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If a= .^(20)C(0) + .^(20)C(3) + .^(20)C(...

If `a= .^(20)C_(0) + .^(20)C_(3) + .^(20)C_(6) + .^(20)C_(9) + "…..", b = .^(20)C_(1) + .^(20)C_(4) + .^(20)C_(7) + "……"'` and `c = .^(20)C_(2) + .^(20)C_(5) + .^(20)C_(8) + "…..",` then
Value of `a^(3) + b^(3) + c^(3) - 3abc` is

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Verified by Experts

The correct Answer is:
B
We have
`a+b+c = 2^(30)`
Now, `a^(3) + b^(3) + c^(3) - c^(3) - 3abc`
`= (a+b+c) (a+bomega + comega^(2)) (a +bomega^(2) + comega)`
`= 2^(20) (1+omega)^(20) (1+omega^(2))^(20)`
`= 2^(20)`
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CENGAGE-BINOMIAL THEOREM-Exercise (Comprehension)
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  2. The sixth term in the expansion of ( sqrt(2^(log(10-3^x))) + (2^((x-2)...

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  3. The sixth term in the expansion of ( sqrt(2^(log(10-3^x))) + (2^((x-2)...

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  4. If the 2nd, 3rd and 4th terms in the binomial expansion of (x+a)^(n) a...

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  5. If the 2nd, 3rd and 4th terms in the binomial expansion of (x+a)^(n) a...

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  6. If the 2nd, 3rd and 4th terms in the binomial expansion of (x+a)^(n) a...

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  7. An equation a0+a1x+a2x^2+...............+a99x^99+x^100=0 has roots 99C...

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  8. An equation a(0) + a(2)x^(2) + "……" + a(99)x^(99) + x^(100) = 0 has ro...

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  9. An equation a(0) + a(2)x^(2) + "……" + a(99)x^(99) + x^(100) = 0 has ro...

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  10. If a= .^(20)C(0) + .^(20)C(3) + .^(20)C(6) + .^(20)C(9) + "…..", b = ....

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  11. If a= .^(20)C(0) + .^(20)C(3) + .^(20)C(6) + .^(20)C(9) + "…..", b = ....

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  12. The sum of all the coefficients of the terms in the expansion of (x+y+...

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  13. Consider the expansion of (a+b+c+d)^(6). Then the sum of all the coef...

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  14. Consider the expansion of (a+b+c+d)^(6). Then the sum of all the coef...

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  15. Let P = sum(r=1)^(50) (""^(50+r)C(r)(2r-1))/(""^(50)C(r)(50+r)), Q = s...

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  16. Let P =sum(r=1)^(50)(""^(50+r)C(r)(2r-1))/(""^(50)C(r)(50+r)), Q = sum...

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  17. Let P = sum(r=1)^(50) (""^(50+r)C(r)(2r-1))/(""^(50)C(r)(50+r)), Q = s...

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  18. If (1+x+x^(2))^(20) = a(0) + a(1)x^(2) "……" + a(40)x^(40), then follow...

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  19. If (1+x+x^(2))^(20) = a(0) + a(1)x^(2) "……" + a(40)x^(40), then follow...

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  20. If (1+x+x^(2))^(20) = a(0) + a(1)x^(2) "……" + a(40)x^(40), then follow...

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