Test Index

EAMCET Engineering 2005 Solved Paper

Section: Mathematics

© examsnet.com

Question : 89 of 160

Marks: +1, -0

The coefficient of

x^3 y^4 z^5

in the expansion of

(xy+yz+xz)^6

70
60
50
None of these

Solution:

We have

(xy+yz+zx)^6=\sum\limits_{r+s+t=6}\frac{6!}{r! s! t!}(xy)^r(yz)^s(zx)^t

=\sum\limits_{r+s+t=6}\frac{6!}{r! s! t!}x^{r+t}y^{r+s}z^{s+t}

If the general term in the above expansion. contains

x^3 y^4 z^5

, then

r+t=3, r+s=4 \text{ and } s+t=5

Also,

r+s+t=6

Solving these equations, we get

r=1, s=3, t=2

\therefore

Coefficient of

x^3 y^4 z^5=\;\frac{6!}{1!3!2!}=\;\frac{6!}{2!3!}=60

© examsnet.com

Go to Question:

Prev Question

Next Question