JEE Main On 08 April 2018 Question 15
Question: The sum of the co-efficient of all odd degree terms in the expansion of $ {{( x+\sqrt{x^{3}-1} )}^{5}}+{{( x-\sqrt{x^{3}-1} )}^{5}},(x>1) $ is: [JEE Main Online 08-04-2018]
Options:
A) 1
B) 2
C) -1
D) 0
Show Answer
Answer:
Correct Answer: B
Solution:
$ [ ^{5}C _0x^{5}{{+}^{5}}C _2x^{3}(x^{3}-1){{+}^{5}}C _4x^{1}{{(x^{3}-1)}^{2}} ] $
$ =2[ ^{5}C _0{{-}^{5}}C _2{{+}^{5}}C _4 ] $
$ =2[ \underbrace{1+10} _{{}}-10 ] $ $ =2 $
