Mathematics · Functions

JEE Main 2025 — 22 January, Evening Shift — Question 13

Let $\mathrm{A}=\{1,2,3,4\}$ and $\mathrm{B}=\{1,4,9,16\}$ . Then the number of many-one functions $f: A \rightarrow B$ such that $1 \in f(\mathrm{~A})$ is equal to :

Option A:
127
Option B:
151
Correct
Option C:
163
Option D:
139

Answer: B

Step-by-step solution

Total $=4^{4}$

One-one $=4!$

Many-one $=256-24=232$

Many-one which $1 \notin f(A)$

$=3 \cdot 3 \cdot 3 \cdot 3=81$

$232-81=151$ .

Answer key and solution verified before publishing.

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Exam: JEE Main 2025
Paper: 22 January, Evening Shift
Subject: Mathematics
Chapter: Functions
Topic: One-One, many-one, onto, into, bijective functions