Question

Maximum sum of the coefficients in the expansion of $(1-x\sin \theta +x^2{)}^n$ is

• A. $1$
• B. $2^n$
• C. $3^n$
• D. $0$

Answer 1

The correct option is C $3^n$

${(1-x\sin \theta +x^2)}^n$

We can get the sum of the coefficient by directly taking $x=1$ in the above expression.

$\Rightarrow S={(1-\sin \theta +1)}^n$

$={(2-\sin \theta )}^n$

$-1\le \sin \theta \le 1$

$\Rightarrow$ Minimum value of $\sin \theta =-1$

$\therefore$ $S_{max}={(2-(-1\left)\right)}^n$

$=3^n.$

Hence, the answer is $3^n.$