Question

Assertion (A) : Greatest binomial coefficient in the expansion of $(1+5x{)}^8$ is ${}^8{C}_4{5}^4$

Reason (R) : Greatest coefficient in the expansion of $(1+x{)}^{2n}$ is the middle term

• A. Both A and R are individually true and R is the correct explanation of A.
• B. Both A and R are individually true and R is not correct explanation of A.
• C. A is true but R is false
• D. A is false but R is true

Answer 1

The correct option is D A is false but R is true

The greatest binomial coefficient is the middle term in the expansion. This is true for any binomial expansion.
Hence Greatest binomial coefficient in the expansion of $(1+5x){}^8$ is of the middle term
${}^8{C}_4\left(5x\right){}^4$ the coefficient being ${}^8{C}_4$
Similarly for $(1+x){}^{2n}$ the middle term is $={}^{2n}{C}_n{x}^n$ and the greatest coefficient is $={}^{2n}{C}_n$