The feasible region for the constraints $x-2 \leqslant y, x \geqslant y-1, x \geqslant 2, y \leqslant 4, x, y \geqslant 0$, is _________

A plane passes through $(2,1,2)$ and $(1,2,1)$ and parallel to the line $2 x=3 y$ and $\mathrm{z}=1$, then the plane also passes through the point

In a game, 3 coins are tossed. A person is paid $Rs \, 150$ if he gets all heads or all tails and he is supposed to pay ₹50 if he gets one head or two heads. The amount he can expect to win / lose on an average per game in ₹ is

If $\sin \left(\sin ^{-1} \frac{1}{5}+\cos ^{-1} x\right)=1$, then the value of $x$ is