Determinants

Bihar Board Class 12 · Mathematics · 70 past questions

30 of 70 · show all

1. Q1 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set D2026 Set J2026 Set B

   $\begin{vmatrix} x & 4 \\ 2 & 2x \end{vmatrix} = 0 \Rightarrow x =$

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2. Q2 2026 Set A2026 Set H2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   $\begin{vmatrix} \cos 15^\circ & \sin 15^\circ \\ \sin 75^\circ & \cos 75^\circ \end{vmatrix} =$

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3. Q4 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

   Prove that $\begin{vmatrix}0&a&b\\c&0&b\\c&a&0\end{vmatrix}=2abc$.

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4. Q5 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set B

   Find the value of $x$, when $\begin{vmatrix}2x&8\\4&x\end{vmatrix}=0$.

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5. Q11 2026 Set F

   $\begin{vmatrix}x&4\\2&2x\end{vmatrix}=0 \Rightarrow x=$

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6. Q12 2026 Set H

   Prove that $\begin{vmatrix} 0 & a & b \\ c & 0 & b \\ c & a & 0 \end{vmatrix} = 2abc$.

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7. Q14 2026 Set J2026 Set H

   Find the value of $x$, when $\begin{vmatrix} 2x & 8 \\ 4 & x \end{vmatrix} = 0$.

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8. Q17 2025

   $\begin{vmatrix} 11 & 7 & 9 \\ 2 & -1 & 5 \\ 22 & 14 & 18 \end{vmatrix} =$

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9. Q19 2025

   If $\begin{vmatrix} x+1 & 3 \\ 5 & x-1 \end{vmatrix} = 0$ then $x =$

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10. Q21 2025 Set A2025 Set E

    $\dfrac{d}{dx}\left\{\begin{vmatrix} x & x \\ 2 & x \end{vmatrix}\right\} =$

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11. Q22 2025 Set A2025 Set E

    $\dfrac{d}{dx}\left\{\begin{vmatrix} x & 15 \\ 4 & 4 \end{vmatrix}\right\} =$

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12. Q24 2025 Set A2025 Set E

    $\begin{vmatrix}10&4\\13&5\end{vmatrix}=$

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13. Q25 2025 Set A2025 Set E

    $\begin{vmatrix}x&15\\4&4\end{vmatrix}=0\ \Rightarrow x=$

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14. Q26 2025 Set A2025 Set E

    $\begin{vmatrix}3&\sqrt3&\sqrt3\\4&0&0\\0&0&0\end{vmatrix}=$

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15. Q27 2025 Set A2025 Set E

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

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16. Q35 2024 Set D

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

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17. Q38 2024 Set D2024 Set J

    $\begin{vmatrix} x & x+1 \\ x-1 & x \end{vmatrix} =$

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18. Q42 2023 Set E

    $\begin{vmatrix} -\sin\theta & \cos\theta \\ \sec\theta & \mathrm{cosec}\,\theta \end{vmatrix} =$

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19. 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

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20. Q50 2021 Set J2021 Set I

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

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21. Q51 2021 Set J2021 Set I

    $\begin{vmatrix}10 & 2\\ 35 & 7\end{vmatrix}=$

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22. Q54 2019 Set F

    $\begin{vmatrix}\sin20^\circ & -\cos20^\circ\\ \sin70^\circ & \cos70^\circ\end{vmatrix}=?$

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23. Q55 2019 Set F

    Evaluate $\begin{vmatrix} 1 & -1 \\ y & x \end{vmatrix}$

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24. Q56 2019 Set F

    Prove that $\begin{vmatrix} \cos 15^\circ & \sin 15^\circ \\ \sin 75^\circ & \cos 75^\circ \end{vmatrix} = 0$

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25. Q58 2018

    If $\lambda\in R$ and $\Delta=\begin{vmatrix}a&b\\c&d\end{vmatrix}$ then $\lambda\Delta=$

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26. Q61 2018

    Let A be a non-singular matrix of the order $2 \times 2$ then $|adj A| =$ ..........

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27. Q64 2017

    $\begin{vmatrix}1&1&2\\2&2&4\\3&5&6\end{vmatrix}=\ldots\ldots\ldots?$

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28. Q65 2017

    If $\begin{vmatrix} x & 5 \\ 5 & x \end{vmatrix} = 0$ then $x = 0$

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29. Q66 2017

    $\begin{vmatrix} 10 & 2 \\ 35 & 7 \end{vmatrix} = \ldots\ldots\ldots\ldots\ldots$

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30. Q70 2015

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

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