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If (1+x-2x^2)^6=1+a1x+a2x^(2)++a(12)x^(1...

If `(1+x-2x^2)^6=1+a_1x+a_2x^(2)++a_(12)x^(12),` then find the value of `a_2+a_4+a_6++a_(12)dot`

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CENGAGE ENGLISH-BINOMIAL THEOREM-All Questions
  1. Find the middle term in the expansion of (x^2+1/(x^2)+2)^ndot

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  2. In the expansion of (1+x)^(50), find the sum of coefficients of odd po...

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  3. If (1+x-2x^2)^6=1+a1x+a2x^(2)++a(12)x^(12), then find the value of a2+...

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  4. If the middle term in the binomial expansion of (1/x+xsinx)^(10) is eq...

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  5. Find the sum C0+3C1+3^2C2++3^n Cndot

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  6. If (1+x)^n=sum(r=0)^n Cr x^r , then prove that C1+2C2+3C3+....+n Cn=n2...

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  7. If T0,T1, T2, ,Tn represent the terms in the expansion of (x+a)^n , t...

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  8. If (1+x+x^2)^n=a0+a1x+a2x^2++a(2n)x^(2n), find the value of a0+a3+a6+...

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  9. Find the sum C0-C2+C4-C6+ ......... ,where Cr=^n Cr .

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  10. Prove that ^n C0+^n C3+^n C6+=1/3(2^n+2cos((npi)/3)) .

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  11. Given that the 4th term in the expansion of [2+(3x//8)]^(10) has the m...

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  12. Find the greatest coefficient in the expansion of (1+2x//3)^(15)dot .

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  13. Find the greatest term in the expansion of sqrt(3)(1+1/(sqrt(3)))^(20)...

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  14. Find the numerically greatest term in the expansion of (3-5x)^(15)w h ...

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  15. Let n be an odd natural number greater than 1. Then , find the number...

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  16. Find the remainder when 27^(40) is divided by 12.

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  17. In the expansion of (1+x)^n , 7th and 8th terms are equal. Find the ...

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  18. Find the sum sum(j=0)^n( ^(4n+1)Cj+^(4n+1)C(2n-j)) .

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  19. Show that no three consecutive binomial coefficients can be in G.P.

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  20. Find the sum sum(r=1)^n r^n (^nCr)/(^nC(r-1)) .

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