Set Theory - General Aptitude - General Aptitude (GA) Previous Year Questions

Let \(\tau_1\) be the usual topology on \(\mathbb{R}\). Let \(\tau_2\) be the topology on \(\mathbb{R}\) generated by \(\mathcal{B} = \{[a,b) \subset \mathbb{R} : -\infty < a < b < \infty\}\). Then the set \(\{ x \in \mathbb{R} : 4 \sin^2 x \le 1 \} \cup \{\frac{\pi}{2}\}\) is

Let \(X\) be a connected topological space such that there exists a non-constant continuous function \(f : X \to \mathbb{R}\) where \(\mathbb{R}\) is equipped with the usual topology. Let \(f(X) = \{ f(x) : x \in X\}\). Then

500 students are taking one or more courses out of Chemistry, Physics, and Mathematics.
Registration records indicate course enrolment as follows: Chemistry (329), Physics (186), Mathematics (295), Chemistry and Physics (83), Chemistry and Mathematics (217), and Physics and Mathematics (63). How many students are taking all 3 subjects?

Forty students watched films A, B and C over a week. Each student watched either only one film or all three. Thirteen students watched film A, sixteen students watched film B and nineteen students watched film C. How many students watched all three films?

In a population, patients who have high cholesterol also have high blood-pressure (BP). Some patients with high BP also have diabetes. There are no patients who have both high cholesterol and diabetes. Furthermore,
1. the total number of patients with at least one of these conditions is 75,
2. the number of patients with high cholesterol is 10,
3. the number of patients with high BP is 45, and
4. the number of patients with only high BP and no other conditions is 20.
Then the number of patients who have both diabetes and high BP is ______