Mathematics - Quadratic Equation
Practise 27 NEST (NISER) previous year questions on Quadratic Equation, compiled from papers spanning 2011 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.
Quadratic Equation has been asked in 13 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 27 questions in all. 7% of them were easy, 74% moderate and 19% tough. Most of its questions came from 2024, with 5 questions that year. In the last three years (2024–2026) it had 9 questions across 4 papers, about 2.3 per paper.
The chapter's 4 topics are not weighted equally: Relation between Roots and Coefficients (18 questions, 67%), N degree equation (7 questions, 26%), and Graph and Sign of Quadratic (1 question, 4%) have been asked the most. Relation between Roots and Coefficients has also led over the last five years, with 9 questions. Relation between Roots and Coefficients has produced the most tough questions (3).
- 1A possible solution of the system of equations is2026N degree equation
- 2Let and be real numbers such that the polynomial has two distinct negative rational roots. Then the polynomial has distinct2026Relation between Roots and Coefficients
- 3Let be the set of all rational numbers such that if with , then the two solutions of the quadratic equation are equal. Then the number of el2025Relation between Roots and Coefficients
- 4Let , where are nonzero integers. Suppose that . Then, all the roots of are integers if and only if2025N degree equation
- 5For positive real numbers and , the number of solutions of in is2024 (Session 1)Relation between Roots and Coefficients
- 6The number of positive integers such that the equation has a solution in is2024 (Session 1)Relation between Roots and Coefficients
- 7Let . Then the number of solutions in , of the equation is2024 (Session 2)Relation between Roots and Coefficients
- 8Let be the roots of the polynomial . Let be any matrix whose entries are from the set . Then2024 (Session 2)Relation between Roots and Coefficients
- 9Let be a polynomial such that for all . Then2024 (Session 2)N degree equation
- 10The number of real roots of is2023 (Session 1)N degree equation
- 11The horizontal line intersects the parabola at points and . If the length of is 8 , then the value of is2023 (Session 1)Relation between Roots and Coefficients
- 12Let and be the vertices of the parabolae and , respectively. If and are the points of intersection of the parabolae then the slope of the li2023 (Session 1)Relation between Roots and Coefficients
- 13If are the roots of , then the value of is2022 (Session 1)Relation between Roots and Coefficients
- 14Let and . Then the number of elements in is2022 (Session 1)N degree equation
- 15Assume that the roots of are and . If are roots of then the value of is2022 (Session 2)N degree equation
- 16The polynomial has2021 (Session 2)Descartes Rule of Sign
- 17Two distinct complex numbers are such that the roots of are squares of the roots of . Let and . Then is2021 (Session 2)Relation between Roots and Coefficients
- 18Let and be the roots of the equation and let and be the roots of the equation . If are in geometric progression with positive common ratio, 2019 (Session 2)Relation between Roots and Coefficients
- 19Suppose and are roots of the equation where are integers and . Then is2018Relation between Roots and Coefficients
- 20Let be distinct real numbers such that . Then is2018Relation between Roots and Coefficients
- 21For every , let be the parabola given by . Then2018Graph and Sign of Quadratic
- 22If are positive real numbers in geometric progression, then the graph of is a curve that2017Relation between Roots and Coefficients
- 23Let be three distinct real numbers. The roots of the equation are2015N degree equation
- 24Let be four integers (not necessarily distinct) in the set . The number of polynomials which is divisible by is2013Relation between Roots and Coefficients
- 25Let be distinct real numbers. Then the number of real solutions of is2013Relation between Roots and Coefficients
- 26For any real number belonging to the open interval consider the quadratic equation in . Let denote the roots of ., Then2012Relation between Roots and Coefficients
- 27Consider the equation , where are integers. Suppose it has an integer solution . Then2011Relation between Roots and Coefficients
Frequently Asked Questions
1.How many questions are available for Quadratic Equation?
This chapter includes 27 questions compiled from NEST (NISER) papers spanning 2011 to 2026.
2.Are these questions only from NEST (NISER), or from other exams too?
These are NEST (NISER) 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 NEST (NISER) Mathematics?
Quadratic Equation has appeared in 13 of the 16 years of NEST (NISER) papers covered here, with 27 questions across 15 papers - about 2 per paper it appears in.
4.What is the difficulty level of Quadratic Equation questions in NEST (NISER)?
Of the 27 questions analysed for this chapter, 7% are easy, 74% moderate and 19% tough. 2024 had the most, with 5 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 - 18 questions (67%)
- N degree equation - 7 questions (26%)
- Graph and Sign of Quadratic - 1 question (4%)
- Relation between Roots and Coefficients has produced the most tough questions (3).
6.Is Quadratic Equation's weightage in NEST (NISER) going up or down?
Across all 15 papers analysed, Quadratic Equation has averaged about 1.8 questions per paper. In the last three years (2024–2026), that average has risen, at about 2.3 questions per paper. Use the year-wise numbers on this page for the exact trend before you decide how much time to give it.