CBSE Class 12 Mathematics MCQs – Chapter Wise Practice Tests

Prepare smarter with CBSE Class 12 Mathematics MCQs – Online Practice Test designed chapter-wise as per the latest NCERT syllabus. Each quiz offers 30 multiple-choice questions with automatic scoring, instant per-question feedback, and a 30-minute timer to simulate real exam conditions. These CBSE Class 12 Mathematics MCQs – Online Practice Tests help students strengthen core concepts, improve problem-solving skills, and boost confidence for board exams. Ideal for self-assessment and quick revision, these MCQs cover every chapter comprehensively, making them a perfect study tool for CBSE board exam preparation and concept mastery.

Chapter 9 — Differential Equations

1. The order and degree of the differential equation \( \dfrac{d^2 y}{dx^2} + \left(\dfrac{dy}{dx}\right)^2 = 0 \) are:

2. Which of the following is a linear differential equation?

3. The general solution of the first order separable equation \( \dfrac{dy}{dx} = xy \) is:

4. An integrating factor for the linear equation \( \dfrac{dy}{dx} + P(x)y = Q(x) \) is:

5. The DE \( \dfrac{dy}{dx} = \dfrac{x+y}{x-y} \) is:

6. The general solution of \( \dfrac{dy}{dx} = \dfrac{y}{x} + x^2 \) can be obtained using:

7. The differential equation \( \dfrac{dy}{dx} = f\left(\dfrac{y}{x}\right) \) is called:

8. The general solution of the homogeneous linear DE with constant coefficients \( y'' - 3y' + 2y = 0 \) is:

9. For the exact equation \( M(x,y) + N(x,y)\dfrac{dy}{dx} = 0 \), the condition for exactness is:

10. The Bernoulli equation \( \dfrac{dy}{dx} + P(x)y = Q(x)y^n \) reduces to a linear DE by the substitution:

11. The initial value problem \( \dfrac{dy}{dx} = 3x^2, \; y(0)=2 \) has solution:

12. Which of the following initial value problems guarantees a unique solution near the initial point by the existence and uniqueness theorem?

13. Orthogonal trajectories of the family \( y = Cx \) are curves satisfying:

14. A Clairaut's differential equation has general solution consisting of:

15. For the differential equation \( \dfrac{dy}{dx} = \dfrac{2x + y}{x} \), substitute \( y = vx \). The resulting equation in v and x is:

16. The particular integral of the non-homogeneous DE \( y'' - y = e^x \) is of the form:

17. The complementary function (C.F.) of \( y'' + 4y = 0 \) is:

18. Which substitution reduces \( \dfrac{dy}{dx} = \dfrac{x+y+1}{x-y+1} \) to a homogeneous form?

19. The DE \( \dfrac{dy}{dx} = y(1-y) \) is separable. Its equilibrium (constant) solutions are:

20. If \( y = f(x) \) satisfies \( y' = 0 \) on an interval, then \( y \) is:

21. The order of the ODE \( \dfrac{d^3 y}{dx^3} + 2\left(\dfrac{dy}{dx}\right)^2 = 0 \) is:

22. For the linear equation \( y' + 2y = \sin x \), an integrating factor is:

23. The substitution \( y = ux \) is most useful for equations that are:

24. The DE \( y'' = 0 \) describes which family of curves?

25. The general solution of \( \dfrac{dy}{dx} = \dfrac{x}{y} \) is:

26. For the IVP \( y' = 2xy, \; y(0)=1 \), the solution is:

27. The DE \( y' = \dfrac{x + y}{x} \) is transformed by \( y = vx \) to:

28. The solution of \( y' = -\dfrac{y}{x} \) is:

29. Which of the following is TRUE about existence and uniqueness for \( y' = f(x,y) \)?

30. The differential equation \( \dfrac{dy}{dx} = \dfrac{x^2}{y^2} \) is separable. Its general solution is:

Chapter 9: Differential Equations