Question

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

• A. minimum value of $P=1$
• B. minimum value of $P=-1$
• C. maximum value of $P=3^n$
• D. maximum value of $P=2^n$

Answer 1

Answer: (A), (C)

The correct options are
A minimum value of $P=1$
C maximum value of $P=3^n$

​​​​​​Sum of coefficients in ${(1-x\sin \theta +x^2)}^n$ is $(1-\sin \theta +1{)}^n$
(putting $x=1)$ This sum is greatest when $\sin \theta =-1,$
Therefore maximum value of sum of coefficient will be $3^n$
And sum will be minimum when $\sin \theta =1$
Therefore minimum value will be $1$