Question

Assertion :In the expansion of ${(1+6x)}^8$ greatest coefficient will be ${{}^{8}C}_4{6}^4$ and Reason: Greatest coeeficeint in the expansion of ${(1+x)}^{2n}$ is of the middle term.

• A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
• B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
• C. Assertion is correct but Reason is incorrect
• D. Assertion is incorrect and Reason is correct

Answer 1

The correct option is A Both Assertion and Reason are correct and Reason is the correct explanation for Assertion

We know that "The greatest binomial coefficient is the binomial coefficient of the middle term."
In the expansion of $(1+x{)}^{2n}$, since $2n$ is even, so greatest term coefficient is ${}^{2n}Cn+1$.
Hence, reason is correct.
Assertion:
Given expansion is $(1+6x{)}^8$.
Here , $n=8\left(even\right)$
So, the greatest term coefficient is $T_5$.
$T_5{=}^8{C}_4(6x{)}^4$
So, the greatest coefficient is ${}^8{C}_4{6}^4$.