First slide

Binomial theorem for positive integral Index

Question

If $(1 + x)^{5} = a_{0} + a_{1} x + a_{2} x^{2} + a_{3} x^{3} + a_{4} x^{4} + a_{5} x^{5}$ , then the value of ${(a_{0} - a_{2} + a_{4})}^{2} + {(a_{1} - a_{3} + a_{5})}^{2}$ is equal to

Easy

A

243
B

32
C

1
D

2¹⁰

Solution

Put x = i
$\begin{array}{l} (1 + i)^{5} = (a_{0} - a_{2} + a_{4}) + i (a_{1} - a_{3} + a_{5}) \\ \Rightarrow | 1 + i |^{5} = |(a_{0} - a_{2} + a_{4}) + i (a_{1} - a_{3} + a_{5})| {z = x + i y, t h e n |z| = \sqrt{x^{2} + y^{2}}} \\ \Rightarrow {(a_{0} - a_{2} + a_{4})}^{2} + {(a_{1} - a_{3} + a_{5})}^{2} = 2^{5} = 32 \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App