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Mathematics - Quadratic Equation

Practise 158 NDA previous year questions on Quadratic Equation, 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.

Quadratic Equation has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 158 questions in all. 20% of them were easy, 77% moderate and 3% tough. Most of its questions came from 2011, with 16 questions that year. In the last three years (2024–2026) it had 24 questions across 5 papers, about 4.8 per paper.

The chapter's 6 topics are not weighted equally: Relation between Roots and Coefficients (138 questions, 87%), N degree equation (8 questions, 5%), and Graph and Sign of Quadratic (4 questions, 3%) have been asked the most. Relation between Roots and Coefficients has also led over the last five years, with 32 questions. Relation between Roots and Coefficients has produced the most tough questions (3).

  1. 1If the highest degree coefficient is equal to , then what is the total number of quadratic equations which are unchanged on squaring their r2026 (Phase 1)Relation between Roots and Coefficients
  2. 2Let and be the roots of the quadratic equation where , are positive real numbers. Let be the arithmetic mean of and ; and be the geometric m2026 (Phase 1)Relation between Roots and Coefficients
  3. 3For a given , what is the minimum value of ?2026 (Phase 1)Range of Quadratic Function
  4. 4Consider the following statements : I. has two irrational roots. II. has two rational roots. Which of the statements given above is/are corr2026 (Phase 1)N degree equation
  5. 5If one root of the equation exceeds the other by , then which one of the following is a value of ?2025 (Phase 1)Relation between Roots and Coefficients
  6. 6If and , then what is equal to?2025 (Phase 1)N degree equation
  7. 7If , and , then what is equal to?2025 (Phase 1)N degree equation
  8. 8If , then what is equal to?2025 (Phase 1)Relation between Roots and Coefficients
  9. 9For the following two (02) items: Let and be the roots of the quadratic equation , where and . Further, . What is equal to?2025 (Phase 2)Relation between Roots and Coefficients
  10. 10For the following two (02) items: Let and be the roots of the quadratic equation , where and . Further, . What is the relation between and ?2025 (Phase 2)Relation between Roots and Coefficients
  11. 11For the following two (02) items: Consider the equation . If the roots of the equation are equal, then which one of the following is correct2025 (Phase 2)Relation between Roots and Coefficients
  12. 12For the following two (02) items: Consider the equation . If the roots of the equation are equal, then , , are in2025 (Phase 2)Relation between Roots and Coefficients
  13. 13For the following two (02) items: Let be a quadratic polynomial such that . Further, 2 is a root of . What is the other root of ?2025 (Phase 2)Relation between Roots and Coefficients
  14. 14For the following two (02) items: Let be a quadratic polynomial such that . Further, 2 is a root of . What is equal to?2025 (Phase 2)Relation between Roots and Coefficients
  15. 15If and are roots of the equation where are integers, then which one of the following is correct?2024 (Phase 1)Relation between Roots and Coefficients
  16. 16If and are in GP, then consider the following in respect of the equation 1. The equation has imaginary roots. 2. The ratio of the roots of t2024 (Phase 1)Relation between Roots and Coefficients
  17. 17If is an integer for all integral values of , then which of the following is/are correct? 1. must be an integer 2. must be an integer Select2024 (Phase 1)Relation between Roots and Coefficients
  18. 18Under which one of the following conditions does the equation in have a real root for ?2024 (Phase 1)Relation between Roots and Coefficients
  19. 19If is a root of the equation and is a root of the equation , where , then what is the value of ?2024 (Phase 2)Relation between Roots and Coefficients
  20. 20The roots of the equation are and , where and are the angles of a triangle. Which one of the following is correct?2024 (Phase 2)Relation between Roots and Coefficients
  21. 21What is the number of real roots of the equation2024 (Phase 2)Relation between Roots and Coefficients
  22. 22Paragraph: The roots of the quadratic equation are equal . Question: Which one of the following statements is correct?2024 (Phase 2)Relation between Roots and Coefficients
  23. 23Paragraph: The roots of the quadratic equation are equal . Question: Which one of the following is a root of the equation?2024 (Phase 2)Relation between Roots and Coefficients
  24. 24If such that , then which one of the following is correct?2024 (Phase 2)Relation between Roots and Coefficients
  25. 25If where is a root of the equation , then what is the value of ?2023 (Phase 1)Relation between Roots and Coefficients
  26. 26For how many integral values of , the equation , where is an integer, has real roots and both of them lie in the interval ?2023 (Phase 1)Location of Roots
  27. 27and are distinct real roots of the quadratic equation . Which of the following statements is/are sufficient to find ? 1. 2. Select the corre2023 (Phase 1)Relation between Roots and Coefficients
  28. 28Paragraph: Consider the following for the next two items that follow: A quadratic equation is given by Question: What is the HM of the roots2023 (Phase 1)Relation between Roots and Coefficients
  29. 29Paragraph: Consider the following for the next two items that follow: A quadratic equation is given by Question: What is the GM of the root 2023 (Phase 1)Relation between Roots and Coefficients
  30. 30Consider the equation What is the number of real roots of the equation?2023 (Phase 2)N degree equation
  31. 31Consider the equation What is the sum of all the roots of the equation?2023 (Phase 2)N degree equation
  32. 32A quadratic equation is given by , where are real. If , then the roots of the equation are:2023 (Phase 2)Relation between Roots and Coefficients
  33. 33A quadratic equation is given by , where are real. If k = c, then the roots of the equation are:2023 (Phase 2)Relation between Roots and Coefficients
  34. 34Let and be the roots of the equation . If and are the roots of the equation , then what is the value of ?2022 (Phase 1)Relation between Roots and Coefficients
  35. 35Let and be the roots of the equation . What is the quadratic equation whose roots are and ?2022 (Phase 1)Relation between Roots and Coefficients
  36. 36If the roots of the equation are equal, then which one of the following is correct?2022 (Phase 1)Relation between Roots and Coefficients
  37. 37Let and be the roots of the equation . If , then what is the value of ?2022 (Phase 1)Relation between Roots and Coefficients
  38. 38For how many quadratic equations, the sum of roots is equal to the product of roots?2022 (Phase 2)Relation between Roots and Coefficients
  39. 39Let be the roots of the quadratic equation where . If , then what is equal to?2022 (Phase 2)Relation between Roots and Coefficients
  40. 40If the roots of the quadratic equation are real, then2021 (Phase 1)Relation between Roots and Coefficients
  41. 41If and are the roots of the equation , then which one of the following is correct?2021 (Phase 1)Relation between Roots and Coefficients
  42. 42If one root of is reciprocal of the other, then what is the value of ?2021 (Phase 1)Relation between Roots and Coefficients
  43. 43If and , then what is the maximum value of ?2021 (Phase 1)Range of Quadratic Function
  44. 44If is one of the roots of the equation , then what is its other root?2021 (Phase 1)Relation between Roots and Coefficients
  45. 45If the roots of the equation differ by unity, then which one of the following is a possible value of ?2021 (Phase 2)Relation between Roots and Coefficients
  46. 46The quadratic equation has real roots of equal magnitude and opposite sign. Which one of the following is correct?2021 (Phase 2)Relation between Roots and Coefficients
  47. 47If and are the non-zero roots of the equation , then how many possible values can have?2021 (Phase 2)Relation between Roots and Coefficients
  48. 48If and are the roots of the equation , then which one of the following is correct?2021 (Phase 2)Relation between Roots and Coefficients
  49. 49Consider all the real roots of the equation . What is the sum of the absolute values of the roots?2021 (Phase 2)Relation between Roots and Coefficients
  50. 50What is the probability that the roots of the equation are real, where and ?2021 (Phase 2)Relation between Roots and Coefficients

Frequently Asked Questions

1.How many questions are available for Quadratic Equation?

This chapter includes 158 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 Quadratic Equation chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Quadratic Equation an important chapter for NDA Mathematics?

Quadratic Equation has appeared in 17 of the 17 years of NDA papers covered here, with 158 questions across 32 papers - about 5 per paper it appears in.

4.What is the difficulty level of Quadratic Equation questions in NDA?

Of the 158 questions analysed for this chapter, 20% are easy, 77% moderate and 3% tough. 2011 had the most, with 16 questions.

5.Which topics in Quadratic Equation should I focus on?

These topics have carried the most weightage in Quadratic Equation:

  • Relation between Roots and Coefficients - 138 questions (87%)
  • N degree equation - 8 questions (5%)
  • Graph and Sign of Quadratic - 4 questions (3%)
  • Relation between Roots and Coefficients has produced the most tough questions (3).
6.Is Quadratic Equation's weightage in NDA going up or down?

Across all 32 papers analysed, Quadratic Equation has averaged about 4.9 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 4.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.