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Given (1-2x+5x^2-10x^3)(1+x)^n=1+a1x+a2x...

Given `(1-2x+5x^2-10x^3)(1+x)^n=1+a_1x+a_2x^2+....` and that `a_1^2=2a_2`, then the value of n is

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. The number of values in set of values of r for which ""^23 Cr+2 ""^(2...

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  2. If the second term of the expansion [a^(1/13)+(a/sqrt(a^(-1))] is 14a^...

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  3. Given (1-2x+5x^2-10x^3)(1+x)^n=1+a1x+a2x^2+.... and that a1^2=2a2, the...

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  4. If A+B=90^oand tanA= 4/3 ​ ,find cosecB.

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  5. If X−k divides x^3−6x^2 +11x−6=0, then k can't be equal to, (a) 1. (b...

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  6. Prove that sum(r=1)^(k) (-3)^(r-1) (3n)^C(2r-1) = 0 , where k = 3n//2...

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  7. The coefficient of the middle term in the binomial expansion in powers...

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  8. The coefficient of three consecutive terms in the expansion of (1+x)^n...

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  9. The sum of G. P 3, 6, 12,... 1536.

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  10. Prove that (25)^(n+1)-24n+5735 is divisible by (24)^2 for all n=1,2,.....

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  11. The coefficient of 1//x in the expansion of (1+x)^n(1+1//x)^n is (a).(...

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  12. Find the coefficient of x^5 in the expansion of (1+x)^21+(1+x)^22+...+...

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  13. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

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  14. If the coefficients of 5^(th), 6^(th) and 7^(th) terms in the expansio...

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  15. If (1+2x+x^(2))^(n) = underset(r=0)overset(2n)suma(r)x^(r), then a(r) ...

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  16. In the expansion of (x^3-1/(x^2))^n ,n in N , if the sum of the coeff...

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  17. If the coefficients of rth and (r+1)t h terms in the expansion of (3+7...

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  18. In the expansion of (1+3x+2x^(2))^(6), find the coefficient of x^(11).

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  19. If .^(n-1)Cr=(k^2-3)^nC(r+1), then k belongs to (a) (-oo,-2] (b) [2,...

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  20. Prove that (3!)/(2(n+3))=sum(r=0)^n(-1)^r((n Cr)/((r+3)C3))

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