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Solution


Q.

Let A = {1, 2, 3, 4} and B = {1, 4, 9, 16}. Then the number of many-one functions f : A → B such that I∈f(A) is equal to :          [2025]
1 163  
2 139  
3 151  
4 127  

Ans.

(3)

Here, n(A) = 4, n(B) = 4

Total number of functions from A to B = 44 = 256

Number of one-one functions from A to B = P44 = 4! = 24

Number of many-one functions from A to B = 256 – 24 = 232

Number of many-one function for which 1∉f(A)=34 = 81

∴   Required number of many-one functions = 232 – 81 = 151.