JEE MAIN - Mathematics (2021 - 25th February Evening Shift - No. 3)
Let x denote the total number of one-one functions from a set A with 3 elements to a set B with 5 elements and y denote the total number of one-one functions form the set A to the set A $$\times$$ B. Then :
2y = 273x
y = 91x
2y = 91x
y = 273x
Explanation
Number of elements in A = 3
Number of elements in B = 5
Number of elements in A $$\times$$ B = 15
_25th_February_Evening_Shift_en_3_1.png)
Number of one-one function
x = 5 $$\times$$ 4 $$\times$$ 3
x = 60
_25th_February_Evening_Shift_en_3_2.png)
Number of one-one function
y = 15 $$\times$$ 14 $$\times$$ 13
y = 15 $$\times$$ 4 $$\times$$ $${{14} \over 4}$$ $$\times$$ 13
y = 60 $$\times$$ $${7 \over 2}$$ $$\times$$ 13
2y = (13)(7x)
2y = 91x
Number of elements in B = 5
Number of elements in A $$\times$$ B = 15
Number of one-one function
x = 5 $$\times$$ 4 $$\times$$ 3
x = 60
Number of one-one function
y = 15 $$\times$$ 14 $$\times$$ 13
y = 15 $$\times$$ 4 $$\times$$ $${{14} \over 4}$$ $$\times$$ 13
y = 60 $$\times$$ $${7 \over 2}$$ $$\times$$ 13
2y = (13)(7x)
2y = 91x
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