Published by:
CGP EDU Academic Team
Published on: August 13, 2026
The ninth term in the expansion of
is equal to 180, then x is
Text Solution
Verified by ExpertsThe correct answer is:
B
We have,
= 
{ 
= N}
Here, T 9 = 180.
⇒ 10 C 8 
{(5 x–1 + 1) –1/8 } 8 = 180
⇒ 10 C 8 (25 x–1 + 7) (5 x–1 + 1) –1 = 180
⇒ 45 
= 180
⇒ 
= 4
⇒ 
= 4, where y = 5 x–1 ⇒ y
2 – 4y + 3 = 0
⇒ y = 3, 1
⇒ 5 x–1 = 3 or 5 x–1 = 1
⇒ 5 x = 15 or 5 x = 5
⇒ x = log 5 15 or x = 1
Hence is correct answer.
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