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Standard XII

Mathematics

One - One function

A function is...

Question

A function is defined from $A$ to $B,$ where number of elements in $A$ and $B$ are $2$ and $6$ respectively. If the total number of functions is $x$ and total number of one one functions is $y,$ then the value of $x + y$ is

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66.0

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66.00

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

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Solution

We have $n (A) = 2$ and $n (B) = 6;$
So, total number of functions $= 6^{2} = 36$
Total number of one one functions $= 6 \times 5 = 30$
So, clearly the values of $x$ and $y$ are $36$ and $30$ respectively.
Thus $x + y = 66$

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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 $A$ to the set $A \times B$ . Then

Q. 1. Let be a set with exactly 5 elements and y be a set with exactly 7 elements. If A Is the number of one - one functions from x to y and B is the number of onto functions from y to X, then find the value of B-A/5!

Q. 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

to the set

A \times B

. Then:

Q. Let

X

be a set having

3

elements and

Y

be a set having

4

elements. If

α

is the number of one-one functions from

X

Y

and

β

is the number of onto functions from

Y

X,

then the value of

(β - α)

Q. Let

A

and

B

be two sets such that

n (A) = 6

and

n (B) = 3.

x

denotes the number of onto functions from

A

B

and

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then the value of

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One - One function

Standard XII Mathematics

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A function is defined from A to B, where number of elements in A and B are 2 and 6 respectively. If the total number of functions is x and total number of one one functions is y, then the value of x+y is

We have n(A)=2 and n(B)=6; So, total number of functions =62=36 Total number of one one functions =6×5=30 So, clearly the values of x and y are 36 and 30 respectively. Thus x+y=66

A function is defined from $A$ to $B,$ where number of elements in $A$ and $B$ are $2$ and $6$ respectively. If the total number of functions is $x$ and total number of one one functions is $y,$ then the value of $x + y$ is

We have $n (A) = 2$ and $n (B) = 6;$
So, total number of functions $= 6^{2} = 36$
Total number of one one functions $= 6 \times 5 = 30$
So, clearly the values of $x$ and $y$ are $36$ and $30$ respectively.
Thus $x + y = 66$