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CBSE Class 12 Math 2023 Delhi Set 1 Solved Paper

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Question : 36 of 38
Marks: +1, -0
Case Study-I
An organization conducted bike race under two different categories - Boys and Girls. There were 28 participants in all. 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={b1,b2,b3}B= \{b_1, b_2, b_3\} and G={g1,g2}G= \{g_1, g_2\}, where BB represents the set of Boys selected and GG the set of Girls selected for the final race.
Based on the above information, answer the following questions:
(I) How many relations are possible from BB to GG ?
(II) Among all the possible relations from BB to GG, how many functions can be formed from BB to GG ?
(III) Let R:B→BR: B \rightarrow B be defined by R={(x,y):xR = \{(x, y): x and yy are students of the same sex }\}. Check if RR is an equivalence relation.
OR
(III) A function f:B→Gf: B \rightarrow G be defined by f={(b1,g1),(b2,g2),(b3,g1)}f = \{(b_1, g_1), (b_2, g_2), (b_3, g_1)\}.
Check if ff is bijective. Justify your answer.
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