Verified Solution • 2025–26 Session moderate

QJEEM22Mae6b7: JEE Main 2022 Mathematics - Class 12 JEEM22Mae6b7 Solution: The probability that a randomly chosen one-one function from…

The probability that a randomly chosen one-one function from the set {a, b, c, d} to the set {1, 2, 3, 4, 5} satisfies f(a) + 2f(b) −- f(c) = f(d) is :

Multiple Choice Options

  • A 124{1 \over {24}}
  • B 140{1 \over {40}}
  • C 130{1 \over {30}}
  • D 120{1 \over {20}}

Step-by-Step Verified Solution

Number of one-one function from {a,b,c,d}\{a, b, c, d\} to set {1,2,3,4,5}\{1,2,3,4,5\} is 5P4=120n(s){ }^{5} P_{4}=120 n(s) .

The required possible set of value (f(a), f(b),f(c),f(d))f(b), f(c), f(d)) such that f(a)+2f(b)−f(c)=f(d)f(a)+2 f(b)-f(c)=f(d) are (5,3,2,1),(5,1,2,3),(4,1,3,5),(3,1,4,5)(5,3,2,1),(5,1,2,3),(4,1,3,5),(3,1,4,5) , (5,4,3,2)(5,4,3,2) and (3,4,5,2)(3,4,5,2)

∴n(E)=6\therefore n(E)=6

∴\therefore Required probability =n(E)n(S)=6120=120=\frac{n(E)}{n(S)}=\frac{6}{120}=\frac{1}{20}

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