If the term independent of x in the expansion of ( x + x 2 k ) 10 is 405, then a value of k may be

The term independent of x in ( x + x 2 k ) 10 Is 10 C 2 ( x ) 8 ⋅ ( x 2 k ) 2 = 405 ⇒ 45 k 2 = 405 ⇒ k 2 = 9 ⇒ k = ± 3

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Mathematics - Binomial Theorem Question with Solution | TestHub

MathematicsBinomial TheoremSpecific TermsMedium2 minQB

MathematicsMediummultiple choice

If the term independent of x in the expansion of $(x + \frac{k}{x ^{2}})^{10}$ is 405, then a value of k may be

Options:(select one or more)

Answer:

A, B

Solution:

The term independent of x in $(x + \frac{k}{x ^{2}})^{10}$ Is $^{10} C_{2} (x)^{8} \cdot (\frac{k}{x ^{2}})^{2} = 405$ $\Rightarrow 45 k^{2} = 405 \Rightarrow k^{2} = 9 \Rightarrow k = \pm 3$

Stream:JEESubject:MathematicsTopic:Binomial TheoremSubtopic:Specific Terms

⏱ 2mℹ️ Source: QB

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