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If (1+2x+x^(2))^(n) = underset(r=0)overs...

If `(1+2x+x^(2))^(n) = underset(r=0)overset(2n)suma_(r)x^(r)`, then `a_(r) = `

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CENGAGE PUBLICATION-BINOMIAL THEOREM-All Questions
  1. If x^m occurs in the expansion of (x+(1/x^2))^(2n) then the coefficien...

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

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

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

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

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

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

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

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  9. Find the 5th term of the GP. 5/2, 1, .....

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  10. The expression (x+((x^3-1)^(1/2))/2)^5+""(x-((x^3-1)^(1/2))/2)^5 is a ...

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  11. Find ((dy) /dx) of sin(cosx) is

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  12. In the binomial expansion of (a-b)^n,ngeq5, the sum of the 5th and 6t...

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  13. Coefficient of x^11 in the expansion of (1+x^2)^4(1+x^3)^7(1+x^4)^12 i...

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  14. Give the integers rgt1 , ngt2 and c0-efficients of (3r)^th and (r+2)^(...

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  15. Find the coefficient of x^4 in the expansion of (x//2-3//x^2)^(10)dot

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  16. If Cr stands for nCr, then the sum of the series (2(n/2)!(n/2)!)/(n...

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  17. If the sum 1+2+2^2+......+2^(n-1)is 255, then find the number of ter...

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  18. The coefficient of X^24in the expansion of (1+X^2 )^12(1+X^12)(1+X^24)

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  19. Find the sum of the GP 1+3+9+27+........ 12terms

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  20. The coefficient of x^(53) in the expansion of sum(m=0)^(100) ^100Cm(x-...

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