z=yf(x). B) Z=xf(y). C) Z=f(y). D) Z=f(x). Show Answer Correct Answer: D) Z=f(x). 17. The nature of the one-dimensional heat equation is A) Circular. B) Elliptic. C) Parabolic. D) Hyperbolic. Show Answer Correct Answer: C) Parabolic. 18. What are the coefficients in the quadratic equation used to solve homogeneous second-order linear differential equations? A) R, s, t. B) M, n, p. C) X, y, z. D) A, b, c. Show Answer Correct Answer: D) A, b, c. 19. You draw a card at random from a standard deck of 52 cards. Find the probability that the card is a heart given that it is black. A) 0.25. B) 0. C) 0 077. D) 0.333. Show Answer Correct Answer: B) 0. 20. $\frac{dy}{dx}=2y\left(3-x\right)$ A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. 21. The particular solution of the differential equation $\frac{\text{d}y}{\text{d}x}=y^2e^{2x}$ A) $y=\frac{2}{3-e^{2x}}$. B) $y=\frac{2}{1+e^{2x}}$. C) $y=\frac{1}{2-e^{2x}}$. D) $y=e^{-2x}$. Show Answer Correct Answer: A) $y=\frac{2}{3-e^{2x}}$. 22. What do mean by linear A) Degree 1. B) Degree 2. C) Degree 3. D) Degree 4. Show Answer Correct Answer: A) Degree 1. 23. Bismuth-210 has a half life of 5 days. Suppose the sample originally has a mass of 800 mg. Determine how long it will take for the mass to be reduced to 1 mg. A) 53.865 days. B) 79.320 days. C) 36.893 days. D) 48.219 days. Show Answer Correct Answer: D) 48.219 days. 24. The rate at which a chemical element decays is directly proportional to the amount of the element remaining. Suppose 20 grams of the element is present at t = 0. At t = 2, 5 grams of the element is present. Which of the following equations can be used to find the correct constant of proportionality, k? A) $20=5e^{2k}$. B) $5=20e^{2k}$. C) $20=2e^{5k}$. D) $2=20e^{5k}$. Show Answer Correct Answer: B) $5=20e^{2k}$. 25. Which method is used to solve separable differential equations? A) Integration by parts. B) Separation of variables. C) Homogeneous method. D) Substitution method. Show Answer Correct Answer: B) Separation of variables. ← 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