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Mathematics - Matrices

Practise 18 NEST (NISER) previous year questions on Matrices, compiled from papers spanning 2011 to 2025. 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.

Matrices has been asked in 12 of the 16 years of NEST (NISER) papers analysed (2011–2026), with 18 questions in all. 11% of them were easy, 67% moderate and 22% tough. Most of its questions came from 2020, 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 8 topics are not weighted equally: Product of Matrices (7 questions, 39%), Inverse of a Matrix (4 questions, 22%), and Basic Algebra of Matrices (2 questions, 11%) have been asked the most. Product of Matrices has also led over the last five years, with 3 questions. Product of Matrices has produced the most tough questions (3).

  1. 1Let , for . Consider the following system of two equations in the variables and : This system does not have a unique solution if and only if2025Determinants
  2. 2Let and be two matrices such that and , where 0 is the zero matrix. Then2024 (Session 1)Basic Algebra of Matrices
  3. 3Let be a nonzero matrix with entries in . For any non-empty subset of the set of all matrices with entries in , we define a relation on by s2024 (Session 2)Product of Matrices
  4. 4If are matrices with entries in , satisfying the condition , then2023 (Session 1)Inverse of a Matrix
  5. 5Let be a complex number such that and . Let and denote the identity matrix. Then the value of is2023 (Session 1)Basic Algebra of Matrices
  6. 6Let be a non-zero matrix with real entries. Let and be distinct natural numbers such that . Then2022 (Session 1)Product of Matrices
  7. 7Let be a matrix with real entries such that . Then2022 (Session 2)Product of Matrices
  8. 8Let be the set of all matrices with integer entries. The function given by is2020 (Session 1)Inverse of a Matrix
  9. 9Let be a matrix with real entries such that zero is the only solution of the equation . Then2020 (Session 1)Inverse of a Matrix
  10. 10Let be a nonsingular matrix with real entries. Suppose the determinant of is . Then is equal to2020 (Session 2)Adjoint and its Properties
  11. 11For a non-zero matrix with real entries, let be the sum of the diagonal entries of for any positive integer . Then2019 (Session 1)Product of Matrices
  12. 12Let be a real matrix. Let where is the transpose of . Then2019 (Session 2)Symmetric & Skew Symmetric Matrices
  13. 13Let and be two matrices. Then the identity is2017Product of Matrices
  14. 14Let be a matrix with real entries. Let where is the transpose of and let be the identity matrix of order . Then2016Product of Matrices
  15. 15The trace of a square matrix is defined as the sum of its diagonal entries and is denoted by . If and are two real matrices, then2015Trace of a Matrix
  16. 16Let be five real square matrices of the same order such that , where is the unit matrix. Then,2013Product of Matrices
  17. 17then2012Inverse of a Matrix
  18. 18For a function , let denotes its -th derivative with respect to evaluated at . Consider the matrix of rows and columns, with Let , and . The2011Formation and Basic of Matrix

Frequently Asked Questions

1.How many questions are available for Matrices?

This chapter includes 18 questions compiled from NEST (NISER) papers spanning 2011 to 2025.

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

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

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

Matrices has appeared in 12 of the 16 years of NEST (NISER) papers covered here, with 18 questions across 16 papers - about one per paper it appears in.

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

Of the 18 questions analysed for this chapter, 11% are easy, 67% moderate and 22% tough. 2020 had the most, with 3 questions.

5.Which topics in Matrices should I focus on?

These topics have carried the most weightage in Matrices:

  • Product of Matrices - 7 questions (39%)
  • Inverse of a Matrix - 4 questions (22%)
  • Basic Algebra of Matrices - 2 questions (11%)
  • Product of Matrices has produced the most tough questions (3).
6.Is Matrices's weightage in NEST (NISER) going up or down?

Across all 16 papers analysed, Matrices has averaged about 1.1 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.