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The sum of all the coefficients of the t...

The sum of all the coefficients of the terms in the expansion of `(x+y+z+w)^(6)` which contain `x` but not `y`, is

A

4096

B

1560

C

3367

D

670

Text Solution

Verified by Experts

The correct Answer is:
B
We have `(a+b+c+d)^(6)`
Sum of coefficient which contains all of a,b,c and d
= Number of ways of distributing six distinct objects in fourt boxes such that no box remains empty
`= 4^(6) - .^(4)C_(1)3^(6) +.^(4)C_(1) - .^(4)C_(1)1^(6) = 1560`
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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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