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JEE Main202311 Apr 2023Evening ShiftMathematicsFunctionsActual

Let A = 1 , 2 , 3 , 4 , 5 and B = 1 , 2 , 3 , 4 , 5 , 6 . Then the number of functions f : A → B satisfying f 1 + f 2 = f 4 - 1 is equal to........

Correct answer

0

Step-by-step solution

Given, f ( 1 ) + f 2 + 1 = f 4 ⇒ f 1 + f 2 ≤ 5 as   f 4 ≤ 6 Now taking cases we get, Case 1 ,   f 1 = 1 ⇒ f 2 = 1 , 2 , 3 , 4 → 4   mappings Case 2 ,   f 1 = 2 ⇒ f 2 = 1 , 2 , 3 → 3   mappings Case 3 ,   f 1 = 3 ⇒ f 2 = 1 , 2 → 2   mappings Case 4 ,   f 1 = 4 ⇒ f 2 = 1 → 1   mappings And f 5   &   f 6 → 6   mapping each So, total number of function will be = 4 + 3 + 2 + 1 &#21

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