Binomial Theorem 1 Question 14

15.

The sum of the coefficients of all odd degree terms in the expansion of (x+x31)5+(xx31)5,(x>1) is

(a) -1

(b) 0

(c) 1

(d) 2

(2018 Main)

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Answer:

Correct Answer: 15. (d)

Solution:

Key Idea Use formula :

=(a+b)n+(ab)n=2(nC0an+nC2an2b2+nC4an4b4+)

We have, (x+x31)5+(xx31)5,x>1

=2(5C0x5+5C2x3(x31)2+5C4x(x31)4)

=2(x5+10x3(x31)+5x(x31)2)

=2(x5+10x610x3+5x710x4+5x)

Sum of coefficients of all odd degree terms is

2(110+5+5)=2



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