Exams › JEE Main › Maths

Let X = {1,2,3,4,5}. The number of different ordered pairs (Y,Z) that can formed such that Y ⊆ X, Z ⊆ X and Y ∩ Z is empty is:

1. 5²
2. 3⁵
3. 2⁵
4. 5³

Correct answer: 3⁵

Solution

Each element of set X can either belong to set Y, set Z, or neither, but not both. Since there are 5 elements in X, and each element has 3 independent choices (in Y, in Z, or in neither), the total number of combinations is 3 raised to the power of 5.

Related JEE Main Maths questions

• Let A be the set {(n, 2n): n ∈ N} and let B be the set {(2n, 3n): n ∈ N}. What is the intersection A ∩ B?
• 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?
• If A and B are non-empty sets with A containing B, then which of the following is true?

⚔️ Practice JEE Main Maths free + battle 1v1 →