Set A has 3 elements and set B has 4 elements. number of injection that can be defined from A to B i

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1.Relation and Function

easy

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injection that can be defined from $A$ to $B$ is

$144$

$12$

$24$

$64$

Solution

(c) The total number of injective functions from a set $A$ containing $3$ elements to a set $B$ containing $4$ elements is equal to the total number of arrangements of $4$ by taking $3$ at a time $i.e.,$ $^4{P_3} = 24$.

Standard 12

Mathematics

Let $f(x)=\frac{x-1}{x+1}, x \in R-\{0,-1,1)$. If $f^{n+1}(x)=f\left(f^{n}(x)\right)$ for all $n \in N$, then $f^{6}(6)+f^{7}(7)=$

hard

(JEE MAIN-2022)

Let for $a \ne {a_1} \ne 0,$ $f\left( x \right) = a{x^2} + bx + c\;,g\left( x \right) = {a_1}{x^2} + {b_1}x + {c_1},p\left( x \right) = f\left( x \right) – g\left( x \right),$ If $p\left( x \right) = 0$ only for $ x=-1 $ and $p\left( { – 2} \right) = 2$ then value of $p\left( 2 \right)$ is

hard

(AIEEE-2011)

If function $f : R \to S, f(x) = (\sin x -\sqrt 3 \cos x+1)$ is onto, then $S$ is equal to

normal

Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then Domain of $f (x)$ is

normal

Let $f$ be a real valued function defined by

$f(x) = sin^{-1} \left( {\frac{{\,\,1 – \,\,\left| x \right|}}{3}} \right) + cos^{-1}\left( {\frac{{\left| x \right|\,\, – \,\,3}}{5}} \right)$ .

Then domain of $f(x)$ is given by :

normal

Set $A$ has $3$ elements and set $B$ has $4$ elements. The number of injection that can be defined from $A$ to $B$ is

Solution

Similar Questions

Let $f(x)=\frac{x-1}{x+1}, x \in R-\{0,-1,1)$. If $f^{n+1}(x)=f\left(f^{n}(x)\right)$ for all $n \in N$, then $f^{6}(6)+f^{7}(7)=$

Let for $a \ne {a_1} \ne 0,$ $f\left( x \right) = a{x^2} + bx + c\;,g\left( x \right) = {a_1}{x^2} + {b_1}x + {c_1},p\left( x \right) = f\left( x \right) – g\left( x \right),$ If $p\left( x \right) = 0$ only for $ x=-1 $ and $p\left( { – 2} \right) = 2$ then value of $p\left( 2 \right)$ is

If function $f : R \to S, f(x) = (\sin x -\sqrt 3 \cos x+1)$ is onto, then $S$ is equal to

Function $f(x)={\left( {1 + \frac{1}{x}} \right)^x}$ then Domain of $f (x)$ is

Let $f$ be a real valued function defined by $f(x) = sin^{-1} \left( {\frac{{\,\,1 – \,\,\left| x \right|}}{3}} \right) + cos^{-1}\left( {\frac{{\left| x \right|\,\, – \,\,3}}{5}} \right)$ . Then domain of $f(x)$ is given by :

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Let $f$ be a real valued function defined by

$f(x) = sin^{-1} \left( {\frac{{\,\,1 – \,\,\left| x \right|}}{3}} \right) + cos^{-1}\left( {\frac{{\left| x \right|\,\, – \,\,3}}{5}} \right)$ .

Then domain of $f(x)$ is given by :