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Mathematics - Area Under Curves

Practise 7 NEST (NISER) previous year questions on Area Under Curves, compiled from papers spanning 2012 to 2024. Each question is pulled directly from the actual exam paper it appeared in, so you're practising in the exact style and difficulty NEST (NISER) tests.

Area Under Curves has been asked in 5 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 7 questions in all. 0% of them were easy, 57% moderate and 43% tough. Most of its questions came from 2024, with 3 questions that year. In the last three years (2024–2026) it had 3 questions across 4 papers, about 0.8 per paper.

The chapter's 2 topics are not weighted equally: Area of Curve along axis (5 questions, 71%) and Area bounded by two curves (2 questions, 29%) have been asked the most. Area of Curve along axis has also led over the last five years, with 2 questions. Area bounded by two curves has produced the most tough questions (2).

  1. 1Let be a square with sides of unit length. Let and be the points in the square such that and are equilateral triangles. Then the area of the2024 (Session 1)Area bounded by two curves
  2. 2Let ABCD be a square inscribed in a circle of unit radius. Let E be the point on the circle such that ABE is an isosceles triangle, containi2024 (Session 2)Area bounded by two curves
  3. 3Let be an equilateral triangle with each side being of length equal to 2 . We construct three discs with centres at the points and respectiv2024 (Session 2)Area of Curve along axis
  4. 4A right circular conical glass bottle with a base radius and height contains a coloured liquid upto half of its height. When the bottle is i2022 (Session 1)Area of Curve along axis
  5. 5A cylindrical tank of height 3 units and diameter 2 units, resting on its base, is partially filled with water up to a height units. Thereaf2017Area of Curve along axis
  6. 6Let and be three regions in -plane. If denotes the area of region , then2014Area of Curve along axis
  7. 7In the figure, PQRS is a square of side length 12 and XPQ is a traingle constructed on outwardly such that . If area of the figure is 192 , 2012Area of Curve along axis

Frequently Asked Questions

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

This chapter includes 7 questions compiled from NEST (NISER) papers spanning 2012 to 2024.

2.Are these questions only from NEST (NISER), or from other exams too?

These are NEST (NISER) 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 NEST (NISER) Mathematics?

Area Under Curves has appeared in 5 of the 16 years of NEST (NISER) papers covered here, with 7 questions across 6 papers - about one per paper it appears in.

4.What is the difficulty level of Area Under Curves questions in NEST (NISER)?

Of the 7 questions analysed for this chapter, 0% are easy, 57% moderate and 43% tough. 2024 had the most, with 3 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 - 5 questions (71%)
  • Area bounded by two curves - 2 questions (29%)
  • Area bounded by two curves has produced the most tough questions (2).
6.Is Area Under Curves's weightage in NEST (NISER) going up or down?

Across all 6 papers analysed, Area Under Curves has averaged about 1.2 questions per paper. In the last three years (2024–2026), that average has fallen, at about 0.8 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.