$$ \text { The domain of the function } f(x)=\sin ^{-1}(\sqrt{x-1}) $$

If the matrix $M=\left[\begin{array}{ccc}x+5 & a & -4 \\ -2 & 0 & b \\ c & 6 & y+1\end{array}\right]$ is a skew symmetric matrix, the value of the expression $\boldsymbol{a} \boldsymbol{b}+\boldsymbol{c}^{\mathbf{2}}-\boldsymbol{x} \boldsymbol{y}$ is:

If $\boldsymbol{k}$ is the arithmetic mean of two given quantities and $\boldsymbol{p}, \boldsymbol{q}$ are the geometric means between the same two quantities, then $\boldsymbol{p}^{\mathbf{3}}+\boldsymbol{q}^{\mathbf{3}}$ is:

The feasible region represented by the constraints:

$$ \begin{aligned} & x+2 y \leq 120 \\ & x+y \geq 60 \\ & x-2 y \geq 0 \\ & x \geq 0 \text { and } y \geq 0 \end{aligned} $$