FunctionsmediumPYQ · JEE Main · 4 Apr 2026 · Shift 1 (Morning)Free

Number of Non-Onto Functions {1,2,3,4}→{a,b,c}: 45 | JEE 2026

JEE Maths question with a full step-by-step solution.

Question
The number of functions f:{1,2,3,4}→{a,b,c}f:\{1,2,3,4\}\to\{a,b,c\}, which are not onto, is
A4848
B4545correct
C5151
D3535
Solution
Step 1: Total functions =34=81=3^4=81. Step 2: Count "into" (not onto) functions directly by inclusion–exclusion — functions missing at least one codomain element:
3C1⋅24−3C2⋅14+0=3⋅16−3⋅1=48−3=45.{}^3C_1\cdot2^4-{}^3C_2\cdot1^4+0=3\cdot16-3\cdot1=48-3=45.
 Step 3: So the number of functions that are not onto is 4545. Correct answer: (2)
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