Question

(iii)To help Satish in his project, Rajat decides to form onto function from set A to

B. How many such functions are possible?

(a) 342 (b) 243 (c) 729 (d) 1024 pls check in meritnation website ​

Answer 1

Answer:

240

Step-by-step explanation:

Answer 2

Note: the question is incomplete, as it does not show the major information , the correct question is atteched below.

Solution:-

Know that, If A and B are two sets having m and n elements respectively such that$\[m \ge n\]$, then total no. of onto functions from set A to set B is $\[ = \sum\limits_{r = 0}^n {{{\left( { - 1} \right)}^r}{ \times ^n}{C_r} \times {{\left( {n - r} \right)}^m}} \]$

Understand that, $\[n\left( A \right) = 5,n\left( B \right) = 4\]$

Therefore, the number of onto functions from set A to set B is,

$\[ = \sum\limits_{r = 0}^4 {{{\left( { - 1} \right)}^r}{ \times ^4}{C_r} \times {{\left( {4 - r} \right)}^5}} \]$

$\[\begin{array}{l} = {\left( { - 1} \right)^0}{ \times ^4}{C_0} \times {\left( {4 - 0} \right)^5} + {\left( { - 1} \right)^1}{ \times ^4}{C_1} \times {\left( {4 - 1} \right)^5}\\\,\,\,\,\,\, + {\left( { - 1} \right)^2}{ \times ^4}{C_2} \times {\left( {4 - 2} \right)^5} + {\left( { - 1} \right)^3}{ \times ^4}{C_3} \times {\left( {4 - 3} \right)^5}\\\,\,\,\,\,\,\, + {\left( { - 1} \right)^4}{ \times ^4}{C_4} \times {\left( {4 - 4} \right)^5}\end{array}\]$

$\[\begin{array}{l} = 1 \times 1 \times {\left( 4 \right)^5} + \left( { - 1} \right) \times 4 \times {\left( 3 \right)^5} + 1 \times 6 \times {\left( 2 \right)^5}\\\,\,\,\,\, + \left( { - 1} \right) \times 4 \times 1 + 1 \times 1 \times 0\\ = 1024 - 972 + 192 - 4\\ = 240\end{array}\]$

Hence, the correct answer is option (b). i.e, 240.