$2x + 3y + 4z = 9$,$4x + 9y + 3z = 10,$$5x + 10y + 5z = 11$ then the value of $ x$ is
$\left| {\,\begin{array}{*{20}{c}}9&3&4\\{10}&9&3\\{11}&{10}&5\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&4\\4&9&3\\5&{10}&5\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}9&4&3\\{10}&3&9\\{11}&5&{10}\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}2&3&4\\4&9&3\\5&{10}&5\end{array}\,} \right|$
$\left| {\,\begin{array}{*{20}{c}}9&4&9\\{10}&3&3\\{11}&5&{10}\end{array}\,} \right| \div \left| {\,\begin{array}{*{20}{c}}3&2&4\\9&4&3\\{10}&5&5\end{array}\,} \right|$
None of these
The determinant $\,\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&2&3\\1&3&6\end{array}\,} \right|$ is not equal to
The number of solutions of the system of equations $2x + y - z = 7,\,\,x - 3y + 2z = 1,\,x + 4y - 3z = 5$ is
If for some $\alpha$ and $\beta$ in $R,$ the intersection of the following three planes $x+4 y-2 z=1$ ; $x+7 y-5 z=\beta$ ; $x+5 y+\alpha z=5$ is a line in $\mathrm{R}^{3},$ then $\alpha+\beta$ is equal to
If $S$ is the set of distinct values of $'b'$ for which the following system of linear equations $x + y + z = 1;x + ay + z = 1;ax + by + z = 0$ has no solution , then $S$ is :
Let $\alpha, \beta, \gamma$ be the real roots of the equation, $x ^{3}+ ax ^{2}+ bx + c =0,( a , b , c \in R$ and $a , b \neq 0)$ If the system of equations (in, $u,v,w$) given by $\alpha u+\beta v+\gamma w=0, \beta u+\gamma v+\alpha w=0$ $\gamma u +\alpha v +\beta w =0$ has non-trivial solution, then the value of $\frac{a^{2}}{b}$ is