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Question: Answered & Verified by Expert
In the expansion of $\left(x+\frac{2}{x^2}\right)^{15}$ the term independent of $x$ is
MathematicsBinomial TheoremJEE Main
Options:
  • A ${ }^{15} C_6 2^6$
  • B ${ }^{15} C_5 2^5$
  • C ${ }^{15} \mathrm{C}_4 2^4$
  • D ${ }^{15} C_8 2^8$
Solution:
1953 Upvotes Verified Answer
The correct answer is: ${ }^{15} C_5 2^5$
$(15-r)(1)+r(-2)=0 \Rightarrow 15-3 r=0 \Rightarrow r=5$
Thus term independent of x is $={ }^{15} C_5(1)^{10}(2)^5={ }^{15} C_5 2^5$

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