Mathematics Mock Test - 8

The normal to the curve $y(x-2)(x-3)=x+6$ at the point where the curve intersects the $y$ -axis passes through the point:

The set of equations $a+b-2c=0$, $2a-3b+c=0$, and $a-5b+4c=\alpha$ is consistent. If the cofactors of the coefficient matrix $A$ are $C_{11}=7,C_{12}=-7,C_{13}=7,C_{21}=6,C_{22}=-6,C_{23}=6,C_{31}=5,C_{32}=-5,C_{33}=5$, find the value of $\alpha$.

If $2A+3B=\left[\begin{array}{ccc}2& -1& 4\\ 3& 2& 5\end{array}\right]$ and $A+2B=\left[\begin{array}{ccc}5& 0& 3\\ 1& 6& 2\end{array}\right]$, then matrix $B$ is:

Find the area bounded by the curves $y\ge x^2$ and $y=|x|$.

The activities or limitations competing with one another to share the amount of resources in linear programming are called: