The number of real negative terms in binomial expansion of $(1 + i x)^{4 n - 2}, n \in N, x > 0$ is:

n

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

n + 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

n - 1

No worries! We‘ve got your back. Try BYJU‘S free classes today!

2 n

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $n$
At first we write the genral term
$T_{r + 1}$ = $^{4 n - 2} C_{r} . {ι . x}^{r}$
We know that $ι^{x}$ is real x=4m where m is an integer
and here r=0, 1, 2 ,3..............................,4n, 4n-1 ,4n-2 ,4n-3
So there are n integers 0, 4, 8.....................,4n of form x=4m
hence there are n real number in expansion

Suggest Corrections

Similar questions

Q. The number of real negative terms in the binomial expansion of

{(1 + i x)}^{4 n + 2}

n \in N, x > 0

, where

i = \sqrt{- 1}

, is-

Q. The number of real negative terms in the bionomial expansion of

(1 + i x)^{4 n - 2}, n \in N, x > 0

Q. The number of real negative terms in the binomial expansion of

{(1 + i x)}^{4 n - 2},

n ϵ N,

x > 0,

Q. The total number of terms which are dependent on the value of

x

, in the expansion

{(x^{2} - 2 + \frac{1}{x^{2}})}^{n}, n \in N

is equal to

Prove that the coefficient of $x^{n}$ in the binomial expansion of $(1 + x)^{2 n}$ is twice the coefficient of $x^{n}$ in the binomial expansion of $(1 + x)^{2 n - 1}$ .

Join BYJU'S Learning Program

The number of real negative terms in binomial expansion of (1+ix)4n−2,n∈N,x>0 is:

The number of real negative terms in binomial expansion of $(1 + i x)^{4 n - 2}, n \in N, x > 0$ is: