First slide

Binomial theorem for positive integral Index

Question

The coefficients of $x^{2} y^{2}, {yzt}^{2}$ and xyzt in the expansion of (r + y + z + t)⁴ are in the ratio

Moderate

A

4:2:1
B

1:2:4
C

2:4:1
D

1:4:2

Solution

Coefficient of $x^{2} y^{2} in (x + y + z + t)^{4} = \frac{4!}{2! 2!} = 6$ and
coefficient of ${yzt}^{2} in (x + y + z + t)^{4} = \frac{4!}{1! 1! 1! 2!} = 12$
AIso, coefficient of xyzt in $(x + y + z + t)^{4} = \frac{4!}{111! 11!} = 24$
.'. Required ratio is 6 :12:24 = 1:2:4

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