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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremIntegral and Fractional Part of a NumberHard2 minQB

MathematicsHardmultiple choice

Let $n \in N$ and $(33 + 5)^{2 n + 1} = α + β$ , where $α$ is an integer and $0 < β < 1$ . Which statements are correct?

Options:(select one or more)

Answer:

A, B

Solution:

Put $β = (33 - 5)^{2 n + 1}$ . The sum of the conjugate powers is an even integer, hence $α$ is even. Their product is $(27 - 25)^{2 n + 1} =$ $2^{2 n + 1}$ , so $(α + β) β = α β + β^{2} = 2^{2 n + 1}$ .

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Integral and Fractional Part of a Number

⏱ 2mℹ️ Source: QB

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