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If the constant term in the binomial expansion of `(x^2-1/x)^n ,n in N` is 15, then the value of `n` is equal to.

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The correct Answer is:
6
`T_(r+1) = .^(n)C_(r)(x^(2))^(n-r)(-1)^(r ) x^(-r)`
`= .^(n)C_(r) x^(2n-3r)(-1)^(r)`
Constant term `= .^(n)C_(r)(-1)^(r)` if `2n = 3r`
i.e, coefficient of `x = 0`
Hence, `.^(n)C_(2pi//3)(-1)^(2n//3) = 15 = .^(6)C_(4)`
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CENGAGE-BINOMIAL THEOREM-Exercise (Numerical)
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  3. If the constant term in the binomial expansion of (x^2-1/x)^n ,n in N...

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  4. The largest value of x for which the fourth tem in the expansion (5^2/...

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  11. The total number of different terms in the product (.^(101)C(0) - .^(1...

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  12. The constant term in the expansion of (log(x^(logx))-log(x^(2))100)^...

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  13. The value of sum(r=0)^(3) ""^(8)C(r)(""^(5)C(r+1)-""^(4)C(r)) is "".

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  14. The sum of the series (.^(101)C(1))/(.^(101)C(0)) + (2..^(101)C(2))/...

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  15. Let a=3^(1/(223))+1 and for all geq3,l e tf(n)=^n C0dota^(n-1)-^n C1do...

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  18. If sum(r=0)^(n) ((r+2)/(r+1))""^(n)C(r)=(2^(8)-1)/(6).then n is equal ...

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  19. If S(n) = (.^(n)C(0))^(2) + (.^(n)C(1))^(2) + (.^(n)C(n))^(n), then ma...

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  20. The value of .^(40)C(0) xx .^(100)C(40) - .^(40)C(1) xx .^(99)C(40) + ...

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