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Mathematics - Area Under Curves

Practise 54 NDA previous year questions on Area Under Curves, 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.

Area Under Curves has been asked in 17 of the 21 years of NDA papers analysed (2006–2026), with 54 questions in all. 26% of them were easy, 74% moderate and 0% tough. Most of its questions came from 2025, with 6 questions that year. In the last three years (2024–2026) it had 13 questions across 5 papers, about 2.6 per paper.

The chapter's 2 topics are not weighted equally: Area of Curve along axis (44 questions, 81%) and Area bounded by two curves (10 questions, 19%) have been asked the most. Area of Curve along axis has also led over the last five years, with 14 questions.

  1. 1Passage: Let be the area between the curve and x-axis in the interval . Question: What is the area between the curve and the x-axis in the i2026 (Phase 1)Area of Curve along axis
  2. 2Passage: Let be the area between the curve and x-axis in the interval . Question: What is the area between the curve and the x-axis in the i2026 (Phase 1)Area of Curve along axis
  3. 3Passage: Consider the curves and . Question: What is the area bounded by the curves, the lines and ?2026 (Phase 1)Area bounded by two curves
  4. 4Consider the following for the two (02) items that follow: The slope of the tangent to the curve at is 4 for every real number and the curve2025 (Phase 1)Area of Curve along axis
  5. 5Consider the following for the two (02) items that follow: Let the curve . What is the area bounded by the curve and ?2025 (Phase 1)Area bounded by two curves
  6. 6Consider the following for the two (02) items that follow: Let the function . What is the area bounded by the function and the -axis?2025 (Phase 1)Area of Curve along axis
  7. 7Consider the following for the two (02) items that follow: Let , where is the greatest integer function. What is equal to?2025 (Phase 1)Area of Curve along axis
  8. 8For the following three (03) items: Consider the function . What is the area bounded by the curve , the -axis and the lines and ?2025 (Phase 2)Area of Curve along axis
  9. 9What is the area of the region bounded by and , where is a positive real number?2025 (Phase 2)Area of Curve along axis
  10. 10The circle is partitioned by line in two segments. Let be the areas of major and minor segments respectively. What is the value of ?2024 (Phase 1)Area bounded by two curves
  11. 11The circle is partitioned by line in two segments. Let be the areas of major and minor segments respectively. What is the value of ?2024 (Phase 1)Area of Curve along axis
  12. 12Paragraph: The area bounded by the parabola and the line , where , is square units. Question: What is the value of ?2024 (Phase 2)Area of Curve along axis
  13. 13Paragraph: The area bounded by the parabola and the line , where , is square units. Question: What is the area of the parabola bounded by th2024 (Phase 2)Area of Curve along axis
  14. 14For what value of with , is the area bounded by the lines and equal to 3 ?2023 (Phase 1)Area bounded by two curves
  15. 15What is the area between the curve and -axis for ?2023 (Phase 2)Area of Curve along axis
  16. 16What is the area included in the first quadrant between the curves and ?2022 (Phase 1)Area bounded by two curves
  17. 17What is the area of the region (in the first quadrant) bounded by and ?2022 (Phase 2)Area of Curve along axis
  18. 18What is the area of the region bounded by and2022 (Phase 2)Area of Curve along axis
  19. 19What is the area of the region enclosed in the first quadrant by and ?2022 (Phase 2)Area of Curve along axis
  20. 20What is the area bounded by and the -axis?2021 (Phase 1)Area of Curve along axis
  21. 21What is the area bounded by , where is the greatest integer function, the -axis and the lines and ?2021 (Phase 2)Area of Curve along axis
  22. 22What is the area of the region enclosed between the curve and the straight line ?2020Area bounded by two curves
  23. 23What is the area of one of the loops between the curve and x -axis?2019 (Phase 1)Area of Curve along axis
  24. 24What is the area of the region bounded by and ?2019 (Phase 2)Area of Curve along axis
  25. 25What is the area of the region enclosed between the curve and the straight line ?2019 (Phase 2)Area bounded by two curves
  26. 26What is the area of the region bounded by the parabolas and2018 (Phase 1)Area bounded by two curves
  27. 27The area bounded by the curve is2017 (Phase 2)Area of Curve along axis
  28. 28Consider the curves and What is the area bounded by the curves?2016 (Phase 1)Area of Curve along axis
  29. 29Consider the function , where . What is the area of the region bounded by x -axis, the curve and the two ordinates and ?2016 (Phase 1)Area of Curve along axis
  30. 30Consider the function , where . What is the area of the region bounded by x -axis, the curve and the two ordinates and2016 (Phase 1)Area of Curve along axis
  31. 31Consider the curves and What is the area of the region bounded by the curves and x-axis?2016 (Phase 1)Area of Curve along axis
  32. 32What is the area bounded by the curves ?2016 (Phase 2)Area of Curve along axis
  33. 33Consider the line and the circle . What is the area of the region in the first quadrant enclosed by the -axis, the line and the circle?2015 (Phase 1)Area of Curve along axis
  34. 34Consider the line and the circle . What is the area of the region in the first quadrant enclosed by the -axis, the line and the circle?2015 (Phase 1)Area of Curve along axis
  35. 35Consider the curves and . What is the area of the region bounded by the above two curves and the lines and ?2015 (Phase 1)Area of Curve along axis
  36. 36Consider the curves and . What is the area of the region bounded by the above two curves and the lines and ?2015 (Phase 1)Area of Curve along axis
  37. 37The area bounded by the coordinate axes and the curve , is2015 (Phase 2)Area of Curve along axis
  38. 38The line cuts the parabola . What is the area enclosed by the parabola and line?2014 (Phase 2)Area bounded by two curves
  39. 39The line cuts the parabola . What is the area enclosed by the parabola, the line and the -axis in the first quadrant?2014 (Phase 2)Area of Curve along axis
  40. 40What is the area of the triangle bounded by the sides and ?2013 (Phase 1)Area of Curve along axis
  41. 41What is the area of the region enclosed by and ?2013 (Phase 1)Area of Curve along axis
  42. 42What is the area of the parabola bounded by the line ?2013 (Phase 2)Area of Curve along axis
  43. 43What is the area bounded by and ?2013 (Phase 2)Area of Curve along axis
  44. 44What is the area bounded by the lines , and ?2013 (Phase 2)Area of Curve along axis
  45. 45The area bounded by the curve , the -axis and the two lines and is equal to:2012 (Phase 1)Area of Curve along axis
  46. 46What is the area of the portion of the curve , lying between and ?2012 (Phase 2)Area of Curve along axis
  47. 47What is the area of the region bounded by the lines and ?2012 (Phase 2)Area of Curve along axis
  48. 48What is the area bounded by the curves , and the straight line ?2011 (Phase 1)Area of Curve along axis
  49. 49What is the area between the curve and the co-ordinate axes?2011 (Phase 2)Area of Curve along axis
  50. 50What is the area bounded by the curve and the coordinate axes?2011 (Phase 2)Area of Curve along axis

Frequently Asked Questions

1.How many questions are available for Area Under Curves?

This chapter includes 54 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 Area Under Curves chapter. Questions from other exams like JEE Main or NTA Abhyas (JEE Main) are organised separately under their respective exam sections.

3.Is Area Under Curves an important chapter for NDA Mathematics?

Area Under Curves has appeared in 17 of the 17 years of NDA papers covered here, with 54 questions across 29 papers - about 2 per paper it appears in.

4.What is the difficulty level of Area Under Curves questions in NDA?

Of the 54 questions analysed for this chapter, 26% are easy, 74% moderate and 0% tough. 2025 had the most, with 6 questions.

5.Which topics in Area Under Curves should I focus on?

These topics have carried the most weightage in Area Under Curves:

  • Area of Curve along axis - 44 questions (81%)
  • Area bounded by two curves - 10 questions (19%)
6.Is Area Under Curves's weightage in NDA going up or down?

Across all 29 papers analysed, Area Under Curves has averaged about 1.9 questions per paper. In the last three years (2024–2026), that average has risen, at about 2.6 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.