Exams › JEE Main › Maths

A class has 55 students. Among them, 23 study Mathematics, 24 study Physics, and 19 study Chemistry. Also, 12 study both Mathematics and Physics, 9 study both Mathematics and Chemistry, 7 study both Physics and Chemistry, and 4 study all three subjects. How many students study exactly one subject?

1. 6
2. 9
3. 7
4. All of these

Correct answer: 6

Solution

Use the given totals and overlaps to find the number studying only Mathematics, only Physics, and only Chemistry. Adding these three exclusive counts gives the number studying exactly one subject.

Related JEE Main Maths questions

• Let A be the set \(\{(n,2n): n \in \mathbb{N}\}\) and let B be the set \(\{(2n,3n): n \in \mathbb{N}\}\). What is the intersection \(A \cap B\)?
• Let A = \(\{ax : x \in \mathbb{N}\}\) and suppose \(B \cap C = \mathbb{N}\), where b and c are natural numbers that are relatively prime. Then which of the following must be true?
• Let set A contain 3 elements and set B contain 6 elements. Then the cardinality of their union must satisfy
• Given the sets A = {1, 2, 5} and B = {3, 4, 5, 9}, what is A ∩ B?
• At a conference with 100 attendees, 29 are Indian women and 23 are Indian men. Among the Indian attendees, 4 are doctors, and 24 are either men or doctors. If there are no foreign doctors, how many foreigners and how many women doctors are present at the conference?
• Let X and Y be two non-empty sets, and let A be a non-empty set such that X ∩ A = Y ∩ A = A and X ∪ A = Y ∪ A. Which of the following must be true?

⚔️ Practice JEE Main Maths free + battle 1v1 →