If n is the number of irrational terms in the expansion of (3¹/? + 5¹/?)??, then (n - 1) is divisible by:
If n is the number of irrational terms in the expansion of (3¹/? + 5¹/?)??, then (n - 1) is divisible by:
Option 1 -
7
Option 2 -
30
Option 3 -
8
Option 4 -
26
-
1 Answer
-
Correct Option - 2
Detailed Solution:(3¹/? + 5¹/? )?
General term =? C? (3¹/? )? (5¹/? )? =? C? 3^ (60-r)/4) 5^ (r/8)
Terms are rational for r being a multiple of 8 and (60-r) being a multiple of 4.
If r is a multiple of 8, then 60-r is 60 - 8k. Since 60 is a multiple of 4, 60-8k is also a multiple of 4.
So, we just need r to be a multiple of 8.
r = 0, 8, 16, 24, 32, 40, 48, 56. (Total 8 rational terms)
Total terms are 61.
Number of irrational terms = 61 - 8 = 53 = n.
∴ n - 1 = 52.
Taking an Exam? Selecting a College?
Get authentic answers from experts, students and alumni that you won't find anywhere else
Sign Up on ShikshaOn Shiksha, get access to
- 65k Colleges
- 1.2k Exams
- 688k Reviews
- 1800k Answers