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
EasyIf one of the roots of $\left|\begin{array}{lll}3 & 5 & x \\ 7 & x & 7 \\ x & 5 & 3\end{array}\right|=0$ is $-10$, then the other roots are
- A$3, 7$
- B$4, 7$
- C$3, 9$
- D$3, 4$
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Similar Questions
If $\left| {\begin{array}{*{20}{c}}{{x^2} + x}&{x + 1}&{x - 2}\\ {2{x^2} + 3x - 1}&{3x}&{3x - 3}\\ {{x^2} + 2x + 3}&{2x - 1}&{2x - 1}\end{array}} \right| = Ax - 12$,then the value of $A$ is
The number of distinct real roots of $\left| {\begin{array}{*{20}{c}}{\sin x}&{\cos x}&{\cos x}\\{\cos x}&{\sin x}&{\cos x}\\{\cos x}&{\cos x}&{\sin x}\end{array}} \right| = 0$ in the interval $-\frac{\pi}{4} \le x \le \frac{\pi}{4}$ is
MediumIIT 2001
View SolutionIf $A, B, C$ are the angles of a triangle,then the system of equations $-x + y \cos C + z \cos B = 0$,$x \cos C - y + z \cos A = 0$,$x \cos B + y \cos A - z = 0$ have
If $a, b, c$ are non-zero real numbers and the system of equations $(a - 1)x = y + z,$ $(b - 1)y = z + x,$ $(c - 1)z = x + y$ has a non-trivial solution,then $ab + bc + ca$ equals
DifficultJEE MAIN 2014
View SolutionConsider three points $P(\cos \alpha, \sin \beta)$, $Q(\sin \alpha, \cos \beta)$, and $R(0,0)$, where $0 < \alpha, \beta < \frac{\pi}{4}$. Then:
MediumWBJEE 2025
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