This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 1 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 1 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Which of the following is the solution to the differential equation $\frac{dy}{dx}=\frac{x^2}{y}$ A) $y=-2e^{\left(-9+\frac{x^3}{3}\right)}$. B) $y=\sqrt{\frac{2x^3}{3}}$. C) $y=\sqrt{\frac{2x^3}{3}-14}$. D) $y=-\sqrt{\frac{2x^3}{3}-14}$. Show Answer Correct Answer: D) $y=-\sqrt{\frac{2x^3}{3}-14}$. 2. The general solution of the differential equation $x\frac{\text{d}y}{\text{d}x}+3y=x^2$ A) $y=\frac{x^2}{5}+\frac{c}{x^3}$. B) $y=x^2+Cx$. C) $y=\frac{x}{5}+C$. D) $y=\frac{x^2}{2}+\frac{c}{x}$. Show Answer Correct Answer: A) $y=\frac{x^2}{5}+\frac{c}{x^3}$. 3. If the auxiliary equation has distinct real roots, the complementary function is a combination of: A) Exponentials. B) Trigonometric functions. C) Polynomials. D) None. Show Answer Correct Answer: A) Exponentials. 4. A partial differential equation which is not linear then it is called ..... A) Semi linear. B) Collinear. C) Quasi linear. D) Non-linear. Show Answer Correct Answer: D) Non-linear. 5. $L\left(e^{-ax}\cos bx\right)=\frac{\left(s+a\right)}{\left(s+a\right)^2+b^2}$ A) False. B) True. C) All the above. D) None of the above. Show Answer Correct Answer: B) True. 6. What is the order of the equation $y" + y^3 + y = 0$ A) 1. B) 2. C) 3. D) None of the above. Show Answer Correct Answer: B) 2. 7. The characteristic equation for [-2 2 2 1] is ..... A) $x^2+x-6$. B) $x^2+3x-6$. C) $x^2+4x+6$. D) $x^2+2x-16$. Show Answer Correct Answer: A) $x^2+x-6$. 8. What is the Integrating factor of Mdx+Ndy if it is in form $yf\left(xy\right)dx+xg\left(xy\right)dy=0$ A) $\frac{1}{M+N}$. B) $\frac{1}{MX+NY}$. C) $\frac{1}{M-N}$. D) $\frac{1}{MX-Ny}$. Show Answer Correct Answer: D) $\frac{1}{MX-Ny}$. 9. The ends A and B of a rod of length20cm are at 30$^{0}$C and 80$^{0}$C at end points until steady state prevails. Then the temperature of the rod at ends are changed to 40$^{0}$C and 60$^{0}$C respectively. Final temperature distribution (i.e. in Steady state) is A) 40+x. B) 50+x. C) 60+x. D) 70+x. Show Answer Correct Answer: A) 40+x. 10. Write a differential equation for the statement:"The rate of change of P is proportional to the product of P and 4-P." A) $\frac{dP}{dt}=kP$. B) $\frac{dP}{dt}=k\left(4-P\right)$. C) $\frac{dP}{dt}=kP\left(4-P\right)$. D) $\frac{dP}{dt}=\frac{kP}{4-P}$. Show Answer Correct Answer: C) $\frac{dP}{dt}=kP\left(4-P\right)$. 11. If $|f(x)|$ $f(x)$ A) Even only. B) Odd only. C) Neither even nor odd. D) Either even or odd. Show Answer Correct Answer: D) Either even or odd. 12. Given the differential equation $\frac{dP}{dt}=5P$ $P_{ }$ $P$ $P\left(0\right)=418$ 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$^{5t}$. 13. Find a general solution of this differential equation $x\frac{dy}{dx}+3y=4x^2-3x$ $x>0$ A) $y=\frac{x^2}{3}-\frac{x}{4}+\frac{c}{2x^3}$. B) $y=\frac{4x^2}{5}-\frac{3x}{4}+\frac{c}{x^3}$. C) $y=-\frac{4x^2}{3}+x+\frac{c}{x^2}$. D) $y=\frac{5x^2}{4}-\frac{x^2}{2}+\frac{c}{x^3}$. Show Answer Correct Answer: B) $y=\frac{4x^2}{5}-\frac{3x}{4}+\frac{c}{x^3}$. 14. $\int_0^{\ln2}e^{2x}dx=$ A) $4$. B) $3$. C) $\frac{3}{2}$. D) $2e^2-1$. Show Answer Correct Answer: C) $\frac{3}{2}$. 15. The complementary function of (D$^{3}$-3D$^{2}$ + 3D-1) y = x$^{3}$ is A) E$^{x}$ (a + bx + cx$^{2}$). B) E$^{-x}$ (a cosx + b sinx + c). C) Ae$^{x}$ + be$^{-x}$ + ce$^{2x}$. D) E$^{-x}$ (a + bx + cx$^{2}$). Show Answer Correct Answer: A) E$^{x}$ (a + bx + cx$^{2}$). 16. $\frac{\text{d}y}{\text{d}x}=\tan x+15x^2+e^x+\frac{1}{x}$ A) Y=-ln|sinx| + 5x$^{3}$ + e$^{x}$ + ln|x| + c. B) Y= secxtanx + 5x$^{3}$ + e$^{x}$ + ln|x| + c. C) Y=-ln|cosx| + 5x$^{3}$ + e$^{x}$ + ln|x| + c. D) Y= sec$^{2}$(x) + 5x$^{3}$ + e$^{x}$ + ln|x| + c. Show Answer Correct Answer: C) Y=-ln|cosx| + 5x$^{3}$ + e$^{x}$ + ln|x| + c. 17. L\{(1/8b$^{4}$)(bt)(sin bt)-(bt)$^{2}$cosbt)\} A) S/(s$^{2}$+b$^{2}$). B) S/(s$^{2}$+b$^{2}$)$^{2}$. C) S/(s$^{2}$+b$^{2}$)$^{3}$. D) S/(s$^{2}$+b$^{2}$)$^{4}$. Show Answer Correct Answer: C) S/(s$^{2}$+b$^{2}$)$^{3}$. 18. $\frac{\text{d}^2y}{\text{d}x^2}-2\frac{dy}{dx}-3y=e^{2x}$ A) $y=Ae^{-x}+Be^{3x}-\frac{1}{3}e^{2x}$. B) $y=Ae^{-2x}+Be^{4x}-3e^{2x}$. C) $y=e^x\left(A\sin3x+B\cos3x\right)-\frac{1}{3}e^{2x}$. D) $y=e^x\left(A\sin3x+B\cos3x\right)-3e^{2x}$. Show Answer Correct Answer: A) $y=Ae^{-x}+Be^{3x}-\frac{1}{3}e^{2x}$. 19. $y\left[\ln\left(\frac{y}{x}\right)+1\right]dx-xdy=0$ A) Linear. B) Separable. C) Bernoulli. D) Homogeneous. Show Answer Correct Answer: D) Homogeneous. 20. A transformation T of functions is said to be linear if $T\left[\alpha f\left(x\right)+\beta g\left(x\right)\right]=$ A) $\alpha T\left[f\left(x\right)\right]-\beta T\left[g\left(x\right)\right]$. B) $T\left[\alpha f\left(x\right)\right]-T\left[\beta g\left(x\right)\right]$. C) $\alpha T\left[f\left(x\right)\right]+\beta T\left[g\left(x\right)\right]$. D) $T\left[\alpha f\left(x\right)\right]+T\left[\beta g\left(x\right)\right]$. Show Answer Correct Answer: C) $\alpha T\left[f\left(x\right)\right]+\beta T\left[g\left(x\right)\right]$. 21. Solve the differential equation $\frac{dy}{dx}+2=2y$ A) $y=1+\sqrt{\frac{4}{-2x-A}}$. B) $y=\frac{\beta e^x+2}{2}$. C) $y=1+\alpha e^{2x}$. D) $y=1+\frac{1}{-4x-A}$. Show Answer Correct Answer: C) $y=1+\alpha e^{2x}$. 22. $\vec{\phi}_1\left(t\right), \ ..... , \\vec{\phi}_n\left(t\right)$ $B\left(t\right)$ A) Is always not invertible. B) Is always invertible. C) Is invertible only for specific times t. D) I don't know. Show Answer Correct Answer: B) Is always invertible. 23. The standard five-point formula assumes that the grid spacing in xand ydirections is: A) Different. B) Unequal. C) Equal. D) Zero. Show Answer Correct Answer: C) Equal. 24. If the roots of the Auxiliary equation are complex conjugates $\alpha\\pm\\beta$ A) $e^{-\alpha x}\left(A\cos\beta x+B\sin\beta x\right)$. B) $e^{\alpha x}\left(A\cos\beta x+B\sin\beta x\right)$. C) $e^{-\beta x}\left(A\cos\alpha x+B\sin\alpha x\right)$. D) $e^{\beta x}\left(A\cos\alpha x+B\sin\alpha x\right)$. Show Answer Correct Answer: B) $e^{\alpha x}\left(A\cos\beta x+B\sin\beta x\right)$. 25. If the roots of A. E are imaginary then C. F is y=e$^{x}$(Acosx+Bsinx) A) True. B) False. C) All the above. D) None of the above. Show Answer Correct Answer: B) False. Next →Related QuizzesClass 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 10Class 12 Mathematics Chapter 9 Differential Equations Quiz 11 🏠 Back to Homepage 📘 Download PDF Books 📕 Premium PDF Books