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[(^n C0+^n C3+)1//2(^n C1+^n C2+^n C4+^n...

`[(^n C_0+^n C_3+)1//2(^n C_1+^n C_2+^n C_4+^n C_5]^2+3//4(^n C_1-^n C_2+^n C_4-^n C_5+)^2=` `3` b. `4` c. `2` d. `1`

A

3

B

4

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
D
`(1+omega)^(n) = .^(n)C_(0) + .^(n)C_(1) +omega+"....."`
`= (.^(n)C_(0)+.^(n)C_(3) +"....")+(.^(n)C_(1)+.^(n)C_(4)+".....")((-1+sqrt(3)i)/(2))+(.^(n)C_(2)+.^(n)C_(5)+"....")((-1-sqrt(3)t)/(2))`
`= (.^(n)C_(0) + .^(n)C_(3) + "....") -1/2 (.^(n)C_(1) + .^(n)C_(2) + .^(n)C_(4) + .^(n)C_(5)".....")+(isqrt(3))/(2)(.^(n)C_(1)-.^(n)C_(2)+.^(n)C_(4)-.^(n)C_(5) + "....")`
Equating the modulus, we get `|(-omega^(2))^(n)| = 1`.
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CENGAGE-BINOMIAL THEOREM-Exercise (Single)
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  11. If a, b and c are three consecutive coefficients terms in the expansio...

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  14. The value of sum(r=1)^(n) (-1)^(r+1)(""^(n)C(r))/(r+1) is equal to

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  17. The value of sum(r=0)^(10)r""^(10)C(r)3^(r)(-2)^(10-r) is

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  19. If (1+x)^n=C0+C1x+C2x^2++Cn x^n ,t h e nC0C2+C1C3+C2C4++C(n-2)Cn= ((2...

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