This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 2 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 2 (25 MCQs) Quiz Instructions Select an option to see the correct answer instantly. 1. Find general solution of by using integrating factor $x^3\frac{\text{d}y}{\text{d}x}+3x^2y=e^x$ A) $y=e^xx^3+c$. B) $y=\frac{e^x+c}{x^3}$. C) $x^2y=e^x+c$. D) $x^3y=\frac{e^x}{x^3}+c$. Show Answer Correct Answer: B) $y=\frac{e^x+c}{x^3}$. 2. What is a general solution of a differential equation? A) A solution containing arbitrary constants. B) A solution that cannot be derived. C) A solution with no arbitrary constants. D) A solution that is always true. Show Answer Correct Answer: A) A solution containing arbitrary constants. 3. What is not Differential Equation? A) Dy/dx = 2x. B) Y' = 2y + 2. C) 2y = 2. D) Y" = g(x) + f(x, y). Show Answer Correct Answer: C) 2y = 2. 4. Determine the general solution of $4y"-4y'+y=0$ A) $y=C_1e^{\frac{x}{2}}+C_2xe^{\frac{x}{2}}$. B) $y=C_1e^{\frac{x}{2}}+C_2xe^{-\frac{x}{2}}$. C) $y=e^{-\frac{x}{3}}\left(C_1\cos x+C_2\sin x\right)$. D) $y=C_1e^{\frac{x}{2}}+C_2e^{\frac{x}{2}}$. Show Answer Correct Answer: A) $y=C_1e^{\frac{x}{2}}+C_2xe^{\frac{x}{2}}$. 5. Identify the equilibrium solution of the differential equation $\frac{dy}{dt} = y(1-y)$ A) $y = 0$. B) $y = 1$. C) $y = 2$. D) Both A and B. Show Answer Correct Answer: D) Both A and B. 6. The complete solution of partial differential equation z=px-qy+6pq is ..... A) Z=ax-by+6xy. B) Z=ax-by+6ab. C) Z=px-qy+6ab. D) Z=ax-by-6ab. Show Answer Correct Answer: B) Z=ax-by+6ab. 7. What is Bessel's equation? A) A first order linear differential equation. B) A second order linear differential equation. C) A non-linear differential equation. D) A polynomial equation. Show Answer Correct Answer: B) A second order linear differential equation. 8. The Clairaut's equation is of the form ..... A) Y=px+f(p). B) Y=px+f(q). C) X=qy+f(p). D) X=py+f(q). Show Answer Correct Answer: A) Y=px+f(p). 9. The following Differential Equation is $\frac{\text{d}y}{\text{d}x}=y^2+xy^2$ A) Separable. B) Non Separable. C) All the above. D) None of the above. Show Answer Correct Answer: A) Separable. 10. Find the nature of the one-dimensional wave equation. A) Hyperbolic. B) Parabolic. C) Elliptic. D) None of These. Show Answer Correct Answer: A) Hyperbolic. 11. L$^{-1 }$\{(s-a)/((s-a)$^{2}$+b$^{2}$)\} A) E$^{at }$sin bt. B) E$^{at }$cos bt. C) Sin bt. D) T$^{n }$e$^{at}$. E) Cos bt. Show Answer Correct Answer: B) E$^{at }$cos bt. 12. The original value of a painting is $ 1400, and the value increases by 9% each year. Write an exponential growth function to model this situation. A) Y=1400(1.09)$^{x}$. B) Y=1.09(1400)$^{x}$. C) Y=1400(.91)$^{x}$. D) Y=1.09$^{x}$. Show Answer Correct Answer: A) Y=1400(1.09)$^{x}$. 13. Which differential equation is separable? A) $\dfrac{dy}{dx}=x+y$. B) $\dfrac{dy}{dx}=xy$. C) $y" +y=0$. D) $\dfrac{dy}{dx}+y=e^x$. Show Answer Correct Answer: B) $\dfrac{dy}{dx}=xy$. 14. What is a differential equation? A) An equation involving only derivatives of a function. B) An equation involving only integrals of a function. C) An equation that relates a function and its derivatives. D) An equation that relates a function and its integrals. Show Answer Correct Answer: C) An equation that relates a function and its derivatives. 15. What are roots of unity in complex numbers? A) Numbers that result in 0 when raised to a certain power. B) Numbers that result in 1 when raised to a certain power. C) Numbers that result in-1 when raised to a certain power. D) Numbers that result in a complex number when raised to a certain power. Show Answer Correct Answer: B) Numbers that result in 1 when raised to a certain power. 16. Find the order and degree of the differential equation are respectively: A) 2, 3. B) 3, 2. C) 3, 7. D) 7, 2. Show Answer Correct Answer: A) 2, 3. 17. The z-transform of a signal X(n) whose definition is given by X(z)= $\sum_{n=0}^{\infty}x\left(n\right)z^{-n}$ A) Unilateral Z-transform. B) Bilateral Z-transform. C) Rational Z-transform. D) None of the above. Show Answer Correct Answer: A) Unilateral Z-transform. 18. F(s) = L\{(t$^{n}$)\} (s) A) 1/s. B) N!/s$^{(n+1)}$. C) 1/(s-a). D) N!/(s-a)$^{(n+1)}$. E) S/(s$^{2}$+b$^{2}$). Show Answer Correct Answer: B) N!/s$^{(n+1)}$. 19. The general solution of $y" +y'=0$ A) $y=c_1+c_2e^x$. B) $y=c_1-c_2e^x$. C) $y=c_1+c_2e^{-x}$. D) $e^{-x}$. Show Answer Correct Answer: C) $y=c_1+c_2e^{-x}$. 20. For a continuous function, the mixed partials satisfy: A) F xy =-f yx. B) F xy = f yx. C) Always zero. D) Only defined for polynomials. Show Answer Correct Answer: B) F xy = f yx. 21. Separate the variables for the equation $\frac{dy}{dx}=\frac{(x^2-1)}{(y^2+1)}$ A) $\frac{dy}{(y+1)}=\frac{dx}{(x-1)}$. B) $(y^2+1)dy=(x^2-1)dx$. C) $(y^2-1)dy=\frac{1}{(x^2+1)}dx$. D) $(y^2-1)dy=(x^2+1)dx$. Show Answer Correct Answer: B) $(y^2+1)dy=(x^2-1)dx$. 22. Given the differential equation dP/Dt=5PA) Find the general solution for P to the differential equationB)Find the particular solution for P to the differential equation given P(0)= 418 A) P=P$_{0}$e$^{5t}$B) P= 5e$^{418t}$. B) P=P$_{0}$e$^{5t}$B) P= 418e$^{5t}$. C) P=P$_{0}$e$^{t}$B) P= 418e$^{t}$. D) P=P$_{0}$e$^{10t}$B) P= 418e$^{10t}$. Show Answer Correct Answer: B) P=P$_{0}$e$^{5t}$B) P= 418e$^{5t}$. 23. The dimension theorem states that A) Rank(T)=Dim(V)-Nullity(T). B) Rank(T)=Dim(V)+Nullity(T). C) Rank(T)+Dim(V)=Nullity(T). D) None. Show Answer Correct Answer: A) Rank(T)=Dim(V)-Nullity(T). 24. Solve $\frac{\partial^3z}{\partial x^3}-2\frac{\partial^3z}{\partial x^2\partial y}=0$ A) $Z=f_1\left(y\right)+xf_2\left(y\right)+f_3\left(y+2x\right)$. B) $Z=f_1\left(y\right)+f_2\left(y+x\right)+f_3\left(y+2x\right)$. C) $Z=f_1\left(y\right)+f_2\left(y-x\right)+f_3\left(y+2x\right)$. D) $Z=f_1\left(x\right)+yf_2\left(x\right)+f_3\left(y+2x\right)$. Show Answer Correct Answer: A) $Z=f_1\left(y\right)+xf_2\left(y\right)+f_3\left(y+2x\right)$. 25. $.$ $\left(D^2-5DD'+6D'^2\right)z=e^{\left(x+y\right)}$ A) $e^{\left(x+y\right)}$. B) $\frac{1}{2}e^{\left(x+y\right)}$. C) $\frac{1}{3}e^{\left(x+y\right)}$. D) $\frac{1}{4}e^{\left(x+y\right)}$. Show Answer Correct Answer: C) $\frac{1}{3}e^{\left(x+y\right)}$. ← PreviousNext →Related QuizzesClass 12 Mathematics Chapter 9 Differential Equations Quiz 1Class 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