Sets, Relations & Functions
Sets and Relations
nta_pyq_2025_jan
Grade 11
Question:
Let S = {p , p \ldots . , p 1 2 10 } be the set of first ten prime numbers. Let A = S \cup P , where P is the set of all possible products of distinct elements of S . Then the number of all ordered pairs ( x, y ), x \in S , y \in A, such that x divides y , is ______.
Step-by-Step Solution
Key Concept: Apply the core result for equivalence relations and set operations and simplify using the given constraints.
Let = \lambda x (5120) y = \lambdax 9 9 9 9 9 = 10 \times ( C0 + C1 + C2 + C3 + \ldots + C9 ) = 10 \times 2 = 10 \times 512 = 5120
Correct Answer: 5120