Determinants

Bihar Board Class 12 · Mathematics · 70 past questions

16 of 70 · show all

1. Q16 2025

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

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2. Q17 2025

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

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3. Q18 2025

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

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4. Q19 2025

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

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5. Q20 2025

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

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6. Q21 2025 Set A2025 Set E

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

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7. Q22 2025 Set A2025 Set E

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

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8. Q23 2025 Set A2025 Set E

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

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9. Q24 2025 Set A2025 Set E

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

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10. Q25 2025 Set A2025 Set E

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

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11. Q26 2025 Set A2025 Set E

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

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12. Q27 2025 Set A2025 Set E

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

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13. Q28 2025 Set E

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

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14. 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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15. Q30 2025 Set E

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

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16. Q31 2025 Set E

    Prove that $\begin{vmatrix} a+b & b & c \\ b+c & c & a \\ c+a & a & b \end{vmatrix}=3abc-a^3-b^3-c^3$.

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