JEE Main 2022 · 28 Jun · Shift 2 · Mathematics Q17

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MathematicsSingle correct+4 / -1Question 17 of 90

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 :

\dfrac1{24}

\dfrac1{40}

\dfrac1{30}

\dfrac1{20}

Answer and worked solution

Official answer: D

Count. Of the $5\cdot4\cdot3\cdot2=120$ one-one functions, those with $f(a)+2f(b)=f(c)+f(d)$ are
$(1,3,2,5),(1,3,5,2),(4,2,3,5),(4,2,5,3),(5,1,3,4),(5,1,4,3)$ : 6.

Probability $\frac6{120}=\frac1{20}$ .

(D)

Topics:Classical probability Types of functions

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JEE Main 2022 · 28 Jun · Shift 2, Mathematics question 17