$${73_x}$$ (in base $$-$$ $$x$$ number system) is equal to $${54_y}$$ (in base $$-y$$ number system), the possible values of $$x$$ and $$y$$ are

In a class of 200 students, 125 students have taken Programming Language course, 85 students have taken Data Structures course, 65 student have taken Computer Organization coures; 50 students have taken both Programming Language and Data Structures, 35 students have taken both Programming Languages and Computer Organization; 30 students have taken both Data Structures and Computer Organization; 15 students have taken all the three course.

How many students have not taken any of the three courses?

What is the number of vertices in an undirected connected graph with $$27$$ edges, $$6$$ vertices of degree $$2$$, $$\,\,$$ $$3$$ vertices of degree 4 and remaining of degree 3?

Let $${G_1} = \left( {V,\,{E_1}} \right)$$ and $${G_2} = \left( {V,\,{E_2}} \right)$$ be connected graphs on the same vertex set $$V$$ with more than two vertices. If $${G_1} \cap {G_2} = \left( {V,{E_1} \cap {E_2}} \right)$$ is not a connected graph, then the graph $${G_1} \cup {G_2} = \left( {V,{E_1} \cup {E_2}} \right)$$