The value of the determinant given below $\left| {{\rm{ }}\begin{array}{*{20}{c}}1&2&3\\3&5&7\\8&{14}&{20}\end{array}} \right|$ is
$20$
$10$
$0$
$5$
The roots of the equation $\left| {\,\begin{array}{*{20}{c}}1&4&{20}\\1&{ - 2}&5\\1&{2x}&{5{x^2}}\end{array}\,} \right| = 0$ are
The number of distinct real roots of $\left|\begin{array}{lll}\sin x & \cos x & \cos x \\ \cos x & \sin x & \cos x \\ \cos x & \cos x & \sin x\end{array}\right|=0$ in the interval $-\frac{\pi}{4} \leq x \leq \frac{\pi}{4}$ is
Consider the following system of equations : $x+2 y-3 z=a$ ; $2 x+6 y-11 z=b$ ; $x-2 y+7 z=c$ where $a , b$ and $c$ are real constants. Then the system of equations :
$\left| {\,\begin{array}{*{20}{c}}5&3&{ - 1}\\{ - 7}&x&{ - 3}\\9&6&{ - 2}\end{array}\,} \right| = 0$, then $ x$ is equal to