Question

Assertion :If the sum of the Coefficients in the expansion of ${(x-2y+3z)}^n=128$ then greatest coefficient in the expansion ${(1+x)}^n$ is $35$. Reason: If 'n' is odd then in the expansion of ${(1+x)}^n$, the greatest coefficients are $\frac{{}^n{C}_{n-1}}{2}$ & $\frac{{}^n{C}_{n+1}}{2}$.

• A. Both Assertion & Reason are individually true & Reason is correct explanation of Assertion,
• B. Both Assertion & Reason are individually true but Reason is not the correct (proper) explanation of Assertion,
• C. Assertion is true but Reason is false,
• D. Assertion is false but Reason is true.

Answer 1

The correct option is A Both Assertion & Reason are individually true & Reason is correct explanation of Assertion,

For the sum of the coefficients, we substitute, $x=y=z=1.$
Hence, we get
$(2{)}^n=128$
$2^n=2^7$
$n=7$
$(1+x{)}^7$
The greatest coefficients will be of the terms
$T_4$ and $T_5$
$T_4={}^7{C}_3{x}^3$
$=35x^3$
$T_5={}^7{C}_4{x}^4$
$=35x^4$
Hence largest coefficient is $35.$