Matrices

JEE Advanced · Mathematics · 56 past questions

1. Q1 2026 Paper 1

   Which one of the following matrices can be obtained by performing elementary row transformations on the…

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2. Q2 2026 Paper 1

   Consider the matrix…

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3. Q3 2026 Paper 1

   For real numbers $\alpha, \beta, \gamma, \delta$ and $\mu$, consider the matrix…

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4. Q4 2026 Paper 2

   Let $\mathbb{R}$ denote the set of all real numbers and let $i=\sqrt{-1}$. Consider the matrices…

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5. Q5 2025 Paper 1

   Consider the matrix…

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6. Q6 2025 Paper 2

   Let $I = \begin{pmatrix} 1 & 0 \\ 0 & 1 \end{pmatrix}$ and…

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7. Q7 2024 Paper 1

   Let $\mathbb{R}^2$ denote $\mathbb{R}\times\mathbb{R}$. Let…

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8. Q8 2024 Paper 1

   Let…

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9. Q9 2023 Paper 2

   Let $M = (a_{ij}),\ i, j \in \{1,2,3\}$, be the $3\times 3$ matrix such that $a_{ij} = 1$ if $j+1$ is…

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10. Q10 2023 Paper 2

    Let…

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11. Q11 2022 Paper 1

    Let $p, q, r$ be nonzero real numbers that are, respectively, the $10^{th}$, $100^{th}$ and $1000^{th}$ terms…

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12. Q12 2022 Paper 2

    Let $\beta$ be a real number. Consider the matrix…

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13. Q13 2022 Paper 2

    If $M=\begin{pmatrix}\frac{5}{2} & \frac{3}{2}\\ -\frac{3}{2} & -\frac{1}{2}\end{pmatrix}$, then which of the…

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14. Q14 2021 Paper 1

    Let $\alpha, \beta$ and $\gamma$ be real numbers such that the system of linear equations…

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15. Q15 2021 Paper 1

    For any $3 \times 3$ matrix $M$, let $|M|$ denote the determinant of $M$. Let…

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16. Q16 2021 Paper 1

    For any $3\times3$ matrix $M$, let $|M|$ denote the determinant of $M$. Let $I$ be the $3\times3$ identity…

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17. Q17 2020 Paper 1

    Let $M$ be a $3\times3$ invertible matrix with real entries and let $I$ denote the $3\times3$ identity…

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18. Q18 2020 Paper 2

    The trace of a square matrix is defined to be the sum of its diagonal entries. If $A$ is a $2 \times 2$…

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19. Q19 2019 Paper 1

    Let…

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20. Q20 2019 Paper 1

    Let…

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21. Q21 2019 Paper 2

    Let $P_1 = I = \begin{bmatrix}1&0&0\\0&1&0\\0&0&1\end{bmatrix}$…

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22. Q22 2019 Paper 2

    Let $x \in \mathbb{R}$ and let $P = \begin{bmatrix}1&1&1\\0&2&2\\0&0&3\end{bmatrix}$…

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23. Q23 2018 Paper 2

    Let $S$ be the set of all column matrices $\begin{bmatrix}b_1\\b_2\\b_3\end{bmatrix}$ such that…

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24. Q24 2018 Paper 2

    Let $P$ be a matrix of order $3 \times 3$ such that all the entries in $P$ are from the set $\{-1, 0, 1\}$.…

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25. Q25 2017 Paper 1

    Which of the following is(are) NOT the square of a $3\times3$ matrix with real entries?

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26. Q26 2017 Paper 1

    For a real number $\alpha$, if the system…

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27. Q27 2017 Paper 2

    How many $3\times3$ matrices $M$ with entries from $\{0,1,2\}$ are there, for which the sum of the diagonal…

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28. Q28 2016 Paper 1

    Let $P=\begin{bmatrix}3&-1&-2\\2&0&\alpha\\3&-5&0\end{bmatrix}$, where $\alpha\in\mathbb{R}$. Suppose…

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29. Q29 2016 Paper 1

    Let $z = \frac{-1+\sqrt{3}\,i}{2}$, where $i=\sqrt{-1}$, and $r, s \in \{1, 2, 3\}$. Let…

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30. Q30 2016 Paper 2

    Let $P=\begin{bmatrix}1&0&0\\4&1&0\\16&4&1\end{bmatrix}$ and $I$ be the identity matrix of order 3. If…

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31. Q31 2015 Paper 1

    Let $X$ and $Y$ be two arbitrary, $3\times3$, non-zero, skew-symmetric matrices and $Z$ be an arbitrary…

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32. Q32 2014 Paper 1

    Let $M$ and $N$ be two $3 \times 3$ matrices such that $MN = NM$. Further, if $M \neq N^2$ and $M^2 = N^4$…

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33. Q33 2014 Paper 1

    Let $M$ be a $2 \times 2$ symmetric matrix with integer entries. Then $M$ is invertible if

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34. Q34 2013 Paper 1

    For $3 \times 3$ matrices $M$ and $N$, which of the following statement(s) is (are) **NOT** correct?

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35. Q35 2013 Paper 2

    Let $\omega$ be a complex cube root of unity with $\omega \neq 1$ and $P = [p_{ij}]$ be a $n \times n$ matrix…

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36. Q36 2012 Paper 2

    If $P$ is a $3 \times 3$ matrix such that $P^T = 2P + I$, where $P^T$ is the transpose of $P$ and $I$ is the…

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37. Q37 2012 Paper 2

    If the adjoint of a $3\times3$ matrix $P$ is $\begin{bmatrix}1&4&4\\2&1&7\\1&1&3\end{bmatrix}$, then the…

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38. Q38 2011 Paper 1

    Paragraph for Question Nos. 58 to 60…

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39. Q39 2011 Paper 1

    Paragraph for Question Nos. 58 to 60…

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40. Q40 2011 Paper 1

    Paragraph for Question Nos. 58 to 60…

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41. Q41 2011 Paper 2

    Let $\omega\neq1$ be a cube root of unity and $S$ be the set of all non-singular matrices of the form…

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42. Q42 2011 Paper 2

    Let $M$ be a $3\times3$ matrix satisfying…

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43. Q43 2011 Paper 2

    Match the statements given in Column I with the values given in Column II

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44. Q44 2011 Paper 2

    Match the statements given in Column I with the intervals/union of intervals given in Column II

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45. Q45 2010 Paper 1

    The number of $3\times3$ matrices A whose entries are either 0 or 1 and for which the system…

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46. Q46 2010 Paper 1

    Paragraph for Questions 42 to 44…

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47. Q47 2010 Paper 1

    Paragraph for Questions 42 to 44…

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48. Q48 2010 Paper 1

    Paragraph for Questions 42 to 44…

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49. Q49 2010 Paper 2

    Let $k$ be a positive real number and let…

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50. Q50 2009 Paper 1

    Paragraph for Question Nos. 33 to 35…

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51. Q51 2009 Paper 1

    Paragraph for Question Nos. 33 to 35…

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52. Q52 2009 Paper 1

    Paragraph for Question Nos. 33 to 35…

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53. Q53 2009 Paper 2

    Match the statements/expressions given in Column I with the values given in Column II.

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54. Q54 2009 Paper 2

    Match the statements/expressions given in Column I with the values given in Column II.

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55. Q55 2008 Paper 1

    Consider the system of equations…

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56. Q56 2008 Paper 2

    Match the Statements / Expressions in Column I with the Statements / Expressions in Column II and indicate…

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