JEE Main 2026 Apr 4 Shift 1, Mathematics Q4: Types of Functions

JEE Main2026Apr 4, Shift 1Mathematics

The number of functions $f : {1, 2, 3, 4} \to {a, b, c}$ , which are not onto, is :

Solution

Total functions from a $4$ -element set to a $3$ -element set: $3^{4} = 81$ .

By inclusion-exclusion, the number of onto functions is

$3^{4} - (1 3) 2^{4} + (2 3) 1^{4} = 81 - 48 + 3 = 36.$

Therefore the count of functions that are NOT onto is

$81 - 36 = 45.$

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