Binomial Theorem 1 Question 7

8. The sum of the coefficients of all even degree terms is x in the expansion of

(2019 Main, 8 April I)

(x+x31)6+(xx31)6,(x>1) is equal to

(a) 29

(b) 32

(c) 26

(d) 24

Show Answer

Answer:

Correct Answer: 8. (a=2,n=4)

Solution:

Key Idea Use formula :

(a+b)n+(ab)n=

2[nC0an+nC2an2b2+nC4an4b4+]

Given expression is (x+x31)6+(xx31)6

Missing \left or extra \right

=2[6C0x6+6C2x4(x31)+6C4x2(x31)2+6C6(x31)3]

The sum of the terms with even power of x

=2[6C0x6+6C2(x4)+6C4x8+6C4x2+6C6(13x6)]=2[6C0x66C2x4+6C4x8+6C4x213x6]

Now, the required sum of the coefficients of even powers of x in

(x+x31)6+(xx31)6=2[6C06C2+6C4+6C413]=2[115+15+1513]=2(153)=24



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