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1. relation and function — Maths STD 12 Science — Question

Gujarat BoardEnglish MediumSTD 12 ScienceMaths1. relation and function1 Mark
MCQ
Let $A = \{ {x_1},\,{x_2},\,............,{x_7}\} $ and $B = \{ {y_1},\,{y_2},\,{y_3}\} $ be two sets containing seven and three distinct elements respectively. Then the total number of functions $f : A \to B$ that are onto, if there exist exactly three elements $x$ in $A$ such that $f(x)\, = y_2$, is equal to
  • ✓
    $14.{}^7{C_3}$
  • B
    $16.{}^7{C_3}$
  • C
    $14.{}^7{C_2}$
  • D
    $12.{}^7{C_2}$
✓

Answer

Correct option: A.
$14.{}^7{C_3}$
a
Number of onto function such that exactly three elements in $x \in A$ such that $f\left( x \right) = \frac{1}{2}$ is

equal to $ = {\,^7}{C_3},\left\{ {{2^4} - 2} \right\} = 14.{\,^7}{C_3}$

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