Determinants

Bihar Board Class 12 · Mathematics · 70 past questions

35 of 70 · show all

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

   Prove that the value of the determinant $\begin{vmatrix}102&18&36\\1&3&4\\17&3&6\end{vmatrix}=0$.

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2. Q7 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set D

   $\begin{vmatrix} 23 & 12 & 11 \\ 36 & 10 & 26 \\ 63 & 26 & 37 \end{vmatrix} =$

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3. Q8 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set D2026 Set B

   $\begin{vmatrix} a-b & b-c & c-a \\ b-c & c-a & a-b \\ c-a & a-b & b-c \end{vmatrix} =$

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4. Q9 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\begin{vmatrix} a+ib & c+id \\ -c+id & a-ib \end{vmatrix} =$

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5. Q10 2026 Set D2026 Set H

   Prove that the value of the determinant…

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6. Q13 2026 Set J2026 Set F2026 Set B

   $\begin{vmatrix}23&12&11\\36&10&26\\63&26&37\end{vmatrix}=$

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7. Q15 2026 Set J2026 Set F

   $\begin{vmatrix}a-b&b-c&c-a\\b-c&c-a&a-b\\c-a&a-b&b-c\end{vmatrix}=$

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8. Q16 2025

   If $\begin{vmatrix} 2 & x \\ x & 8 \end{vmatrix} = \begin{vmatrix} 10 & 7 \\ 30 & 21 \end{vmatrix}$, then…

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9. Q18 2025

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

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10. Q20 2025

    Solve: $\begin{vmatrix}x^2-x+1 & x-1\\x+1 & x+1\end{vmatrix} = 2$

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11. Q23 2025 Set A2025 Set E

    $\begin{vmatrix}21&11&10\\25&15&10\\64&27&37\end{vmatrix}=$

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12. Q28 2025 Set E

    Prove that $\begin{vmatrix} 23 & 12 & 11 \\ 36 & 10 & 26 \\ 63 & 26 & 37 \end{vmatrix} = 0$.

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13. Q29 2025 Set E2019 Set F

    Evaluate the determinant $\begin{vmatrix} 4 & 9 & 7 \\ 3 & 5 & 7 \\ 5 & 4 & 5 \end{vmatrix}$.

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14. Q30 2025 Set E

    If $\begin{vmatrix} x & 5 \\ x & x \end{vmatrix}=24$, then find the value of $x$.

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15. Q33 2024 Set D2024 Set J

    $\begin{vmatrix} 1 & 1 & -2 \\ 2 & 1 & -3 \\ 5 & 4 & -9 \end{vmatrix}=$

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16. Q34 2024 Set D2024 Set J

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

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17. Q36 2024 Set D

    Evaluate the determinant $\begin{vmatrix}1&1&1\\a&b&c\\a^3&b^3&c^3\end{vmatrix}$.

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18. Q37 2024 Set D2024 Set J

    Evaluate the determinant $\begin{vmatrix}1+a&1&1\\1&1+b&1\\1&1&1+c\end{vmatrix}$.

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19. Q39 20232023 Set E

    $\begin{vmatrix}1 & 1 & 5\\4 & 9 & 17\\5 & 10 & 22\end{vmatrix} =$

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20. Q40 20232023 Set E

    $\begin{vmatrix}1 & 2 & -1\\5 & 4 & 1\\7 & 6 & 1\end{vmatrix} =$

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21. Q41 2023

    $\begin{vmatrix}-\sin\theta & \cos\theta\\ \sec\theta & \csc\theta\end{vmatrix} =$

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22. Q43 2023 Set E

    Factorize the determinant…

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23. Q44 2021 Set I

    Prove that $\begin{vmatrix} 23 & 11 & 12 \\ 46 & 20 & 26 \\ 65 & 45 & 20 \end{vmatrix}=0$.

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24. 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

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25. 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

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26. Q52 2021 Set J

    Prove that $\begin{vmatrix}23&11&12\\46&20&26\\65&45&20\end{vmatrix}=0$.

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27. Q53 2019 Set F

    The value of the determinant $\begin{vmatrix} 1 & 2 & 4 \\ 1 & 3 & 6 \\ 1 & 4 & 9 \end{vmatrix}$ is -

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28. Q57 2019 Set F

    Prove that -…

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29. Q59 2018

    If a, b and c are in A.P. then $\begin{vmatrix}x+1&x+2&x+a\\x+2&x+3&x+b\\x+3&x+4&x+c\end{vmatrix}=$

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30. 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…

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31. Q62 2018

    Find the values of x and y when $\begin{vmatrix}2&3\\y&x\end{vmatrix}$ and…

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32. Q63 2018

    Prove that: $\begin{vmatrix} x+a & b & c \\ a & x+b & c \\ a & b & x+c \end{vmatrix} = x^2(x+a+b+c)$

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33. Q67 2016

    $\begin{vmatrix}1&a&a^2\\1&b&b^2\end{vmatrix}$

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34. Q68 2016

    Evaluate $\begin{bmatrix} x & x^2 & x^3 \\ y & y^2 & y^3 \\ z & z^2 & z^3 \end{bmatrix}$

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35. Q69 2015

    $\begin{vmatrix} 1 & x & x^2 \\ 1 & y & y^2 \\ 1 & z & z^2 \end{vmatrix} =$

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