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If (x+1/x+1)^(6)=a(0)+(a(1)x+(b(1))/(x))...

If `(x+1/x+1)^(6)=a_(0)+(a_(1)x+(b_(1))/(x))+(a_(2)x^(2)+(b_(2))/(x^(2)))+"...."+(a_(6)x^(6)+(b_(6))/(x^(6)))`, then find the value of `a_0`

A

121

B

131

C

141

D

151

Text Solution

Verified by Experts

The correct Answer is:
c
`because (x+1/x+1)^(6) = sum_(r=0)^(6) ""^(6)C_(r) (x+1/x)^(r)` for constant term r
must be even integer.
`therefore a_(0) = ""^(6)C_(0) + ""^(6) C_(2) xx^(2) C_(1) +""^(6)C_(4)xx^(4) C_(2) +""^(6) C_(6) xx""^(6)C_(3)`
`= 1 + 30 + 90 + 20 =141`
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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Questions Asked In Previous 13 Years Exam)
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  4. If the coefficient of x^(7)in [ax^(2) + (1/bx)]^(11) equals the coeffi...

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  5. For natural numbers m ,n ,if(1-y)^m(1+y)^n=1+a1y+a2y^2+... , and a1=a2...

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  6. In the binomial expansion of (a - b)^n , n ge 5 the sum of the 5th ...

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  7. The sum of series .^(20)C0-^(20)C1+^(20)C2-^(20)C3+....+^(20)C 10 is

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  8. Statement-1: sum(r =0)^(n) (r +1)""^(n)C(r) = (n +2) 2^(n-1) Stat...

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  10. For r = 0, 1,"…..",10, let A(r),B(r), and C(r) denote, respectively, t...

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  11. Let S(1) = sum(j=1)^(10) j(j-1).""^(10)C(j), S(2) = sum(j=1)^(10)j."...

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  12. Find the coefficient of x^7 in the expansion of (1 - x -x^2 + x^3)^(6)...

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  13. If n is a positive integer, then (sqrt(3)+1)^(2n)-(sqrt(3)-1)^(2n) is

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  14. The term independent of x in expansion of ((x+1)/(x^(2/3)-x^(1/3)+1)-(...

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  15. The coefficients of three consecutive terms of (1+x)^(n+5) are in the ...

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  16. If the coefficient of x^(3) and x^(4) in the expansion of (1+ax+bx^(2)...

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  17. Coefficient of x^(11) in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^(1...

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  18. The sum of coefficient of integral powers of x in the binomial expansi...

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  19. The coefficient of x^9 in the expansion of (1+x)(16 x^2)(1+x^3)(1+x^(1...

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  20. If the number of terms in the expansion of (1-2/x+4/(x^(2)))^n x ne 0,...

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  21. Let m be the smallest positive integer such that the coefficient of x^...

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