Set A has three elements and set B has four elements. The number …

MCQ

Set $A$ has three elements and set $B$ has four elements. The number of injections that can be defined from $A$ to $B$ is

A
144
B
12
✓
24
D
64

✓

Answer

Correct option: C.

(c) : Since $3<4$, injective functions from $A$ to $B$ are defined and the total number of such functions is
$
{ }^4 P_3=\frac{4 !}{(4-3) !}=4 \times 3 \times 2 \times 1=24 .
$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Relations and Functions→Relations and Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If the numbers appeared on the two throws of a fair six faced die are $\alpha$ and $\beta$, then the probability that $x ^{2}+\alpha x+\beta>0$, for all $x \in R$, is.

→

If $\text{y}=\Big(1+\frac{1}{\text{x}}\Big)^\text{x},$ then $\frac{\text{dy}}{\text{dx}}=$

$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big(\text{x}+\frac{1}{\text{x}}\Big)-\frac{1}{\text{x}+1}$
$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\log\Big(1+\frac{1}{\text{x}}\Big)$
$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big\{\log(\text{x}+1)-\frac{\text{x}}{\text{x}+1}\Big\}$
$\Big(1+\frac{1}{\text{x}}\Big)^\text{x}\Big\{\log\Big(\text{x}+\frac{1}{\text{x}}\Big)-\frac{1}{\text{x}+1}\Big\}$

→

Let $f(x)=\sin ^{-1} x$ and $g(x)=\frac{x^{2}-x-2}{2 x^{2}-x-6} .$ If $g(2)=\lim _{x \rightarrow 2} g(x)$, then the domain of the function $fog$ is .... .

→

4 numbers are taken from 1, 2, 3, 4, 5, 6, 7. Probability of getting sum of 4 numbers is less than 12 .

→

Let $f$ be a function such that $f(x)\, = \,\sum\limits_{n\, - \,1}^n {\left[ {r\, + \,\cos \frac{x}{r}} \right]} $ where [.] denotes greatest integer function and $x \in [0,\pi]$, then range of $f(x)$ is-

→

The value of the determinant $\begin{vmatrix}\text{a}-\text{b}&\text{b}+\text{c}&\text{c}\\\text{b}-\text{c}&\text{c}+\text{b}&\text{b}\\\text{c}+\text{a}&\text{a}+\text{b}&\text{c}\end{vmatrix}$ is: