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
Difficultજો $\left| \begin{array}{ccc} 3x - 8 & 3 & 3 \\ 3 & 3x - 8 & 3 \\ 3 & 3 & 3x - 8 \end{array} \right| = 0$ હોય,તો $x$ ની કિંમતો શોધો.
- A$0, 2/3$
- B$2/3, 11/3$
- C$1/2, 1$
- D$11/3, 1$
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ધારો કે $A = \begin{bmatrix} 1 & \sin \theta & 1 \\ -\sin \theta & 1 & \sin \theta \\ -1 & -\sin \theta & 1 \end{bmatrix}$,જ્યાં $0 \le \theta < 2\pi$,તો:
જો $\left|\begin{array}{cc}x & 2 \\ 18 & x\end{array}\right|=\left|\begin{array}{cc}6 & 2 \\ 18 & 6\end{array}\right|,$ હોય,તો $x$ ની કિંમત શોધો.
Easy
View Solutionજો $\Delta=\left|\begin{array}{lll}1 & a & a^2 \\ 1 & b & b^2 \\ 1 & c & c^2\end{array}\right|=K(a-b)(b-c)(c-a)$,હોય તો $K=$
જો $D = \left|\begin{array}{ccc}1 & -\cos \theta & -1 \\ \cos \theta & 1 & -\cos \theta \\ 1 & \cos \theta & 1\end{array}\right|$ હોય,અને $p$ અને $q$ એ અનુક્રમે $D$ ની મહત્તમ અને ન્યૂનતમ કિંમતો હોય,તો $2p + 3q$ ની કિંમત . . . . . . છે.
જો સમીકરણોની સિસ્ટમ
$x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0$
$x+(\cos \alpha) y+(\sin \alpha) z=0$
$x+(\sin \alpha) y-(\cos \alpha) z=0$
નો શૂન્યેતર ઉકેલ હોય,તો $\alpha \in \left(0, \frac{\pi}{2}\right)$ ની કિંમત શોધો:
$x+(\sqrt{2} \sin \alpha) y+(\sqrt{2} \cos \alpha) z=0$
$x+(\cos \alpha) y+(\sin \alpha) z=0$
$x+(\sin \alpha) y-(\cos \alpha) z=0$
નો શૂન્યેતર ઉકેલ હોય,તો $\alpha \in \left(0, \frac{\pi}{2}\right)$ ની કિંમત શોધો:
DifficultJEE MAIN 2024
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