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JEE Main 20264 AprilMorning Shift

Exam: JEE Main
Year: 2026
Date: 4 April
Shift: Morning Shift
Subject: Mathematics
Chapter: Functions

JEE Main 2026 · 4 April · Morning Shift · Mathematics · Functions

The number of functions f: \ 1, 2, 3, 4\ arrow \ a, b, c\ , which...

The number of functions

f: \{1, 2, 3, 4\} \rightarrow \{a, b, c\}

, which are not onto, is:

Options

A $48$
B $45$
C $51$
D $35$

Correct answer

B. $45$

Step-by-step solution

Total number of functions from a set of

4

elements to a set of

3

elements is

3^4 = 81

.

The number of onto functions is given by the inclusion-exclusion principle:

3^4 - ^{3}C_{1} 2^4 + ^{3}C_{2} 1^4

= 81 - 3 \times 16 + 3 \times 1

= 81 - 48 + 3 = 36

The number of functions which are not onto is the total number of functions minus the number of onto functions:

81 - 36 = 45

Answer:

45

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