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MathsHardMCQ2024 ยท 01 Feb Shift 1

Q81.Let ๐‘ƒ= ๐‘งโˆˆโ„‚: ๐‘ง+ 2 โˆ’3๐‘–โ‰ค1 and ๐‘„= ๐‘งโˆˆโ„‚: ๐‘ง1 + ๐‘–+ ยฏ๐‘ง1 โˆ’๐‘–โ‰คโˆ’8. Let in ๐‘ƒโˆฉ๐‘„, ๐‘งโˆ’3 + 2๐‘– be maximum and minimum at ๐‘ง1 and ๐‘ง2 respectively. If ๐‘ง12 + 2๐‘ง2 = ๐›ผ+ ๐›ฝโˆš2, where ๐›ผ, ๐›ฝ are integers, then ๐›ผ+ ๐›ฝ equals __________

What This Question Tests

This problem is a classic application of Bayes' Theorem, requiring the setup of different hypotheses for the composition of balls in the bag and calculating conditional probabilities using combinations.

Concepts Tested

Conditional probabilityBayes' TheoremCombinations (nCr)Total probability

Formulas Used

P(A|B) = P(B|A)P(A) / P(B)

P(B) = ฮฃ P(B|A_i)P(A_i)

nCr = n! / (r!(n-r)!)

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๐Ÿ“‹ Question Details

Chapter
Probability
Topic
Conditional probability (Bayes' Theorem)
Year
2024
Shift
01 Feb Shift 1
Q Number
Q81
Type
MCQ
NCERT Ref
Class 12 Mathematics Ch 13: Probability

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