$ A $ is a set having $ 6 $ distinct elements. The number of distinct functions from $ A $ to $ A $ which are not bijections is

  • A
    $ 6 ! - 6 $
  • B
    $ 6^{6} - 6 $
  • C
    $ 6^{6} - 6 ! $
  • D
    $ 6 ! $

Explore More

Similar Questions

For equality of functions $f$ and $g$,which of the following conditions must be satisfied?
$(i)$ $\text{domain of } f = \text{domain of } g$
(ii) $f(x) = g(x)$ for all $x$ in the domain
(iii) $x \in \text{domain of } f$

If $f(x)=2\{x\}+5x$,where $\{x\}$ is the fractional part function,then $f(-1.4)$ is

Let the function $f(x) = x^2 + x + \sin x - \cos x + \log(1 + |x|)$ be defined over the interval $[0, 1]$. The odd extension of $f(x)$ to the interval $[-1, 1]$ is:

Difficult
View Solution

Match the items of List-$I$ with those of the items of List-$II$:
List-$I$ List-$II$
$A$. Range of $\sec ^{-1}\left[1+\cos ^2 x\right]$,where $[.]$ denotes the greatest integer function $I$. Odd function
$B$. Domain of $f(x)$ where $f\left(x+\frac{1}{x}\right)=x^2+\frac{1}{x^2}$ $II$. $\left\{0, \frac{1}{2}\right\}$
$C$. $f(x+y)=f(x)+f(y) ; f(1)=5$ $III$. $\left\{\sec ^{-1} 5, \sec ^{-1} 4\right\}$
$D$. $\sin ^{-1} x-\cos ^{-1} x+\sin ^{-1}(1-x)=0 \Rightarrow x \in$ $IV$. $R$
$V$. $\left\{\sec ^{-1} 1, \sec ^{-1} 2\right\}$

For some $a, b, c \in N$,let $f(x)=ax-3$ and $g(x)=x^b+c$,$x \in R$. If $(fog)^{-1}(x)=\left(\frac{x-7}{2}\right)^{1/3}$,then $(fog)(ac) + (gof)(b)$ is equal to $..........$

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial
For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free
For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo