The value of the determinant $\left| {\,\begin{array}{*{20}{c}}1&2&3\\3&5&7\\8&{14}&{20}\end{array}\,} \right|$is

If ${A_\lambda } = \left( {\begin{array}{*{20}{c}}
\lambda &{\lambda  - 1}\\
{\lambda  - 1}&\lambda 
\end{array}} \right);\,\lambda  \in N$ then $|A_1| + |A_2| + ..... + |A_{300}|$ is equal to

If $\left| {\,\begin{array}{*{20}{c}}a&b&c\\m&n&p\\x&y&z\end{array}\,} \right| = k$, then $\left| {\,\begin{array}{*{20}{c}}{6a}&{2b}&{2c}\\{3m}&n&p\\{3x}&y&z\end{array}\,} \right| = $

For which of the following ordered pairs $(\mu, \delta)$ the system of linear equations  $x+2 y+3 z=1$ ; $3 x+4 y+5 z=\mu$ ; $4 x+4 y+4 z=\delta$ is inconsistent?

The value of $k \in R$, for which the following system of linear equations

$3 x-y+4 z=3$

$x+2 y-3 x=-2$

$6 x+5 y+k z=-3$

has infinitely many solutions, is:

Consider the system of linear equations

$x+y+z=5, x+2 y+\lambda^2 z=9$

$x+3 y+\lambda z=\mu$, where $\lambda, \mu \in R$. Then, which of the following statement is NOT correct?