Let $\mathbb{R}$ and $\mathbb{R}^3$ denote the set of real numbers and the three dimensional vector space over it, respectively. The value of $\alpha$ for which the set of vectors

$$ \{ [2 \ -3 \ \alpha], \ [3 \ -1 \ 3], \ [1 \ -5 \ 7] \}$$

does not form a basis of $\mathbb{R}^3$ is _______.

Suppose $X$ and $Y$ are independent and identically distributed random variables that are distributed uniformly in the interval $[0,1]$. The probability that $X \geq Y$ is _______ .

Consider the Earth to be a perfect sphere of radius $R$. Then the surface area of the region, enclosed by the 60°N latitude circle, that contains the north pole in its interior is _______.

Let $z$ be a complex variable. If $f(z)=\frac{\sin(\pi z)}{z^{7}(z-2)}$ and $C$ is the circle in the complex plane with $|z|=3$ then $\oint\limits_{C} f(z)dz$ is _______.