The value of the determinant$\left| {\,\begin{array}{*{20}{c}}1&1&1\\1&{1 - x}&1\\1&1&{1 + y}\end{array}\,} \right|$is
$3 - x + y$
$(1 - x)(1 + y)$
$xy$
$ - xy$
The number of values of $k $ for which the system of equations $(k + 1)x + 8y = 4k,$ $kx + (k + 3)y = 3k - 1$ has infinitely many solutions, is
Find area of the triangle with vertices at the point given in each of the following: $(1,0),(6,0),(4,3)$
In a $\Delta ABC,$ if $\left| {\,\begin{array}{*{20}{c}}1&a&b\\1&c&a\\1&b&c\end{array}\,} \right| = 0$, then ${\sin ^2}A + {\sin ^2}B + {\sin ^2}C = $
The system of linear equation $x + y + z = 2, 2x + 3y + 2z = 5$, $2x + 3y + (a^2 -1)\,z = a + 1$ then