wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the expansion of (x31x2)n, nN, if the sum of the coefficients of x5 and x10 is 0, then n is

A
25
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
20
No worries! We‘ve got your back. Try BYJU‘S free classes today!
C
15
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
D
10
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is C 15
(x31x2)n
General term Tr+1=n!r!(nr)!(1)nrx5r2n
If 5r2n=5, then 5r=2n+5 or r=2n5+1

If 5r2n=10, then 5r=2n+10 or r=2n5+2
x5 and x10 terms occur if n=5k

Given, the sum of coefficients x5 and x10 is zero.
(5k)!(2k+1)!(3k1)!(5k)!(2k+2)!(3k2)!=0
or, 13k112k+2=0
or, k=3n=15

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
General Term
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon