Sets, Relations & Functions
Functions
nta_pyq_2025_jan
Grade 11
Question:
Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16}. Then the number of many-one functions f : A \to B such that 1 \in f ( A) is equal to :
Step-by-Step Solution
Key Concept: Apply the core result for domains, ranges and functional equations and simplify using the given constraints.
A = {1, 2, 3, 4} (1) B = {1, 4, 9, 16} Total number of functions = 4 4 Total number of one-one functions = 4! Total number of many one functions = 4 - 4! = 232 4 Total number of many-one functions in which 1 $\notin$ f (A) = 3 \times 3 \times 3 \times 3 = 81 \therefore Total number of many one functions 1 $\notin$ f (A) = 232 - 81 = 151
Correct Answer: 1