Join the Most Relevant JEE Main 2025 Test Series & get 99+ percentile! Join Now
Search any question & find its solution
Question: Answered & Verified by Expert
If the third term in the binomial expansion of $(1+x)^m$ is $-\frac{1}{8} x^2$, then the rational value of $m$ is
MathematicsBinomial TheoremJEE Main
Options:
  • A $2$
  • B $1/2$
  • C $3$
  • D $4$
Solution:
2210 Upvotes Verified Answer
The correct answer is: $1/2$
We have $(1+x)^m=1+m x+\frac{m(m-1)}{2!} x^2+\ldots$
By hypothesis, $\frac{m(m-1)}{2} x^2=-\frac{1}{8} x^2$
$\Rightarrow 4 m^2-4 m=-1 \Rightarrow(2 m-1)^2=0 \Rightarrow m=\frac{1}{2}$

Looking for more such questions to practice?

Download the MARKS App - The ultimate prep app for IIT JEE & NEET with chapter-wise PYQs, revision notes, formula sheets, custom tests & much more.