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If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,the...

If `(1+2x+x^2)^n=sum_(r=0)^(2n)a_r x^r` ,then `a_r ` is a.`(.^nC_2)^2` b. `.^n C_r .^n C_(r+1)` c. `.^(2n) C_r` d. `.^(2n) C_(r+1)`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Let (1+x^2)^2(1+x)^n=sum(k=0)^(n+4)ak x^k. If a1, a2 and a3 are in ari...

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  2. The middle term in the expansion of (x//2+2)^8 is 1120, then x in R i...

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  3. If (1+2x+x^2)^n=sum(r=0)^(2n)ar x^r ,then ar is a.(.^nC2)^2 b. .^n ...

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  4. [(^nC0+^n C3+)-1/2(^n C1+^n C2+^n C4+^n C5]^2 + 3/4(^n C1-^n C2+^n C4 ...

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  5. If sum(r=0)^(n)((r+2)/(r+1)).^n Cr=(2^8-1)/6 , then n is (A) 8 (B...

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  6. Let f(x)=a0+a1x+a2x^2+...+an x^n and (f(x))/(1-x)=b0+b1x+b2x^2+...+bn ...

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  7. If (1+x^(2))^(n) = underset(r=0)overset(n)suma(r)x^(r )= (1+x+x^(2)+x^...

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  8. The value of sum(r=1)^(n+1)(sum(k=1)^n "^k C(r-1))( where r ,k ,n in ...

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  9. If (x^2+x+1)/(1-x)=a0+a1x+a2x^2+ ,t h e nsum(r=1)^(50)ar is equal to 1...

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  10. Find dy/dt , if y = (1 - cost)/(1 + cost) is

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

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

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  13. If (1-x)^(-n)=a0+a1x+a2x^2+...+ar x^r+ ,t h e na0+a1+a2+...+ar is equa...

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  14. The value of sum(r=0)^(20)r(20-r)(.^(20) Cr)^2 is equal to a. 400^(...

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  15. The coefficient of x^(10) in the expansion of (1+x^2-x^3)^8 is 476 b. ...

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  16. If the term independent of x in the (sqrt(x)-k/(x^2))^(10) is 405, the...

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  17. The coefficient of x^2y^3 in the expansion of (1-x+y)^(20) is (20 !)/(...

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  18. The coefficient of x^5 in the expansion of (x^2-x-2)^5 is -83 b. -82 c...

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  19. The coefficient of a^8b^4c^9d^9 in (a b c+a b d+a c d+b c d)^(10) is...

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  20. If the coefficient of x^7in[a x^2-(1/(b x^2))]^(11) equal the coeffici...

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