Let $$S=\left\{M=\left[a_{i j}\right], a_{i j} \in\{0,1,2\}, 1 \leq i, j \leq 2\right\}$$ be a sample space and $$A=\{M \in S: M$$ is invertible $$\}$$ be an event. Then $$P(A)$$ is equal to :

Let $$x_{1}, x_{2}, \ldots, x_{100}$$ be in an arithmetic progression, with $$x_{1}=2$$ and their mean equal to 200 . If $$y_{i}=i\left(x_{i}-i\right), 1 \leq i \leq 100$$, then the mean of $$y_{1}, y_{2}, \ldots, y_{100}$$ is :

Let $$w_{1}$$ be the point obtained by the rotation of $$z_{1}=5+4 i$$ about the origin through a right angle in the anticlockwise direction, and $$w_{2}$$ be the point obtained by the rotation of $$z_{2}=3+5 i$$ about the origin through a right angle in the clockwise direction. Then the principal argument of $$w_{1}-w_{2}$$ is equal to :

Let $$y=y(x)$$ be a solution curve of the differential equation.

$$\left(1-x^{2} y^{2}\right) d x=y d x+x d y$$.

If the line $$x=1$$ intersects the curve $$y=y(x)$$ at $$y=2$$ and the line $$x=2$$ intersects the curve $$y=y(x)$$ at $$y=\alpha$$, then a value of $$\alpha$$ is :