Verified Solution • 2025–26 Session moderate

QJEEM21Mab06d: JEE Main 2021 Mathematics - Class 12 JEEM21Mab06d Solution: Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a…

Let S = {1, 2, 3, 4, 5, 6}. Then the probability that a randomly chosen onto function g from S to S satisfies g(3) = 2g(1) is :

Multiple Choice Options

  • A 110{1 \over {10}}
  • B 115{1 \over {15}}
  • C 15{1 \over {5}}
  • D 130{1 \over {30}}

Step-by-Step Verified Solution

g(3) = 2g(1) can be defined in 3 ways

number of onto functions in this condition = 3 ×\times 4!

Total number of onto functions = 6!

Required probability = 3×4!6!=110{{3 \times 4!} \over {6!}} = {1 \over {10}}

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