Question

Match the Elements of List 1 with Elements of List 2:

$1)$ The number of relations from $A=\{1,3,5\}$ to $B=\{a,b,c\}$ is	$a)$ 15
$2)$ The number of constant functions that can be defined from $R$ to $A=\{0,2,4,6,8,..,28\}$	$b)$ 6
$3)$ The number of one-one functions from $A$ to $A$ is $720$, then $n\left(A\right)$	$c)$ 512
$4)$ The number of identity functions on the set $A=\{1,2,3,4,5,6\}$	$d)$ 1
	e) 14

Then the correct order for $1,2,3,4$ is:

• A. $c,e,a,d$
• B. $c,a,e,d$
• C. $c,a,b,d$
• D. $c,e,a,b$

Answer 1

The correct option is C $c,a,b,d$

$1)$ No. of relations from A to B $=2^{mn}$
$=2^{3\times 3}$
$=512\to c$
$2)$ No. of constant functions from $R$ to $A$ is number of elements in $A$ i.e.$15\to a$
$3)$ Let number of elements in $A=n$
So one - one functions from $A$ to $A$ is $n!$
& $n!=720$
$\therefore n=6\to b$
$4)$ Identity function $f\left(x\right)=x$
So there will be only one function.$\to d$