← Back to shiwamsclass.com← Website
← Bihar Board Class 12 PYQ

Determinants

Bihar Board Class 12 · Mathematics · 70 past questions

  1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set D2026 Set J2026 Set B
    $\begin{vmatrix} x & 4 \\ 2 & 2x \end{vmatrix} = 0 \Rightarrow x =$
  2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\begin{vmatrix} \cos 15^\circ & \sin 15^\circ \\ \sin 75^\circ & \cos 75^\circ \end{vmatrix} =$
  3. Q3 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set J2026 Set B
    Prove that the value of the determinant $\begin{vmatrix}102&18&36\\1&3&4\\17&3&6\end{vmatrix}=0$.
  4. Q4 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Prove that $\begin{vmatrix}0&a&b\\c&0&b\\c&a&0\end{vmatrix}=2abc$.
  5. Q5 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B
    Find the value of $x$, when $\begin{vmatrix}2x&8\\4&x\end{vmatrix}=0$.
  6. Q6 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    Prove that…
  7. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set D
    $\begin{vmatrix} 23 & 12 & 11 \\ 36 & 10 & 26 \\ 63 & 26 & 37 \end{vmatrix} =$
  8. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set D2026 Set B
    $\begin{vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{vmatrix} =$
  9. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B
    $\begin{vmatrix} a+ib & c+id \\ -c+id & a-ib \end{vmatrix} =$
  10. Q10 2026 Set D2026 Set H
    Prove that the value of the determinant…
  11. Q11 2026 Set F
    $\begin{vmatrix}x&4\\2&2x\end{vmatrix}=0 \Rightarrow x=$
  12. Q12 2026 Set H
    Prove that $\begin{vmatrix} 0 & a & b \\ c & 0 & b \\ c & a & 0 \end{vmatrix} = 2abc$.
  13. Q13 2026 Set J2026 Set F2026 Set B
    $\begin{vmatrix}23&12&11\\36&10&26\\63&26&37\end{vmatrix}=$
  14. Q14 2026 Set J2026 Set H
    Find the value of $x$, when $\begin{vmatrix} 2x & 8 \\ 4 & x \end{vmatrix} = 0$.
  15. Q15 2026 Set J2026 Set F
    $\begin{vmatrix}a-b&b-c&c-a\\b-c&c-a&a-b\\c-a&a-b&b-c\end{vmatrix}=$
  16. Q16 2025
    If $\begin{vmatrix} 2 & x \\ x & 8 \end{vmatrix} = \begin{vmatrix} 10 & 7 \\ 30 & 21 \end{vmatrix}$, then…
  17. Q17 2025
    $\begin{vmatrix} 11 & 7 & 9 \\ 2 & -1 & 5 \\ 22 & 14 & 18 \end{vmatrix} =$
  18. Q18 2025
    $\begin{vmatrix} -1 & 3 & 0 \\ 1 & 2 & 4 \\ 4 & 1 & 0 \end{vmatrix} =$
  19. Q19 2025
    If $\begin{vmatrix} x+1 & 3 \\ 5 & x-1 \end{vmatrix} = 0$ then $x =$
  20. Q20 2025
    Solve: $\begin{vmatrix}x^2-x+1 & x-1\\x+1 & x+1\end{vmatrix} = 2$
  21. Q21 2025 Set A2025 Set E
    $\dfrac{d}{dx}\left\{\begin{vmatrix} x & x \\ 2 & x \end{vmatrix}\right\} =$
  22. Q22 2025 Set A2025 Set E
    $\dfrac{d}{dx}\left\{\begin{vmatrix} x & 15 \\ 4 & 4 \end{vmatrix}\right\} =$
  23. Q23 2025 Set A2025 Set E
    $\begin{vmatrix}21&11&10\\25&15&10\\64&27&37\end{vmatrix}=$
  24. Q24 2025 Set A2025 Set E
    $\begin{vmatrix}10&4\\13&5\end{vmatrix}=$
  25. Q25 2025 Set A2025 Set E
    $\begin{vmatrix}x&15\\4&4\end{vmatrix}=0\ \Rightarrow x=$
  26. Q26 2025 Set A2025 Set E
    $\begin{vmatrix}3&\sqrt3&\sqrt3\\4&0&0\\0&0&0\end{vmatrix}=$
  27. Q27 2025 Set A2025 Set E
    $5\begin{vmatrix}1&2\\3&4\end{vmatrix}=$
  28. Q28 2025 Set E
    Prove that $\begin{vmatrix} 23 & 12 & 11 \\ 36 & 10 & 26 \\ 63 & 26 & 37 \end{vmatrix} = 0$.
  29. Q29 2025 Set E2019 Set F
    Evaluate the determinant $\begin{vmatrix} 4 & 9 & 7 \\ 3 & 5 & 7 \\ 5 & 4 & 5 \end{vmatrix}$.
  30. Q30 2025 Set E
    If $\begin{vmatrix} x & 5 \\ x & x \end{vmatrix}=24$, then find the value of $x$.
  31. Q31 2025 Set E
    Prove that $\begin{vmatrix} a+b & b & c \\ b+c & c & a \\ c+a & a & b \end{vmatrix}=3abc-a^3-b^3-c^3$.
  32. Q32 2024 Set D2024 Set J
    If $\begin{vmatrix} x & 2 \\ 18 & x \end{vmatrix} = \begin{vmatrix} 6 & 2 \\ 18 & 6 \end{vmatrix}$…
  33. Q33 2024 Set D2024 Set J
    $\begin{vmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{vmatrix}=$
  34. Q34 2024 Set D2024 Set J
    $\begin{vmatrix} 3 & -4 & 5 \\ 1 & 1 & -2 \\ 2 & 3 & 1 \end{vmatrix}=$
  35. Q35 2024 Set D
    If $A=\begin{bmatrix}3&-5\\-1&2\end{bmatrix}$ then adjoint $A=$
  36. Q36 2024 Set D
    Evaluate the determinant $\begin{vmatrix}1&1&1\\a&b&c\\a^3&b^3&c^3\end{vmatrix}$.
  37. Q37 2024 Set D2024 Set J
    Evaluate the determinant $\begin{vmatrix}1+a&1&1\\1&1+b&1\\1&1&1+c\end{vmatrix}$.
  38. Q38 2024 Set D2024 Set J
    $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix} =$
  39. Q39 20232023 Set E
    $\begin{vmatrix}1 & 1 & 5\\4 & 9 & 17\\5 & 10 & 22\end{vmatrix} =$
  40. Q40 20232023 Set E
    $\begin{vmatrix}1 & 2 & -1\\5 & 4 & 1\\7 & 6 & 1\end{vmatrix} =$
  41. Q41 2023
    $\begin{vmatrix}-\sin\theta & \cos\theta\\ \sec\theta & \csc\theta\end{vmatrix} =$
  42. Q42 2023 Set E
    $\begin{vmatrix} -\sin\theta & \cos\theta \\ \sec\theta & \mathrm{cosec}\,\theta \end{vmatrix} =$
  43. Q43 2023 Set E
    Factorize the determinant…
  44. Q44 2021 Set I
    Prove that $\begin{vmatrix} 23 & 11 & 12 \\ 46 & 20 & 26 \\ 65 & 45 & 20 \end{vmatrix}=0$.
  45. Q45 2021 Set J2021 Set I2018
    If $\omega\ne1,\ \omega^3=1$ and…
  46. Q46 2021 Set J2021 Set I
    The value of the determinant $\begin{vmatrix}1&2&4\\3&7&9\\4&8&16\end{vmatrix}$ is
  47. Q47 2021 Set J2021 Set I
    The value of the determinant $\begin{vmatrix}1&a&b+c\\1&b&c+a\\1&c&a+b\end{vmatrix}$ is
  48. Q48 2021 Set J2021 Set I
    The value of the determinant $\begin{vmatrix}7&11&13\\17&19&23\\29&31&37\end{vmatrix}$ is
  49. Q49 2021 Set J2021 Set I
    Factorize $\begin{vmatrix}(b+c)^2&a^2&a^2\\b^2&(c+a)^2&b^2\\c^2&c^2&(a+b)^2\end{vmatrix}$.
  50. Q50 2021 Set J2021 Set I
    $\begin{vmatrix} \cos\theta & -\sin\theta \\ \sin\theta & \cos\theta \end{vmatrix} =$
  51. Q51 2021 Set J2021 Set I
    $\begin{vmatrix}10 & 2\\ 35 & 7\end{vmatrix}=$
  52. Q52 2021 Set J
    Prove that $\begin{vmatrix}23&11&12\\46&20&26\\65&45&20\end{vmatrix}=0$.
  53. Q53 2019 Set F
    The value of the determinant $\begin{vmatrix} 1 & 2 & 4 \\ 1 & 3 & 6 \\ 1 & 4 & 9 \end{vmatrix}$ is -
  54. Q54 2019 Set F
    $\begin{vmatrix}\sin20^\circ & -\cos20^\circ\\ \sin70^\circ & \cos70^\circ\end{vmatrix}=?$
  55. Q55 2019 Set F
    Evaluate $\begin{vmatrix} 1 & -1 \\ y & x \end{vmatrix}$
  56. Q56 2019 Set F
    Prove that $\begin{vmatrix} \cos 15^\circ & \sin 15^\circ \\ \sin 75^\circ & \cos 75^\circ \end{vmatrix} = 0$
  57. Q57 2019 Set F
    Prove that -…
  58. Q58 2018
    If $\lambda\in R$ and $\Delta=\begin{vmatrix}a&b\\c&d\end{vmatrix}$ then $\lambda\Delta=$
  59. Q59 2018
    If a, b and c are in A.P. then $\begin{vmatrix}x+1&x+2&x+a\\x+2&x+3&x+b\\x+3&x+4&x+c\end{vmatrix}=$
  60. Q60 2018
    If 7 and 2 are two roots of the equation $\begin{vmatrix}x&3&7\\2&x&2\\7&6&x\end{vmatrix}=0$ then the third…
  61. Q61 2018
    Let A be a non-singular matrix of the order $2 \times 2$ then $|adj A| =$ ..........
  62. Q62 2018
    Find the values of x and y when $\begin{vmatrix}2&3\\y&x\end{vmatrix}$ and…
  63. Q63 2018
    Prove that: $\begin{vmatrix} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{vmatrix} = x^2(x+a+b+c)$
  64. Q64 2017
    $\begin{vmatrix}1&1&2\\2&2&4\\3&5&6\end{vmatrix}=\ldots\ldots\ldots?$
  65. Q65 2017
    If $\begin{vmatrix} x & 5 \\ 5 & x \end{vmatrix} = 0$ then $x = 0$
  66. Q66 2017
    $\begin{vmatrix} 10 & 2 \\ 35 & 7 \end{vmatrix} = \ldots\ldots\ldots\ldots\ldots$
  67. Q67 2016
    $\begin{vmatrix}1&a&a^2\\1&b&b^2\end{vmatrix}$
  68. Q68 2016
    Evaluate $\begin{bmatrix} x & x^2 & x^3 \\ y & y^2 & y^3 \\ z & z^2 & z^3 \end{bmatrix}$
  69. Q69 2015
    $\begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{vmatrix} =$
  70. Q70 2015
    $\begin{vmatrix}3&4&5\\0&2&3\\0&0&7\end{vmatrix}=$