Determinants

Bihar Board Class 12 · Mathematics · 70 past questions

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

   Prove that…

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4. Q10 2026 Set D2026 Set H

   Prove that the value of the determinant…

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5. Q12 2026 Set H

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

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6. Q28 2025 Set E

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

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7. 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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8. Q44 2021 Set I

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

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9. Q52 2021 Set J

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

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10. 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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11. Q57 2019 Set F

    Prove that -…

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12. 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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