Matrices

Bihar Board Class 12 · Mathematics · 84 past questions

1. Q1 2026 Set A2026 Set C2026 Set D2026 Set H

   $A=[4\;2\;3]\Rightarrow A'=$

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2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I

   If $A = \begin{bmatrix} 1 & -1 \\ -1 & 1 \end{bmatrix}$, then $A^3 =$

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3. Q3 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set J2026 Set B

   If $A = \begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}$ then $\operatorname{adj} A =$

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4. Q4 2026 Set A2026 Set C2026 Set B2026 Set D

   If $A = [\,1\ \ 2\ \ 3\ \ 4\,]$ and $B = \begin{bmatrix} 1 \\ 2 \\ 3 \\ 4 \end{bmatrix}$ then $AB =$

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5. Q5 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2024 Set J2024 Set D

   $A = [\,a_{ij}\,]_{m\times n}$ is a square matrix if

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6. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $A = \begin{bmatrix} 3 & -4 \\ 1 & -1 \end{bmatrix} \Rightarrow A + A' =$

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7. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B2021 Set J2021 Set I

   If $A=\begin{bmatrix}\cos\alpha & \sin\alpha\\ -\sin\alpha & \cos\alpha\end{bmatrix}$ and $A+A'=I$ then…

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8. Q8 2026 Set D

   If $A=\begin{bmatrix}3 & -5\\ -1 & 2\end{bmatrix}$ then $\text{adj}\,A =$

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9. Q9 2026 Set E

   If $A = \begin{bmatrix}1 & 2 & 3 & 4\end{bmatrix}$ and $B = \begin{bmatrix}1\\2\\3\\4\end{bmatrix}$ then…

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10. Q10 2026 Set H

    If $A=\begin{bmatrix}3&-5\\-1&2\end{bmatrix}$ then $adj\,A =$

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11. Q11 2026 Set J2026 Set E2026 Set B2026 Set F

    $A=[\,4\ \ 2\ \ 3\,] \Rightarrow A' =$

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12. Q12 2026 Set J2026 Set F2026 Set H

    If $A=[\,1\;\,2\;\,3\;\,4\,]$ and $B=\begin{bmatrix}1\\2\\3\\4\end{bmatrix}$ then $AB =$

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13. Q13 2025

    The number of all possible matrices of order 2 × 2 with each entry 3 or 7 is

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14. Q14 2025

    $6\begin{bmatrix} -2 & 1 \\ 3 & 5 \end{bmatrix} =$

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15. Q15 2025

    $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \Rightarrow A^4 =$

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16. Q16 2025

    $[1\ {-2}\ 0]\begin{bmatrix} 3 \\ -2 \\ 11 \end{bmatrix} =$

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17. Q17 2025

    If $A$ and $B$ are invertible matrices of same order then $(AB)^{-1} =$

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18. Q18 2025

    $2\begin{bmatrix} 3 & 7 \\ 1 & -2 \end{bmatrix} + 5\begin{bmatrix} 1 & 3 \\ 0 & 4 \end{bmatrix} =$

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19. Q19 2025

    If $A = \begin{bmatrix} 2 & -1 & 0 \\ 7 & 3 & 5 \end{bmatrix}$ then $A' =$

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20. Q20 2025

    If $A = \begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix}$ then $A^{-1} =$

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21. Q21 2025

    If $A = \begin{bmatrix}2 & -1 & 0\\3 & 4 & 5\end{bmatrix}$ and…

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22. Q22 2025

    Find the inverse matrix of the matrix $A = \begin{bmatrix}3 & 2\\5 & -1\end{bmatrix}$.

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23. Q23 2025

    Solve the following linear equations by matrix method. $2x+3y+3z=5$, $x-2y+z=-4$, $3x-y-2z=3$.

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24. Q24 2025 Set A2025 Set E2023

    $\begin{bmatrix}6 & 5\end{bmatrix}\begin{bmatrix}1\\-1\end{bmatrix} =$

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25. Q25 2025 Set A2025 Set E20232023 Set E

    $\begin{bmatrix}2 & 3\\5 & 7\end{bmatrix}\begin{bmatrix}2\\5\end{bmatrix} =$

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26. Q26 2025 Set A2025 Set E

    $\begin{bmatrix}3 & -2\end{bmatrix}\begin{bmatrix}1\\-1\end{bmatrix}=$

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27. Q27 2025 Set A2025 Set E

    $\begin{bmatrix}4\end{bmatrix}\begin{bmatrix}2 & -2\end{bmatrix}=$

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28. Q28 2025 Set A2025 Set E

    $\begin{bmatrix}5&-1\\6&7\end{bmatrix}\cdot\begin{bmatrix}2&1\\3&4\end{bmatrix}=$

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29. Q29 2025 Set A2025 Set E

    $A=\begin{bmatrix}1&2&3\end{bmatrix}\Rightarrow A'=$

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30. Q30 2025 Set A

    $\begin{bmatrix}1&2\\3&4\end{bmatrix}\begin{bmatrix}1&0\\0&1\end{bmatrix} =$

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31. Q31 2025 Set A2025 Set E

    $A=\begin{bmatrix}1&0\\0&1\end{bmatrix} \Rightarrow A^{100} =$

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32. Q32 2025 Set A2025 Set E

    $\begin{bmatrix}1&2\\3&4\end{bmatrix}\begin{bmatrix}4&0\\0&4\end{bmatrix} =$

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33. Q33 2025 Set A

    The adjoint of the matrix $\begin{bmatrix}2&3\\5&4\end{bmatrix}$ is

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34. Q34 2025 Set E20232023 Set E

    $\begin{bmatrix}1 & 0\\0 & 1\end{bmatrix}\begin{bmatrix}2 & -3\\0 & 4\end{bmatrix} =$

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35. Q35 2025 Set E

    Adjoint matrix of matrix $\begin{bmatrix}2 & 3\\5 & 4\end{bmatrix}=$

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36. Q36 2024 Set D2024 Set J

    If $A=\begin{bmatrix}2&-3\\4&6\end{bmatrix}$ then $A^{-1}=$

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37. Q37 2024 Set D2024 Set J

    If $A=\begin{bmatrix}3&6\\-5&4\end{bmatrix}$ and $B=\begin{bmatrix}7&8\\5&6\end{bmatrix}$ then $6A-5B=$

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38. Q38 2024 Set D

    If $A=\begin{bmatrix}2&\sqrt2&0\\3&-2&\frac25\end{bmatrix}$ then $A'=$

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39. Q39 2024 Set D2024 Set J

    If $2A+B+X=0$, where $A=\begin{bmatrix}-1&2\\3&4\end{bmatrix}$ and $B=\begin{bmatrix}3&-2\\1&5\end{bmatrix}$…

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40. Q40 2024 Set D

    $5\begin{bmatrix}5&6\\7&8\end{bmatrix}=$

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41. Q41 2024 Set D

    $\begin{bmatrix}-3\\5\\2\end{bmatrix}\begin{bmatrix}1&6&-4\end{bmatrix}=$

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42. Q42 2024 Set D

    $A=\begin{bmatrix}0&1\\1&0\end{bmatrix}\Rightarrow A^5=$

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43. Q43 2024 Set D2024 Set J

    $[x\ \ y]=[2x-1\ \ \ 9]\Rightarrow$

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44. Q44 2024 Set J

    $5\begin{bmatrix} 5 & 6 \\ 7 & 8 \end{bmatrix} =$

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45. Q45 2024 Set J

    $\begin{bmatrix} -3 \\ 5 \\ 2 \end{bmatrix} \begin{bmatrix} 1 & 6 & -4 \end{bmatrix} =$

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46. Q46 2024 Set J

    $A = \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} \Rightarrow A^5 =$

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47. Q47 2024 Set J

    If $A = \begin{bmatrix} 3 & -5 \\ -1 & 2 \end{bmatrix}$ then adjoint $A =$

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48. Q48 2024 Set J

    If $A=\begin{bmatrix}2&\sqrt{2}&0\\3&-2&\frac{2}{5}\end{bmatrix}$ then $A'=$

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49. Q49 2023

    $[2a-7 \quad 1] = [a \quad b-1] \Rightarrow (a, b) =$

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50. Q50 2023

    $[-1][1\ \ {-1}] =$

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51. Q51 2023

    $3\begin{bmatrix} 7 & -2 \\ 8 & 0 \end{bmatrix} =$

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52. Q52 2023

    $\begin{bmatrix}13 & 15\\-1 & 4\end{bmatrix}\begin{bmatrix}2 & 0\\0 & 2\end{bmatrix} =$

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53. Q53 20232023 Set E

    The adjoint matrix of matrix $\begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix}$

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54. Q54 2023 Set E

    If $A=\begin{bmatrix}1&0\\0&1\end{bmatrix}$ then the value of $A^{25}$ is

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55. Q55 2023 Set E

    $[-1]\,[1\;\;-1] =$

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56. Q56 2023 Set E

    $3\begin{bmatrix}7&-2\\8&0\end{bmatrix}=$

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57. Q57 2023 Set E

    $\begin{bmatrix}13&15\\-1&4\end{bmatrix}\begin{bmatrix}2&0\\0&2\end{bmatrix} =$

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58. Q58 2023 Set E

    $[2a-7 \;\; 1] = [a \;\; b-1] \Rightarrow (a,b) =$

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59. Q59 2023 Set E

    $[6 \;\; 5]\begin{bmatrix} 1 \\ -1 \end{bmatrix} =$

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60. Q60 2021 Set I

    If $A=\begin{bmatrix}1&1&1\\1&1&1\\1&1&1\end{bmatrix}$, then $A^2 =$

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61. Q61 2021 Set I

    $\begin{bmatrix} 1 & 0 \\ 0 & 1 \end{bmatrix} + \begin{bmatrix} 0 & 1 \\ 1 & 0 \end{bmatrix} =$

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62. Q62 2021 Set J2021 Set I

    Matrix $\begin{bmatrix}a&h&g\\h&b&f\\g&f&c\end{bmatrix}$ is

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63. Q63 2021 Set J2021 Set I

    $A$ is a square matrix, then $A+A'$ is necessarily

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64. Q64 2021 Set J2021 Set I

    If $A=\begin{bmatrix}\lambda&0\\1&1\end{bmatrix}$, $B=\begin{bmatrix}1&0\\2&1\end{bmatrix}$ and $A^2=B$, then…

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65. Q65 2021 Set J2021 Set I

    If $A=\begin{bmatrix}1&0\\0&1\end{bmatrix}$, then

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66. Q66 2021 Set J2021 Set I

    Find the value of $x$ from the following…

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67. Q67 2021 Set J2021 Set I

    If $A = \begin{bmatrix} 4\alpha & 0 \\ 5 & 1 \end{bmatrix}$…

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68. Q68 2021 Set J

    If $A = \begin{bmatrix} 1 & 1 & 1 \\ 1 & 1 & 1 \\ 1 & 1 & 1 \end{bmatrix}$, then $A^2 =$

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69. Q69 2021 Set J

    $\begin{bmatrix}1&0\\0&1\end{bmatrix}+\begin{bmatrix}0&1\\1&0\end{bmatrix}=$

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70. Q70 2019 Set F

    If $A=\begin{bmatrix}1&2&3\\4&5&6\end{bmatrix}$, then which one of the following is equal to $A'$?

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71. Q71 2019 Set F

    If…

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72. Q72 2019 Set F

    Which of the following is the unit matrix of order $3\times3$?

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73. Q73 2019 Set F2016

    $A=\begin{bmatrix}3&6\\5&-4\end{bmatrix},\ B=\begin{bmatrix}7&8\\5&6\end{bmatrix}\Rightarrow 2A+3B=$

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74. Q74 2019 Set F

    Find $x$ and $y$, if…

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75. Q75 2018

    If $A=\begin{bmatrix}\cos\alpha&-\sin\alpha\\\sin\alpha&\cos\alpha\end{bmatrix}$ and $A+A'=I_2$ then $\alpha=$

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76. Q76 2018

    If A be a square matrix. Then $A + A'$ will be ..........

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77. Q77 2017

    If $A=\begin{bmatrix}9&10&11\\12&13&14\end{bmatrix}$ and $B=\begin{bmatrix}11&10&9\\8&7&6\end{bmatrix}$ then…

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78. Q78 2017

    If $A=\begin{bmatrix}2&5\\3&1\end{bmatrix}$ and $B=\begin{bmatrix}1&5\\6&2\end{bmatrix}$ then find $(A+B)$…

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79. Q79 2016

    $\begin{vmatrix} 2 & 3 & 5 \\ 0 & 4 & 7 \\ 0 & 0 & 5 \end{vmatrix}$

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80. Q80 2016

    If $A = \begin{vmatrix} 1 & 2 \\ 3 & 4 \end{vmatrix}$, then find the value of $A^2 + 3A + 2I$.

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81. Q81 2015

    If $\begin{bmatrix} 2x-y & 5 \\ 3 & y \end{bmatrix} = \begin{bmatrix} 6 & 5 \\ 3 & -2 \end{bmatrix}$, then…

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82. Q82 2015

    The inverse of $A=\begin{bmatrix}2&3\\5&k\end{bmatrix}$ will not be obtained if k has the value

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83. Q83 2015

    For any unit matrix $I$

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84. Q84 2015

    Find the value of $X$ and $Y$…

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