Test Index

Functions Part 1

Section: Mathematics

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Question : 48 of 100

Marks: +1, -0

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 from the set

A

A \times B

[25 Feb 2021 Shift 2]

$2 y=91 x$
$2 y=273 x$
$y=91 x$
$y=273 x$

Solution:

x=\{f: A \rightarrow B, f

is one - one

\}

y=\{g: A \rightarrow A \times B, g

is one one

\}

Number of elements in

A=3

i.e.

|A|=3

Similarly,

|B|=5

Then,

|A \times B|=|A| \times |B|=3 \times 5=15

Now, number of one-one function from

A

to

B

will be

{}^5P_3 = \; \frac{5!}{(5-3)!} = \; \frac{5!}{2!} = 5 \times 4 \times 3 = 60

\therefore \;\; x=60

Now, number of one-one function from

A

to

A \times B

will be

\;\; = {}^15P_3 = \frac{15!}{(15-3)!} = \frac{15!}{12!}

\;\; = 15 \times 14 \times 13 = 2730

y=2730

Thus,

2 \times (2730) = 91 \times (60)

2 y=91 x

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