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JEE MATHEMATICS MCQ: FUNCTIONS

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Application +4 | -1
Let A={x1,x2,………,x7}\mathrm{A}=\left\{x_{1}, x_{2}, \ldots \ldots \ldots, x_{7}\right\} and B={y1,y2,y3}\mathrm{B}=\left\{y_{1}, y_{2}, y_{3}\right\} be two sets containing seven and three distinct elements respectively. Then the total number of functions f:A→B\mathrm{f}: \mathrm{A} \rightarrow \mathrm{B} that are onto, if there exist exactly three elements xx in A such that f(x)=y2\mathrm{f}(x)=y_{2}, is equal to :
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Correct option: A
14.7C314 .{ }^{7} \mathrm{C}_{3}
The correct answer is A (14.*7C3) because it correctly counts the number of surjective functions with the given constraint.

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