| Directions : (11 - 15) |
| An organization conducted bike race under 2 different categories-boys and girls. Totally there were 250 participants. Among all of them finally three from Category 1 and two from Category 2 were selected for the final race. Ravi forms two sets B and G with these participants for his college project. |
| Let \[B=\left\{ {{b}_{1}},\,{{b}_{2}},\,{{b}_{3}} \right\}\] \[G=\left\{ {{g}_{1}},\,{{g}_{2}} \right\}\] where B represents the set of boys selected and G the set of girls who were selected for the final race. |
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| Ravi decides to explore these sets for various types of relations and functions |
A) \[{{2}^{6}}\]
B) \[{{2}^{5}}\]
C) 0
D) \[{{2}^{3}}\]
Correct Answer: A
Solution :
\[B=\left\{ {{b}_{1}},\,{{b}_{2}},\,{{b}_{3}} \right\},\,G=\left\{ {{g}_{1}},\,{{g}_{2}} \right\}\] Number of relations from B to G \[={{2}^{n\left( B \right)\times n\left( G \right)}}={{2}^{3\times 2}}={{2}^{6}}\]
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