wiz-icon
MyQuestionIcon
MyQuestionIcon
15
You visited us 15 times! Enjoying our articles? Unlock Full Access!
Question

If the ratio of the 5th term from the beginning to the 5th term from the end in the expansion of (42+143)n is 6:1, then the value of n is

A
12
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
10
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
8
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
14
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 10
The given expression may be written as (214+314)n.
The general term in this expansion is given by Tr+1= nCr×(214)(nr)×(314)r
Tr+1= nCr×2(nr)4×(314)r ...(1)
Now, pth term from the end
=(np+2)th term from the beginning.
5th term from the end
=(n5+2)th term from the beginning
=(n3)th term from the beginning

Now, T5=T4+1
= nC4×2(n4)4×3(44)
= nC4×2(n4)4×31 ...(2)
And, Tn3=T(n4)+1
= nCn4×21×3(n4)4
(putting r=(n4) in eqn (1))

= nC4×2×3(n4)4 ...(3)
[ nCnr= nCr]
T5Tn3=61
nC4×2n44×31 nC4×2×3(n4)4=61
2((n4)41) ×3(n441)=6
(2×3)(n8)4=612
(n8)4=12
n8=2n=10.
Hence, n=10.

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
Join BYJU'S Learning Program
CrossIcon