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Mathematics - Differential Equations

Practise 127 NDA previous year questions on Differential Equations, compiled from papers spanning 2010 to 2026. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NDA tests.

Differential Equations has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 127 questions in all. 30% of them were easy, 70% moderate and 0% tough. Most of its questions came from 2014, with 12 questions that year. In the last three years (2024–2026) it had 12 questions across 5 papers, about 2.4 per paper.

The chapter's 6 topics are not weighted equally: Variable Separable Form (47 questions, 37%), Order and Degree (41 questions, 32%), and Formation of Differential Equation (28 questions, 22%) have been asked the most. Variable Separable Form has also led over the last five years, with 12 questions.

  1. 1What is the solution of the differential equation when ?2026 (Phase 1)Variable Separable Form
  2. 2Passage: Consider the differential equation . Question: What is equal to ?2026 (Phase 1)Variable Separable Form
  3. 3Passage: Consider the differential equation . Question: What is the solution of the differential equation with ?2026 (Phase 1)Variable Separable Form
  4. 4What is the degree of the differential equation ?2025 (Phase 2)Order and Degree
  5. 5Consider the following statements: I. is the solution of . II. is the solution of . Which of the statements given above is/are correct?2025 (Phase 2)Variable Separable Form
  6. 6If is an arbitrary constant, then what is the general solution of the equation ?2025 (Phase 2)Variable Separable Form
  7. 7Let and be two solutions of the differential equation . If and , then what is the number of points of intersection of curves and ?2024 (Phase 1)Applications of DE
  8. 8The differential equation, representing the curve where and are arbitrary constants, is:2024 (Phase 1)Formation of Differential Equation
  9. 9What are the order and degree respectively of the differential equation ?2024 (Phase 1)Order and Degree
  10. 10If then what is equal to?2024 (Phase 1)Variable Separable Form
  11. 11Paragraph: Let be a differential equation. Question: What are the order and degree respectively of the differential equation?2024 (Phase 2)Order and Degree
  12. 12Paragraph: Let be a differential equation. Question: What is the solution of the differential equation?2024 (Phase 2)Linear Differential Equation
  13. 13Paragraph: Let , where are real numbers. Further and Question: What is equal to?2023 (Phase 1)Formation of Differential Equation
  14. 14Paragraph: Suppose E is the differential equation representing family of curves where c is a positive parameter. Question: What is the order2023 (Phase 1)Order and Degree
  15. 15Paragraph: Suppose E is the differential equation representing family of curves where c is a positive parameter. Question: What is the degre2023 (Phase 1)Order and Degree
  16. 16A solution of the differential equation is2023 (Phase 1)Variable Separable Form
  17. 17A parabola pases through and satisfies the differential equation . What is the directrix of the parabola?2023 (Phase 2)Variable Separable Form
  18. 18A parabola pases through and satisfies the differential equation . What is the length of latus rectum of the parabola?2023 (Phase 2)Variable Separable Form
  19. 19What are the order and the degree respectively of the differential equation2023 (Phase 2)Order and Degree
  20. 20What is the differential equation of all parabolas of the type ?2023 (Phase 2)Formation of Differential Equation
  21. 21What is the degree of the differential equation2022 (Phase 1)Order and Degree
  22. 22A radioactive substance decays at a rate proportional to the amount of substance present. If half of the substance decays in 100 years, then2022 (Phase 1)Applications of DE
  23. 23If with , then what is equal to?2022 (Phase 1)Variable Separable Form
  24. 24What does the equation represent?2022 (Phase 1)Variable Separable Form
  25. 25Consider the following statements : 1. The degree of the differential is 1 . 2. The order of the differential equation is 2. Which of the st2022 (Phase 2)Order and Degree
  26. 26What is the differential equation of the family of parabolas having vertex at origin and axis along positive -axis ?2022 (Phase 2)Formation of Differential Equation
  27. 27What is the solution of the differential equation2022 (Phase 2)Variable Separable Form
  28. 28A particle starts from origin with a velocity (in ) given by the equation . The time (in second) taken by the particle to traverse a distanc2021 (Phase 1)Variable Separable Form
  29. 29If the general solution of a differential equation is , where is an arbitrary constant, then what is the order of the differential equation?2021 (Phase 1)Order and Degree
  30. 30What is the degree of the following differential equation?2021 (Phase 1)Order and Degree
  31. 31Which one of the following differential equations has the general solution ?2021 (Phase 1)Formation of Differential Equation
  32. 32What is the solution of the following differential equation?2021 (Phase 1)Variable Separable Form
  33. 33What is the order of the differential equation of all ellipses whose axes are along the coordinate axes?2021 (Phase 2)Order and Degree
  34. 34What is the degree of the differential equation of all circles touching both the coordinate axes in the first quadrant?2021 (Phase 2)Formation of Differential Equation
  35. 35What is the differential equation of ?2021 (Phase 2)Formation of Differential Equation
  36. 36The function which satisfies the differential equation , is2020Variable Separable Form
  37. 37What is the solution of the differential equation2020Variable Separable Form
  38. 38The solution of the differential equation is2020Variable Separable Form
  39. 39The order and degree of the differential equation are respectively2020Order and Degree
  40. 40The solution of the differential equation is2019 (Phase 1)Variable Separable Form
  41. 41The differential equation of the system of circles touching the -axis at the origin is2019 (Phase 1)Formation of Differential Equation
  42. 42Consider the following in respect of the differential equation : 1. The degree of the differential equation is 1 . 2. The order of the diffe2019 (Phase 1)Order and Degree
  43. 43What is the general solution of the differential equation ?2019 (Phase 1)Variable Separable Form
  44. 44What is the degree of the differential equation ?2019 (Phase 2)Order and Degree
  45. 45Which one of the following is the differential equation that represents the family of curves where is an arbitrary constant?2019 (Phase 2)Formation of Differential Equation
  46. 46The differential equation which represents the family of curves given by is2019 (Phase 2)Formation of Differential Equation
  47. 47What is the solution of the differential equation2018 (Phase 1)Variable Separable Form
  48. 48Which one of the following differential equations has a periodic solution?2018 (Phase 1)Order and Degree
  49. 49The order and degree of the differential equation , where ' ' is an arbitrary constant, are respectively2018 (Phase 1)Order and Degree
  50. 50What is the solution of ?2018 (Phase 1)Variable Separable Form

Frequently Asked Questions

1.How many questions are available for Differential Equations?

This chapter includes 127 questions compiled from NDA papers spanning 2010 to 2026.

2.Are these questions only from NDA, or from other exams too?

These are NDA questions specifically for the Differential Equations chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Differential Equations an important chapter for NDA Mathematics?

Differential Equations has appeared in 17 of the 17 years of NDA papers covered here, with 127 questions across 31 papers - about 4 per paper it appears in.

4.What is the difficulty level of Differential Equations questions in NDA?

Of the 127 questions analysed for this chapter, 30% are easy, 70% moderate and 0% tough. 2014 had the most, with 12 questions.

5.Which topics in Differential Equations should I focus on?

These topics have carried the most weightage in Differential Equations:

  • Variable Separable Form - 47 questions (37%)
  • Order and Degree - 41 questions (32%)
  • Formation of Differential Equation - 28 questions (22%)
6.Is Differential Equations's weightage in NDA going up or down?

Across all 31 papers analysed, Differential Equations has averaged about 4.1 questions per paper. In the last three years (2024–2026), that average has fallen, at about 2.4 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.