Question

If `(1+x)^5=a_0+a_1x+a2x2+a_3x^3=a_4x^4+a_5x^5,` then the value of `(a_0-a_2+a_4)^2+(a_1-a_3+a_5)^2` is equal to `243` b. `32` c. `1` d. `2^(10)`
A. 243
B. 32
C. 1
D. `2^(10)`

Answer 1

Correct Answer - B
Put `x = i`
`(1+i)^(5) = (a_(0) - a_(2) + a_(4)) + i(a_(1)-a_(3)+a_(5))`
`rArr |1+i|^(5) = |(a_(0) - a_(2) + a_(4)) + i(a_(1) - a_(3) + a_(5))|`
`rArr (a_(0)-a_(2)+a_(4))^(2)+(a_(1)-a_(3)+a_(5))^(2)=2^(5) = 32`