If $$P, Q, R$$ are subsets of the universal set $$U$$, then
$$\left( {P \cap Q \cap R} \right) \cup \left( {{P^c} \cap Q \cap R} \right) \cup {Q^c} \cup {R^c}$$ is

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?

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