Question

The number of real negative terms in the binomial expansion of `(1+i x)^(4n-2),n in N ,x >0` is
A. n
B. n+1
C. n-1
D. 2n

Answer 1

Correct Answer - A
`T_(r+1) = .^(4n-2)C_(r)("ix")^(r )`
`T_(r+1)` is negative, if `i^(r)` is negative and real.
`i^(r ) = - 1`
`rArr r = 2, 6, 10,"……"` which form an `A.P.`
`0 le r le 4n - 2`
`4n - 2 = 2 + (r-1)4`
`rArr r = n`
The required number of terms is n.