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If the middle term of the expansion of `(x^3/3+3/x)^8` is `5670` then sum of all real values of `x` is equal to (A) `6` (B) `3` (C) `0` (D) `2`

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The correct Answer is:
C
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ALLEN-Solutions of Triangle & Binomial Theorem-EXERCISE (J-M)
  1. The sum of coefficients in integral powers of x in the binominal expan...

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  2. The value of (.^(21)C(1) - .^(10)C(1)) + (.^(21)C(2) - .^(10)C(2)) + (...

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  3. The sum of the co-efficients of all odd degree terms in the expansion ...

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  4. If the fractional part of the number (2^(403))/(15) is (k)/(15), then ...

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  5. The coefficient of t^4 in ((1-t^6)/(1-t))^3 (a) 18 (b) 12 ...

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  6. The positive value of lambda for which the coefficient of x^(2) in the...

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  7. If Sigma(r=0)^(25) { ""^(50)Cr.""^(50-r)C(25-r)}=K(""^(50)C(25)) then...

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  8. If the middle term of the expansion of (x^3/3+3/x)^8 is 5670 then sum ...

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  9. The value of r for which .^(20)C(r ), .^(20)C(r - 1) .^(20)C(1) + .^...

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  10. Let (x + 10)^(50) + (x - 10)^(50) = a(0) + a(1) x + a(2)X^(2) + ….. +...

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  11. Let Sn=1+q+q^2 +?+q^n and Tn =1+((q+1)/2)+((q+1)/2)^2+?+((q+1)/2)^n If...

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  12. A ratio of the 5^(th) term from the beginning and from the end in the...

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  13. The number of irrational terms in expansion (7^(1/5)-3^(1/10))^60 is ...

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  14. The sum of the series 2.""^(20)C0+5.""^(20)C1+8.""^(20)C2+11.""^(20)C(...

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  15. If some three consecutive coefficeints in the binomial expanison of (x...

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  16. If the coefficients of x^(2) and x^(3)are both zero, in the expansion ...

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  17. The smallest natural number n, such that the coefficient of x in the e...

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  18. The cofficient of x^(18) in the product (1 + x) (1 - x)^(1) (1 + x + x...

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  19. If .^(20)C(1)+(2^(2)) .^(20)C(2) + (3^(2)).^(20)C(3) +......+(20^(2))....

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  20. The term independent of x in the expansion of ((1)/(60) - (x^(8))/(81)...

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