This quiz works best with JavaScript enabled. Home > Class 12 > Class 12 Mathematics Chapter 9 Differential Equations – Quiz 36 🏠 Homepage 📘 Download PDF Books 📕 Premium PDF Books Class 12 Mathematics Chapter 9 Differential Equations Quiz 36 (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 $\frac{dy}{dx}=2e^{3x}$ $y(\ln 2)=5$ A) $y=\frac{2}{3}e^{3x}-\frac{1}{3}$. B) $y=\frac{2}{3}e^{3x}+\frac{1}{3}$. C) $y=2e^{3x}-\frac{1}{3}$. D) $y=\frac{2}{3}e^{x}-\frac{1}{3}$. Show Answer Correct Answer: A) $y=\frac{2}{3}e^{3x}-\frac{1}{3}$. 2. If T is a linear transformation from V to W, which of the following is correct? A) R(T) is a subspace of V. B) R(T) is a subspace of W. C) N(T) is a subspace of W. D) None of the others. Show Answer Correct Answer: B) R(T) is a subspace of W. 3. Identify the type of differential equation:y" -4y = 0 A) Second-order non-linear differential equation. B) Third-order linear homogeneous differential equation. C) First-order non-linear differential equation. D) Second-order linear homogeneous differential equation. Show Answer Correct Answer: D) Second-order linear homogeneous differential equation. 4. Solve $x\left(y-2\right)\frac{\text{d}y}{\text{d}x}-\ln x=0$ $y=10$ $x=1$ A) $\frac{\left(y-2\right)^2}{2}=\frac{1}{2}\left(\ln x\right)^2+32$. B) $\left(y-2\right)^2=2\left(\ln x\right)^2-16$. C) $\frac{\left(\ln x\right)^2}{2}=-\left(y-2\right)^2+8$. D) $\left(\ln x\right)^2=-\frac{1}{2}\left(y-2\right)^2-4$. Show Answer Correct Answer: A) $\frac{\left(y-2\right)^2}{2}=\frac{1}{2}\left(\ln x\right)^2+32$. 5. SOLVE USING LAGRANGE'S LINEAR EQUATON4(p+q)=z A) F(x-y, y/5-logz)=0. B) F(x-y, y/4-logy)=0. C) F(x-y, y/4 logz)=0. D) F(x-y, y/4)=7. Show Answer Correct Answer: C) F(x-y, y/4 logz)=0. 6. In $\frac{\text{d}y}{\text{d}x}$ A) X. B) Y. C) D. D) None of the options syempre!. Show Answer Correct Answer: A) X. 7. The complementary function of the equation $2\frac{d^2y}{dt^2}+5\frac{\text{d}y}{\text{d}t}-12y=0$ A) $c_1e^{\frac{3}{2}x}+c_2e^{-4x}$. B) $c_1e^{\frac{3}{2}t}+c_2e^{-4t}$. C) $c_1e^{-\frac{3}{2}x}+c_2e^{4x}$. D) $c_1e^{-\frac{3}{2}t}+c_2e^{4t}$. Show Answer Correct Answer: B) $c_1e^{\frac{3}{2}t}+c_2e^{-4t}$. 8. If the PDE is of the type f(x, p)=g(y, q), then we will take ..... A) F(x, p)=a=g(y, q). B) P=q. C) P=aq. D) P=a. Show Answer Correct Answer: A) F(x, p)=a=g(y, q). 9. The particular integral of (D$^{2}$+1)y=x is A) X$^{2}$. B) 1. C) 0. D) X. Show Answer Correct Answer: D) X. 10. What is the characteristic equation / auxiliary equation for $\frac{\text{d}^2y}{\text{d}x^2}-2y=0$ A) $\lambda^2+2=0$. B) $\lambda^2-2\lambda=0$. C) $\lambda^2-2=0$. D) None of the above. Show Answer Correct Answer: C) $\lambda^2-2=0$. 11. If the PDE is of the type f(p, q)=0, then we will take ..... A) F(y, q)=a. B) F(x, p)=a. C) P=q. D) P=a. Show Answer Correct Answer: D) P=a. 12. The complete integral of $F_1\left(x, p\right)=F_2\left(y, q\right)$ A) $z=\int_{ }^{ }qdx+\int_{ }^{ }pdy$. B) $z=\int_{ }^{ }pdx-\int_{ }^{ }qdy$. C) $z=\int_{ }^{ }pdx+\int_{ }^{ }qdy$. D) None of the above. Show Answer Correct Answer: C) $z=\int_{ }^{ }pdx+\int_{ }^{ }qdy$. 13. In R$^{2}$, define (x, y)+(a, b) = (x+a-1, y+b-1) and $\alpha$(x, y)=($\alpha$x, $\alpha$y), which is of the following axiom of the vector space is fails: A) Identity. B) ($\alpha$ + $\beta$)u = $\alpha$u + $\beta$u. C) Commutative. D) Associative. Show Answer Correct Answer: B) ($\alpha$ + $\beta$)u = $\alpha$u + $\beta$u. 14. The roots of the auxiliary equation $m^2-7m+12=0$ A) -3, -4. B) 3, -4. C) 3, 4. D) -3, 4. Show Answer Correct Answer: C) 3, 4. 15. $1 + x + x^2 + x^3 + ..... = i$ A) $(1-x)^{-2}$. B) $(1-x)^{-1}$. C) $(1-x)^{-1}$. D) None of these. Show Answer Correct Answer: B) $(1-x)^{-1}$. 16. The singular solution of Clairaut's equation represents: A) The envelope of the family of lines. B) A particular integral. C) A complementary function. D) None. Show Answer Correct Answer: A) The envelope of the family of lines. 17. What mathematical operation is used to eliminate the reciprocal in an equation? A) Differentiation. B) Integration. C) Taking the reciprocal of both sides. D) Multiplying by the derivative. Show Answer Correct Answer: C) Taking the reciprocal of both sides. 18. The solution of linear differential equation $x\frac{\text{d}y}{\text{d}x}+2y=x^2$ A) $y=\frac{x^2+c}{4x^2}$. B) $y=\frac{x^2}{4}+c$. C) $y=\frac{x^4+c}{x^2}$. D) $y=\frac{x^4+c}{4x^2}$. Show Answer Correct Answer: D) $y=\frac{x^4+c}{4x^2}$. 19. A differential equation is an equation involving ..... of a function. A) Derivatives. B) Ranges. C) Logarithms. D) Cube roots. Show Answer Correct Answer: A) Derivatives. 20. Solve $(D^2 + 1)y = 0$ A) Y = Acosx + Bsinx. B) Y = Acosx-iBsinx. C) $e^{x}i$. D) None of these. Show Answer Correct Answer: A) Y = Acosx + Bsinx. 21. Differential equation of y=mx+c, where m, c are arbitrary constant is A) Y$^{'}$=0. B) Y$^{"}$=0. C) Y$^{" '}$=0. D) Y$^{'}$+xy"=0. Show Answer Correct Answer: B) Y$^{"}$=0. 22. The Wronskian of two solutions of a second-order linear differential equation is: A) Always zero. B) Always constant. C) Either zero or nonzero constant. D) May be zero or nonzero function of x. Show Answer Correct Answer: C) Either zero or nonzero constant. 23. Apa akar dari persamaan karakteristik untuk y" + 2y' + y = 0? A) R =-1 (akar ganda). B) R =-2 (akar tunggal). C) R = 1 (akar ganda). D) R = 0 (akar tunggal). Show Answer Correct Answer: A) R =-1 (akar ganda). 24. Determine whether the functions $y_{1} = e^{-2x}$ $y_{2} = e^{4x-5x}$ A) Yes, the functions are linearly independent. B) No, the functions are linearly dependent. C) The functions are not defined. D) The functions are identical. Show Answer Correct Answer: B) No, the functions are linearly dependent. 25. The complementary function is the solution of ..... A) Homogeneous ordinary differential equation. B) Linear equation. C) Non linear equation. D) Partial differential equation. Show Answer Correct Answer: A) Homogeneous ordinary differential equation. ← 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