JEE Main 2021 — Functions Question with Solution
From: JEE Main 2021 (Online) 27th July Morning Shift
Question
Let S = {1, 2, 3, 4, 5, 6, 7}. Then the number of possible functions f : S S
such that f(m . n) = f(m) . f(n) for every m, n S and m . n S is equal to _____________.
such that f(m . n) = f(m) . f(n) for every m, n S and m . n S is equal to _____________.
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Show full solutionCorrect answer: 490
Correct answer
490
Step-by-step explanation
F(mn) = f(m) . f(n)
Put m = 1 f(n) = f(1) . f(n) f(1) = 1
Put m = n = 2
Put m = 2, n = 3
f(5), f(7) can take any value
Total = (1 1 7 1 7 1 7) + (1 1 3 1 7 1 7)
= 490
Put m = 1 f(n) = f(1) . f(n) f(1) = 1
Put m = n = 2
Put m = 2, n = 3
f(5), f(7) can take any value
Total = (1 1 7 1 7 1 7) + (1 1 3 1 7 1 7)
= 490
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This is a previous-year question from JEE Main 2021, covering the Functions chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.