Mathematics Mock Test - 11

For the function $f(x)=\sin x-\sqrt{3}\cos x-x$ on the interval $[0,\pi ]$, the stationary points will be:

Which of the following is one of the feasible solutions for a Linear Programming Problem with constraints: $x+2y\ge 2$, $5x+4y\le 20$, $2x-y\le 4$, $x\ge 0$, $y\ge 0$?

Consider a system of linear equations:$4x-2y=3$$6x+\alpha y=5$ For what values of constant $\alpha$ does the system have a unique solution?

Consider a plane passing through the points $A(2,2,1)$, $B(3,4,2)$ and $C(7,0,6)$. Which one of the following points lies on this plane?

Consider the plane passing through the points $A(2,2,1)$, $B(3,4,2)$ and $C(7,0,6)$. What are the direction ratios of the normal to the plane?