If the third term in the expansion of ( x 1 + x l o g 10 x ) 5 is 1000 then x is equal to

T 3 = 5 C 2 x 3 1 ⋅ ( x l o g 10 x ) 2 = 10 x − 3 + 2 l o g 10 x = 1000 ∴ x − 3 + 2 l o g 10 x = 100 ⇒ x = 100 , 10 1

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremSpecific TermsMedium2 minQB

MathematicsMediummultiple choice

If the third term in the expansion of $(\frac{1}{x} + x^{l o g_{10} x})^{5}$ is 1000 then x is equal to

Options:(select one or more)

Answer:

A, D

Solution:

$T_{3} =^{5} C_{2} \frac{1}{x ^{3}} \cdot (x^{l o g_{10} x})^{2} = 10 x^{- 3 + 2 l o g_{10} x} = 1000$ $∴ x^{- 3 + 2 l o g_{10} x} = 100 \Rightarrow x = 100, \frac{1}{10}$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Specific Terms

⏱ 2mℹ️ Source: QB

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