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Mathematics - Circle

Practise 12 NEST (NISER) previous year questions on Circle, compiled from papers spanning 2013 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 NEST (NISER) tests.

Circle has been asked in 9 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 12 questions in all. 17% of them were easy, 42% moderate and 42% tough. Most of its questions came from 2024, with 3 questions that year. In the last three years (2024–2026) it had 5 questions across 4 papers, about 1.3 per paper.

The chapter's 6 topics are not weighted equally: Equation of Circle & its intercept (7 questions, 58%), Locus (1 question, 8%), and Chord with given Middle Point (1 question, 8%) have been asked the most. Equation of Circle & its intercept has also led over the last five years, with 5 questions. Equation of Circle & its intercept has produced the most tough questions (4).

  1. 1Let and be two circles drawn inside a unit square ABCD, touching each other externally. Further, the circle touches the sides AD and DC; and2026Equation of Circle & its intercept
  2. 2A circle with centre at and radius touches another circle with centre at and radius internally as shown in the figure. If and a diameter of 2025Tangent to circle
  3. 3Let and be the points of intersection of the circles and Let be the point . The distance between the point and the line is2024 (Session 1)Common Chord
  4. 4Let be the diameter of a circle with radius 1 centred at the point . Let be a point on the circle such that . Let be the foot of the perpend2024 (Session 1)Equation of Circle & its intercept
  5. 5Let be a square with each side of length 1 . Let be circles inside the square, such that touches side and touches sides and , and touches th2024 (Session 2)Equation of Circle & its intercept
  6. 6Let and , be three circles having the same radius , which touch each other externally. Then2023 (Session 2)Equation of Circle & its intercept
  7. 7The ratio of the perimeter and the diameter of a circle is always2022 (Session 1)Equation of Circle & its intercept
  8. 8Let and be two circles with positive radii such that the distance between their centers is equal to the sum of their radii. Then the number 2022 (Session 2)Common Tangents
  9. 9For a positive integer , let be the parabola given by and let C be the circle given by Then2020 (Session 1)Equation of Circle & its intercept
  10. 10Let an acute-angled triangle be inscribed in a circle whose centre is the origin. Let and . Then is2016Equation of Circle & its intercept
  11. 11Let be an interior point of a circle , different from its center. The locus of the midpoints of all the chords passing through the point is2015Chord with given Middle Point
  12. 12Let and be two fixed points on a fixed straight line. Two circles touch this line at and respectively and tangent to each other at . When th2013Locus

Frequently Asked Questions

1.How many questions are available for Circle?

This chapter includes 12 questions compiled from NEST (NISER) papers spanning 2013 to 2026.

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

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

3.Is Circle an important chapter for NEST (NISER) Mathematics?

Circle has appeared in 9 of the 16 years of NEST (NISER) papers covered here, with 12 questions across 11 papers - about one per paper it appears in.

4.What is the difficulty level of Circle questions in NEST (NISER)?

Of the 12 questions analysed for this chapter, 17% are easy, 42% moderate and 42% tough. 2024 had the most, with 3 questions.

5.Which topics in Circle should I focus on?

These topics have carried the most weightage in Circle:

  • Equation of Circle & its intercept - 7 questions (58%)
  • Locus - 1 question (8%)
  • Chord with given Middle Point - 1 question (8%)
  • Equation of Circle & its intercept has produced the most tough questions (4).
6.Is Circle's weightage in NEST (NISER) going up or down?

Across all 11 papers analysed, Circle has averaged about 1.1 questions per paper. In the last three years (2024–2026), that average has stayed about the same, at about 1.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.