The following system of equations
$${x_1}\, + \,{x_2}\, + 2{x_3}\, = 1$$
$${x_1}\, + \,2 {x_2}\, + 3{x_3}\, = 2$$
$${x_1}\, + \,4{x_2}\, + a{x_3}\, = 4$$ has a unique solution. The only possible value (s) for $$\alpha $$ is/are

What is the size of the smallest MIS (Maximal Independent Set) of a chain of nine nodes?

$$\mathop {\lim }\limits_{x \to \infty } {{x - \sin x} \over {x + \cos \,x}}\,\,Equals$$

If $$\,\,\,\,f\,\,\,\,\left( x \right)$$ is defined as follows, what is the minimum value of $$f\,\left( x \right)$$ for $$x \in \left( {0,2} \right)$$ ? $$$f\left( x \right) = \left\{ {\matrix{ {{{25} \over {8x}}\,\,when\,\,x \le {3 \over 2}} \cr {x + {1 \over x}other\,wise} \cr } } \right.$$$