Determinants

Bihar Board Class 12 · Mathematics · 70 past questions

15 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. 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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4. Q4 2026 Set A2026 Set E2026 Set C2026 Set F2026 Set D2026 Set J2026 Set B

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

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

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

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

   Prove that…

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

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

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

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

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

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

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10. Q10 2026 Set D2026 Set H

    Prove that the value of the determinant…

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11. Q11 2026 Set F

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

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12. Q12 2026 Set H

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

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13. 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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14. 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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15. Q15 2026 Set J2026 Set F

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

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