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
Difficult$\left| {\begin{array}{ccc} bc & bc' + b'c & b'c' \\ ca & ca' + c'a & c'a' \\ ab & ab' + a'b & a'b' \end{array}} \right|$ ની કિંમત શોધો.
- A$(ab - a'b')(bc - b'c')(ca - c'a')$
- B$(ab + a'b')(bc + b'c')(ca + c'a')$
- C$(ab' - a'b)(bc' - b'c)(ca' - c'a)$
- D$(ab' + a'b)(bc' + b'c)(ca' + c'a)$
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જો $\left| \begin{array}{ccc} a & b & a\alpha - b \\ b & c & b\alpha - c \\ 2 & 1 & 0 \end{array} \right| = 0$ અને $\alpha \neq \frac{1}{2}$ હોય,તો
Medium
View Solutionધારો 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 $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ ના બીજ પૈકીનું એક બીજ $-10$ હોય,તો અન્ય બીજ કયા છે?
$\theta \in (0, \pi)$ માટે એવા $\theta$ ના મૂલ્યોની સંખ્યા શોધો જેના માટે સુરેખ સમીકરણોની સંહતિ $x + 3y + 7z = 0$,$-x + 4y + 7z = 0$,અને $(\sin 3\theta)x + (\cos 2\theta)y + 2z = 0$ નો ઉકેલ અશૂન્ય (non-trivial) હોય.
DifficultJEE MAIN 2019
View Solutionનિશ્ચાયક $ \left|\begin{array}{cc}\cos 15^{\circ} & \sin 15^{\circ} \\ \sin 75^{\circ} & \cos 75^{\circ}\end{array}\right| $ ની કિંમત શોધો.
MediumKCET 2015
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