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If for z as real or complex . (1+z^(...

If for z as real or complex .
` (1+z^(2) + z^(4))^(8) = C_(0) C_(1) z^(2) C_(2) z^(4) + …+ C_(16) z^(32)` ,
prove that
`C_(0) + C_(3) + C_(6) + C_(9) + C_(12) + C_(15)`
` + (C_(2) + C_(5) + C_(8) + C_(11) + C_(14))`
` + (C_(1) + C_(4) + C_(7) + C_(10) + C_(16)) omega^(2) = 0 ` ,
where `omega` is a cube root of unity .

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If for z as real or complex,(1+z^(2)+z^(4))^(8)=C_(0)+C1z2+C2z4++C_(16)z^(32)then(a)C_(0)-C_(1)+C_(2)-C_(3)+C_(16)=1(b)C_(0)+C_(3)+C_(6)+C_(9)+C_(12)+C_(15)=3^(7)(c)C_(2)+C_(5)+C_(6)+C_(11)+C_(14)=3^(6)(d)C_(1)+C_(4)+C_(7)+C_(10)+C_(13)+C_(16)=3^(7)

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ARIHANT MATHS-BIONOMIAL THEOREM-Exercise (Subjective Type Questions)
  1. Determine the term independent of a in the expansion of ((a+1)/(a^(2/...

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  2. If in the expansion of (1+x)^n ,a ,b ,c are three consecutive coeffici...

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  3. Find n in the binomaial [ root (3)(2) + (1) /root(3)(3)]^(n) , if ...

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  4. if Sn = C0C1 + C1C2 +...+ C(n-1)Cn and S(n+1)/Sn = 15/4 then n is

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  5. C1/C0+2C2/C1+3C3/C2+............+nCn/C(n-1)=(n(n+1))/2

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  6. Find the term in (a/(sqrt(b))3+sqrt(b/(a3)))^(21) which has the same p...

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  7. The coefficient of x^r[0lt=rlt=(n-1)] in lthe expansion of (x+3)^(n-1)...

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  8. Prove that if p is a prime number greater than 2, then the difference ...

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  9. Integer just greater tehn (sqrt(3)+1)^(2n) is necessarily divisible by...

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  10. Solve the equation ""^(11)C(1) x^(10) - ""^(11)C(3) x^(8) + ""^(11)...

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  11. If (1 + x)^(n) = C(0) + C(1) x + C(2) x^(2) + …+ C(n) x^(n) , find th...

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  12. Evaluate sum(0 le i lne j le 10) ""^(21)C(i) * ""^(21)C(j).

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  13. Find the coefficient of x^4 in the expansion of (1+x+x^2+x^3)^(11)dot

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  14. Find the coefficients of x^(4) in the expansions of (2 - x + 3x^(2...

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  15. If for z as real or complex, (1+z^2+z^4)^8=C0+C1z2+C2z4++C(16)z^(32)t ...

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  16. If for z as real or complex . (1+z^(2) + z^(4))^(8) = C(0) C(1) z^...

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  17. Let f(x) = a(0) + a(1)x + a(2)x^(2) + …+ a(2n) x^(2n) and g(x) = b...

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  18. If a0,a1,a2,.... be the coefficients in the expansion of (1+x+x^2)^n ...

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  19. If a(0), a(1), a(2),… are the coefficients in the expansion of (1 ...

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  20. If a(0), a(1), a(2),… are the coefficients in the expansion of (1 ...

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