Class 12Mathematics3 and 4 .Determinants and MatricesExpansion of determinants, Solution of equation in the form of determinants and area of triangle and Equation of Line
Easy$\Delta = \begin{vmatrix} 0 & \sin \alpha & -\cos \alpha \\ -\sin \alpha & 0 & \sin \beta \\ \cos \alpha & -\sin \beta & 0 \end{vmatrix}$ का मान ज्ञात कीजिए।
- A$-2$
- B$2$
- C$3$
- D$0$
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यदि $a, b, c$ क्रमशः एक समांतर श्रेणी के $5^{\text{th}}, 8^{\text{th}}, 13^{\text{th}}$ पद हैं,तो $\left|\begin{array}{ccc}a & 5 & 1 \\ b & 8 & 1 \\ c & 13 & 1\end{array}\right|=$
यदि $\left| \begin{array}{ccc} \cos 2x & \sin^2 x & \cos 4x \\ \sin^2 x & \cos 2x & \cos^2 x \\ \cos 4x & \cos^2 x & \cos 2x \end{array} \right| = a_0 + a_1 \sin x + a_2 \sin^2 x + \dots$ है,तो $a_0$ का मान ज्ञात कीजिए।
यदि $\alpha$ समीकरण $x^3+6x^2+5x-42=0$ का एक वास्तविक मूल है,तो आव्यूह $\left[\begin{array}{ccc}\alpha-1 & \alpha+1 & \alpha+2 \\ \alpha-2 & \alpha+3 & \alpha-3 \\ \alpha+4 & \alpha-4 & \alpha+5\end{array}\right]$ का सारणिक ज्ञात कीजिए।
यदि $A = \begin{bmatrix} k & 2 \\ 2 & k \end{bmatrix}$ और $|A^3| = 125$ है,तो $k$ का मान ज्ञात कीजिए।
$\Delta = \left| \begin{array}{ccc} a & a+b & a+b+c \\ 3a & 4a+3b & 5a+4b+3c \\ 6a & 9a+6b & 11a+9b+6c \end{array} \right|$ जहाँ $a = i, b = \omega, c = \omega^2$ है,तो $\Delta$ का मान ज्ञात कीजिए।
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